Dendrography and Art History: a computer-assisted analysis of Cézanne’s Bathers.

Introduction

Wölfflin V.2

Art history as an academic discipline is relatively new ¹. ² Formally established in 1834 at the University of Berlin with the appointment of Franz Kugler (1808-1858) as the first professor of art history, Kugler and his successors Jacob Burkhardt (1818-1897), and Heinrich Wölfflin (1864-1945) instituted methods for the formal analysis of art and specified many categories used today for classifying art ¹. ³ Wölfflin is noted for “using parallel projectors in the delivery of art history lectures so that images could be compared.” ⁴ If art history is relatively new as an academic course of study in the west, computer-assisted analysis of art is in its “infancy,” with Wölfflin, aided by slide projectors, as the first scholar to demonstrate the utility of technology in the field. ⁵ As the editors of Digital Art History note in their 2015 inaugural issue, Wölfflin’s mode of comparison “changed the method of art history for good:” “His scientific achievements were a game changer in perceiving, analyzing, and presenting works of art in the scientific world and beyond” ⁶.

To say that comparisons have produced the categories that structure art history as we know it today is not overstating the case. In “Collections and/of Data: Art History and the Art Museum in the DH Mode,” Matthew Battles and Michael Maizels stress the centrality of the comparative slide lecture in the discipline. They write: “The slide lecture maintains a powerful grip on the collective art-historical imagination; it is the format through which art historical [sic] training begins, and it is by far the most popular means by which the discipline spreads its views and virtues to the mass of uninitiated undergraduates.” ⁷ Lev Manovich, in the first issue of DAH concurs: “to explore is to compare. And to compare, we first need to see” ⁸. While computer-assisted text analysis has a robust history since the 1950’s, the Proceedings of Computer Vision and Image Analysis of Art in 2008, 2010 and 2011 are the only journals devoted to exploring computer-assisted methods for art analysis prior to DAH in 2015. In the 2008 Proceedings , editors David Stork and Jim Coddington propose that computers “can reveal the fallibility in our perception and teach all of us to see with a more informed eye and mind” ⁹. ¹⁰ Computer-assisted methods of analysis can “question the categories we already have, generate new ones, or create cultural maps that relate cultural artifacts in original ways” ⁹. Since 2008, computer scientists in collaboration with museum curators have applied computational methods to art for conservation, reconstruction, and restoration. X-ray imaging, infrared reflectography, UV-induced fluorescent imaging, and photo-induced luminescence photography can reveal the under-layers of paintings, identify the properties of pigments and binders, authenticate artworks, detect forgeries, and gauge optimal designs for museum and digital displays. Computer algorithms are used to measure and count brushstrokes, sort and classify artworks by style, identify the salient features of an artist’s style, and produce three-dimensional models that illustrate an artist’s working methods.

Even though digital tools make art available for viewing, pedagogy, and research like never before, ¹¹ the use of data-enabled science, or algorithms, to interpret digitized art and compare painting styles continues to provoke skepticism among humanists. ¹² As Stephen Ramsay observes in “Humane Computing” : “They fear an epistemology that does not merely value empirical data, but which (in its extreme philosophical forms) considers empirical data to be the only valid form of evidence” ¹³. We believe that the visualizations produced by computer applications do not replace direct experience of the artifact. Correlations do not necessarily indicate causality or an ultimate relationship in every instance. While a computer may place together certain artists with similar styles in a cluster, this does not always imply that there is a historical relationship between them, as their styles may have simply undergone convergent evolution. The computer’s lack of historical and artistic context means that the process always has a requirement of human interpretation.

We propose here computer-assisted techniques for comparing color, saturation, brightness and complexity between digitized paintings that updates Wölfflin’s method. No studies of digitized art to date use dendrography, a well-established method in computational biology since 1990. DIAS ¹⁴, an image analysis program, and DENDRON ¹⁵, a method for generating trees reflecting relatedness, are patented, tried-and-true software programs. Over 400 citations in peer-reviewed literature for the basic methods paper describing DENDRON support efficacy ¹⁴. Dendrography pre-dates the bourgeoning field of artificial intelligence and machine learning. The efficacy of the very latest computer cognition systems based in machine learning is viewed at this time as inconclusive. As Science Daily (1/7/19) reports in “Can artificial intelligence tell a teapot from a golf ball? Severe limitations of deep learning machines” — even the latest programs cannot accurately identify shape when a pattern associated with another shape is grafted onto it. Machine learning systems “are easily fooled.” ¹⁶ Dendrography is a traditional computer-assisted method of comparing images and patterns. To that end, we believe that the computer applications DIAS and DENDRON, having been validated in many fields, may reliably “extend the senses,” ¹⁷ of the art historian. The visualizations they produce suggest similarities between paintings easily missed by human beings whose capacity to compare is limited by conceptual and subjective bias, lack of access to a work, or any number of reasons that make creating interesting comparisons challenging.

Dendrography has enormously productive applications for the comparison of formal and iconographic elements in paintings. Since formal analysis is often viewed as outdated in today’s art history, its potential as a subject for computational analysis has been overlooked (except for the few curatorial forays in this direction). As such, our approach not only attempts to see the value of the computational method, but also what DENDRON and DIAS may do to open up in surprising new ways what has been considered a finished part of the field. This may be the first study in digital art history that uses dendrography to cluster similar paintings and that employs computer programs to calculate golden rectangles in paintings for comparative purposes. The ever-growing raft of digitized paintings online, and the continual improvement of digital photography, calls for computer-assisted methods as long as these programs are reliable, the questions posed are appropriate for computer-assisted investigation, and the final interpretations are considered just that, namely interpretations.

Using the newly customized DIAS/DENDRON (DDA) programs (Appendix I), we investigate in Part I a persistent connection between Les Noces de Cana by Veronese and Cézanne’s first female bather La Baigneuse debout, s’essuyant les cheveux . Les Noces de Cana is enormous in scale, more than twenty-two feet by thirty-two feet in height and length, while the baigneuse is tiny, only eleven inches in height and five inches in width. Les Noces de Cana ’s subject matter is biblical, Christ transforming water into wine at the marriage feast, while Cézanne’s work is prosaic, a woman drying her hair after a bath. A traditional art historian, guided by genre expectations, might conclude that scale and theme obviate potential connections between the works, but using DDA, which normalizes scale, we can grasp surprising connections. Now, using DDA analysis, we can see how Cézanne capitalizes on Veronese’s color scheme in his first female baigneuse . We may also use DDA to suggest new approaches to old problems. For example, Cézanne painted over eighty bathers in his lifetime, but these paintings continue to mystify scholars. To date, they are mostly interpreted in psychanalytic terms as representing Cézanne’s repressed sexuality and/or aggression.¹⁸ When we saw that Cézanne’s baigneuse might be intimately connected to Les Noces de Cana , we then employed DDA to explore potential similarities in composition. In Part 2, using DDA analysis, we discovered that the composition of Les Noces de Cana is based on axial symmetry and the golden ratio (phi). When we apply DDA to identify axial symmetry and the golden ratio to Baigneuse debout, s’essuyant les cheveux and the rest of Cézanne’s bathers, we find that Cézanne imitates the composition of Les Noces de Cana in virtually every bather painting. Based on axial symmetry and the golden section, then, we have formulated a computer-assisted approach to “seeing” Cézanne’s composition in his Bather series. Cézanne’s bathers, formerly perceived as “awkward” and composed with “baffling imbalance,” can now be viewed as “golden” ¹⁹. With DDA, we find that Cézanne is more likely guided by mathematics in designing his bather paintings, rather than by unconscious drives or motives.

This approach is an intervention in the newly established trend within the digital humanities of the “micro-digital humanities.” ²⁰ We are not, as Michael Greenhalgh imagines of digital art historians, throw[ing] data at the computer while hoping that somehow “the computer will make sense of them” ²¹. We are not sifting “the great unknown” ²² for connections between texts or visual images, instead, we are comparing smaller curated datasets in order to measure influence between a master and student, a source and a re-imagining.²³ In this case, we are comparing fifty-five curated digital facsimiles of Cézanne’s oil paintings exhibited in Ambroise Vollard’s 1895 Salon to Veronese’s Le Noces de Cana , a source Cézanne identified as influential to him as an artist .

Standing before Les Noces de Cana , Cézanne is reported to have said regarding its color:

That is what a painting should give us, a harmonious warmth, an abyss in which the eye can sink, a silent germination. A state of grace in colors…To love a painting, first you have to drink it in this way, in long drafts, lose consciousness; descend with the painter into the dark, complicated roots of objects come up again with colors, bloom with them in the sun. You have to know how to see, to feel, especially in front of a great machine such as the one Veronese built
²⁴. Art Historian Susan Sidlauskas describes Cézanne’s experience of the Veronese painting as like “a mystic’s fusion with the deity” ²⁵. Cézanne thought of Veronese’s colors as “great noumenal entities, living ideas, creatures of pure reason…with whom we might correspond” ²⁴. By “great machine,” we take Cézanne to mean that Veronese’s work delivers to the aspiring painter figure studies, compositions, color combinations and more, structures that an artist can imitate.

Quality of digital reproductions

As Philip Ball observes in Bright Earth , “all reproductions are approximations” ²⁶.²⁷ And in regards to Les Noces de Cana and Cézanne’s bathers, we must ask of any facsimile whether it is “well or badly reproduced” ²⁸. Digital reproductions must be as close to the original as possible. Bruno Latour and Adam Lowe discuss at length Les Noces de Cana ’s complex “trajectory” as an image. What Cézanne saw between 1861, his first trip to Paris, until his death in 1906 is not the Les Noces de Cana that we see now in the Louvre, as conservationist efforts have modified the painting. Currently Les Noces de Cana exists in its “original” (though repainted) version at the Louvre, and it exists in a fully “restored” version, based on digitization, housed in its “original” context, in a Benedictine refectory in Venice. The Louvre Les Noces de Cana is considerably darker than the Benedictine digital facsimile. The coat of the server depicted in the foreground of the Louvre Les Noces de Cana was originally red but was changed to green in 1989. Thus, no version today is exactly what Cézanne saw. For our purposes here, we use a digitized image of the pre-1989 Les Noces de Cana , with the tabard in his “original” red coat. This, perhaps begrimed with more dust, is the closest “approximation” to what Cézanne would have seen. However, we demonstrate that DDA grouped Baigneuse debout, s’essuyant les cheveux in the same cluster with both renditions of Le Noces de Cana in dendrograms (Appendix II).

Choosing Cézanne’s paintings for computer-assisted analysis is also complicated. Cézanne left many works unfinished, therefore, we selected for this study paintings exhibited during his lifetime. The paintings exhibited in the 1895 Vollard exhibition is an exemplary dataset for computation, as it was Cézanne’s first one-man show, with examples of paintings from every stage of his development. Most important, we can presume Ambroise Vollard, Cézanne’s friend and patron exhibited the works as “finished” with the artist’s support. For information about Cézanne’s paintings, and for digital facsimiles, we relied on John Rewald’s printed Catalogue Raisonné and Walter Feichenfeldt, Jayne Warman and David Nash’s The Paintings of Paul Cézanne: an Online Catalogue Raisonné ²⁹. Supplemental Table I lists all paintings used for this study and their digital and material provenance. All digital images are in the public domain for research and educational use. When there were multiple versions of digitized images on the web with different levels of brightness, saturation, and coloring, we consulted the online Catalogue Raisonné , for the best match, or the websites of the museums that housed the work. In many cases, we checked digital facsimiles against original paintings on site in New York, Philadelphia, Chicago, and Detroit, not only for accuracy in color, brightness, and saturation, but also for correct margin between figure and frame for our geometric partitioning.

Generating dendrograms

The software program we have developed to compare digitized paintings is a composite of two patented programs DIAS (US patent #5,655,028 1997) and DENDRON (US patent #5,400,249 1995). The customized program DDA, allows the user to store and sort digitized images of pictures in a data file, measure parameters for comparison and then generate dendrograms, visual phylogenies of relatedness based on one or any combination of parameters. Both DIAS and DENDRON began development in the late 1980’s. DIAS was developed to analyze cell morphology, shape, cell movement and the dynamics of populations of cells, and has recently been used to study tumorigenesis in 2D and 3D. Dendron was developed to analyze and compare DNA fingerprints of infectious organisms and has been used to follow the progression of diseases in human populations. In “The Ins and Outs of DNA Fingerprinting the Infectious Fungi,” DENDRON is described in terms that we apply here for the comparison of paintings between the same or different painters. The combined programs, including the parameters we have measured and compared, and the generation of dendrograms, are described in Appendix I in more detail, with relevant references. In brief, images of a collection of pictures were scanned into a DDA data file. The DIAS portion of the program then automatically computed nine parameters, which included brightness, saturation, complexity, redness, orangeness, yellowness, greenness, blueness and purpleness. These parameters are described in Appendix I. To assess a similarity coefficient between two pictures for any one of these parameters or amongst any combination of these parameters, each parameter is assessed in a range of 0.00 to 1.00, 0.00 representing no relatedness and 0.01 to 1.00 representing progressively increasing values. The similarity coefficient (SAB) for one or any combination of parameters is then computed between all pairs of paintings in a collection, generating a matrix of SAB’s as demonstrated in Appendix I, Table A. Based on the matrix of SAB’s, a dendrogram (i.e., a phylogenetic tree of relatedness) is then generated by the unweighted pairgroup method based upon the arithmetic averages (UPGMA), originally used by Rohlf ³⁰, discussed in detail by Sneath and Sokal ³¹ and developed for DENDRON by Schmid et al. ³². The accuracy of the program was validated by Pujol et al ³³, with more than 410 citations in the literature reported by Google Scholar just for the methods paper “The Ins and Outs of Fingerprinting for Infectious Fungi” ¹⁵. In the generated dendrogram (e.g., in Figures 2 and 3), the nodes (i.e., vertical connections) approximate the hierarchy of similarity. An arbitrary threshold is drawn as a black vertical line through the dendrogram simply is a tool for visualizing the refutation of similarity or clades, related groups and clusters of paintings.

Analysis of relatedness using dendrography

Using DDA, we compared Cézanne’s fifty-five oil paintings presented at the Galerie Vollard in 1895 and Veronese’s Les Noces de Cana . The SAB’s for all DIAS parameters were used in generating the dendrogram in Figure 2. The dendrogram generated in this case could be separated into seven clades, a through f, using an SAB threshold of 0.83. Both Veronese’s Les Noces de Cana , Baigneuse debout, s’essuyant les cheveux and six additional Cézanne paintings were included in clade f (Figure 2). Interestingly, of the three paintings painted in the 1860s by Cézanne after first viewing Les Noces de Cana , two of them, Baigneuse debout, s’essuyant les cheveux (1869) and L’orgie de Nabuchodonosor (1967), resided in clade f, and were highly related. Since it was obvious that the one color assessed by DIAS in the unrestored Les Noces de Cana that appeared disproportionally faded was “green” , (and since the painting lacks the heavy green coat of the tabard as in post-1989 retouched versions), we generated a dendrogram in which the composite SAB was computed for all parameters but green (see table in the right lower corner of Figure 3). Using a high threshold, 14 clades were distinguished (Figure 3). One clade, b, clustered six pictures, which included Baigneuse debout, s’essuyant les cheveux and Les Noces de Cana in a subclade with a node of 0.92 and a subcluster of four paintings, three of which ( Les Begonias , La Baignade , Nature Morte ) also resided in the clade b, containing Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux , using all parameters in Figure 2. Since a digital version of the restored Les Noces de Cana is widely accessable on the web, we generated a dendrogram using the complete collection of parameters and obtained similar clustering of the restored facsimile of Les Noces de Cana and Cézanne’s Baigneuse debout, s’essuyant les cheveux (Appendix II). Again, Cézanne’s L’Orgie de Nabuchodonosor clustered with Veronese’s Les Noces de Cana and Cézanne’s Baigneuse debout, s’essuyant les cheveux . The two Cézanne paintings were painted in 1867 and 1869, respectively, so both reflect early works potentially highly related to Le Noce de Cana . We also analyzed the restored Les Noces de Cana facsimile and the Cézanne collection using all parameters but green, and found that the restored facsimile was in a cluster containing Cézanne’s Baigneuse debout, s’essuyant les cheveux and the other clustered paintings (Appendix II). We generated a dendrogram of the Cézanne collection that included, both the unrestored and restored Les Noces de Cana . The Baigneuse debout, s’essuyant les cheveux and both unrestored and restored Les Noces de Cana paintings clustered, and the cluster contained the same additional paintings in the clusters of the dendrograms generated with either the unrestored Les Noces de Cana alone or the restored Les Noces de Cana (Appendix II, Figure A, B, C, D). In support of the similarity assessed by DDA in the collection in Figure 2, we generated a dendrogram that included Veronese’s Les Noces de Cana , Cézanne’s Baigneuse debout, s’essuyant les cheveux , and 19 paintings by other artists including Delacroix, Rubens and Tintoretto, all of which were shown in the Louvre between 1861 and 1906 (Appendix III, Figure A). The Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux paintings grouped into a primary cluster, indicated by thick red lines, again indicating not only the similarity between Veronese’s Les Noce de Cana and Cézanne’s Baigneuse paintings, but also the accuracy of the DDA programs.

In our first experiment (Figure 2), we found potential correlation between the Les Noces de Cana and the Baigneuse , along with other paintings. In our second experiment (Figure 3), we found that when we control for green, Les Noces de Cana and the Baigneuse correlate more closely at .9.

In Figure 3, Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux cluster with three other paintings: Les Bégonias , La Baignade , Pommes et Linge , and Nature Morte at .9 with Le Noces de Cana and Baigneuse debout, s’essuyant les cheveux further discriminating as similar at .91.

Part 2. Hidden Patterns

Just like Veronese’s Les Noces de Cana , Paul Cézanne’s paintings continue to inspire wonder in his admirers. His contemporaries, Renoir and Matisse, spoke of his deployment of color and composition in godlike terms, while scholars today “struggle to know” his secret. Cézanne’s last words in 1904 to the young painter Emile Bernard heighten the sense of mystery and unknowability that surround the painter’s process. Richard Shiff’s 2004 Introduction to Conversations with Cézanne illustrates this mystery:

“He takes his secret to the grave,” remarked Bernard to his wife, upon receiving word of Cézanne’s death: “he wrote that he wanted to tell me everything, and I don’t know what he meant by that.” Regretting his failure to visit Aix in 1906 as planned, Bernard knew that Cézanne, only a month before, had suggested that both men would better “explain themselves” whenever they finally met again in person. Even more poignantly, Bernard could recall the cryptic promise Cézanne included in a letter of the previous year: “I owe you the truth in painting [en peinture], and I will tell it to you”
²⁴.

Shiff concludes, “Like Bernard-like Cézanne himself-we struggle to know” (my italics). We propose Cézanne worked from a plan, and that his comments to Bernard indicate guardedness about sharing his process. As he advised the fellow painter Maurice Denis: “You have to have a method. My father [said], People have to play games. That’s what I search for in painting…theories, sensations and theories…I wanted to copy nature but I never could do it” ²⁴. In this second part of our analysis we identified parameters for DDA which we believed would allow us to begin to assess similarities based on composition. We tested whether Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux shared potential compositional similarities, and we sought parameters related to composition that could be quantified. Because of Cézanne’s frequent references to “harmony” in his conversations and letters, and his documented love for classical Greek and Roman culture, we turned to Classical conceptions of harmony, based on numbers and geometry, for parameters that we could quantify.

In this section, we compare only the relationship between axial lines and golden rectangles as determined by the picture’s frame in Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux . We decided to automate identification of the center and central axis of a painting, because of their technical importance to an artist, and because of their semantic weight. For Rudolf Arnheim, the dead center of a painting is not dead but “alive with tension” ³⁴. The vertical and horizontal bisecting lines emanating from the center establish a “solid spatial trellis in the brain.” An artist must master the axis first, according to Arnheim, as it “remains the base of reference that alone make obliqueness possible. Obliqueness is always perceived as a deviation [from the axis] hence its strongly dynamic character.” Computer-assisted methods for identifying centers and axial lines are helpful as these can be mis-apprehended by a viewer. For example, upon first glance, many people see Christ as the center of Les Noces de Cana , as opposed to the men carving meat on the balustrade above him. Once we used DDA to identify the center and the horizontal and vertical bisecting lines of Les Noces de Cana , we chose to automate the identification of golden sections in a painting as determined by the square picture plane. In Appendix IV, we present the steps in the DDA program employed to automatically identify a number of geometric landmarks including what we have defined as the “golden window,” in a painting. This involves identifying the “golden rectangle” and the axial lines bisecting both vertically and horizontally the picture plane.

Many scholars have attempted to find hidden patterns in art works based on numbers. Most recently, Robert Bork’s studies of golden sections in medieval cathedral ground plans show that for centuries, artists and architects have used the mysterious divine proportion or golden ratio (1.618…) in their designs ³⁵. For Arnheim, the golden ratio is satisfying “because of its combination of unity and dynamic variety, whole and parts are nicely adjusted in strength so that the whole prevails without being threatened by a split, but at the same time, the parts retain some self-sufficiency” ³⁴. Veronese and Cézanne would have been familiar with Luca Pacioli’s handbook for artists, De Divina Proportione , published in 1509. Seventy-one chapters are dedicated to demonstrating the golden section, a mathematical proportion based on an equation that produces phi or the never-ending value of 1.618… in artworks ³⁶. Cézanne’s contemporary Symbolists, Odilon Redon and Paul Serusier, considered Platonic geometry, holy, or mystical, because it appeared in nature as repeated numbers and patterns. Cézanne and Veronese absorbed the concept of divine proportion in their training, and when they had the problem of creating a two-dimensional structure that expressed “witnessing the holy,” they found a rule or “game” in the golden section that suited their purposes. Using DDA, as a tool to section a painting geometrically, we show that the golden section may have a formal and thematic purpose for Veronese in Les Noces de Cana (Figure 4) and that Cézanne might have elaborated on this compositional structure in his Bather paintings.

While we could have discovered this hidden composition by applying a ruler and compass to reproductions from books, the advantage of DDA in studying composition is the mechanization of the geometer’s tools, and the quantity of digital reproductions we can quickly, and more precisely, rule than with human hands. It also allows for the quantification of parameters from the digitized image for further comparison using DDA software. DDA determines and saves golden ratio rectangles from any point on a painting, drawing up to nine symmetrical vertical or horizontal staves across a painting, and imposing and saving geometrical shapes on digital paintings. Since these parameters are associated with Neoplatonic ideals and classical harmony, we feel these might have bearing on Cézanne’s painterly concerns in his Bathers series. Baigneuse debout, s’essuyant les cheveux achieves its uniqueness not only from a masterful deployment of color modelled on Veronese’s Les Noces de Cana , but also from its invisible scaffolding, based on Platonic geometry. We believe that Cézanne hides this game in plain sight.

Cézanne left eighty Bather paintings in various states of completion after his death in 1906 at the age of 68. He repeats this, heretofore unidentified, compositional structure throughout his Bather series. Since Cézanne appears to have modeled his first female bather on Les Noces de Cana , as our dendrograms imply, it is likely that Cézanne is linking Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux semantically. The subject of Les Noces de Cana is a wedding feast at Canaan where Christ performs the miracle of turning water into wine, a potent metaphor for the artist translating raw materials into representations. Christ transmutes water, something common, into something holy, strange, and magical; likewise, Cézanne divinizes his bathers; he makes them noumenal, by way of his predecessor Veronese — through color harmonies and divine geometry.

Cézanne viewed geometry as a divine architecture, and he understood the center of a bounded four-sided square to be its axial eye. The center of a painting represents the “truth” or the “eye of god” ³⁷. In its aggressively axial construction Figure 4, Veronese appears to take account of the square frame, its center, the golden rectangle, and the golden window in organizing his composition for thematic effect (Appendix IV). The sacrificial meat above Christ’s head is at the exact center of Les Noces de Cana . Like a blade, the vertical and horizontal axes divide the meat. The axis signifies that the focus of the painting is sacrifice, and its cognates, Christ, directly below the sacrificial meat, and the dog at the bottom of the painting. The vertical axis bisecting the painting runs directly through Christ’s right eye and the left eye of the dog. As a dog signifies loyalty in medieval/renaissance Christian iconography, the implied vertical line uniting sacrifice/Christ’s eye/loyalty appears to emphasize Veronese’s aim of producing a sensually enlightening painting. To make the painting’s purpose legible, he provides a strong horizontal balcony across the middle of the painting above Christ’s head. The top of the balcony passes through the exact center of the painting.

In Les Noces de Cana Figure 4, just as axial intersection emphasizes theme, so too does the golden section. The golden section intersects Christ’s eyes, and the eyes or mouths of the witnesses flanking Christ. The “golden window” we have identified frames a quarter of Christ’s face, partial faces of three witnesses to his left (specifically through the mouth and eyes). Then, above and behind them, three convex columns supporting the balustrade where butchers are preparing sacrificial meat. Technically, the benefit of a “golden window” for Veronese is that it allows him to represent depth by mediating the distance between flat wall and blue sky with a band of recessing modulations. In the golden window of Figure 4, we glimpse the tablecloth behind the columns of the balustrade above Christ’s head, as well as the robes of the butcher, and a building in the distance. In Figure 4, the golden window underscores theme and creates a sense of depth or of “descended” figures within the composition of the painting. As Christ has “descended” from his godlike nature to be among humans, the golden ratio becomes the line along which Veronese arranges Christ and his witnesses at the feast. In Figure 5, we see the lowering effect afforded by the golden window. Through the golden window, we see Cézanne’s central bather (whose right knee and shoulder are aligned with the vertical axis of the picture frame), descending into a pool of water. We can now say that, in addition to discovering surprising connections in color, saturation, complexity and brightness in paintings, there are landmarks in paintings that DDA automatically computes. These are the center of the painting, the horizontal and vertical bisecting lines (axis), the golden rectangle, the golden strips (the space between the vertical and horizontal bisecting lines and the golden sections of the upper right and lower left sides of the picture plane), and the golden window (located at the right base of the golden rectangle).

Like Leonardo da Vinci, Cézanne thought paintings were superior to poems because they inspired reverence in viewers ³⁸. As he expressed to Leo Larguier, “Art is a religion. Its goal is the elevation of thought” ²⁴. He wanted to create in paintings a “harmony parallel to nature,” a noumenon, in that the painting would be a thing in itself (with a life of its own) whose purpose was to “enlighten” ²⁴. Cézanne stated his commitment to the “law of harmony,” numerical patterns he saw in nature, throughout his letters and conversations. He stated: “To read nature is to see it beneath the veil of interpretation as colored patches succeeding one another according to a law of harmony. The major hues are thus analyzed through modulations” ” ²⁴.

By harmony, Cézanne means harmonia in a Platonic sense of “fitting together:” not only the ideal forms and proportional arrangements of forms based on number found in nature, but also as “the reconciliation of opposites by a third element, bringing them all into a new unity” ³⁹. Cézanne synthesized contrasts: he “modulated” color as a way of building form. He saw the task of reconciling opposites as a magician’s task. He stated: “Painting is not beautiful if the surface plane remains flat. Objects must turn, grow distant, live. That is the magic of our art” ²⁴. To restate, in the golden section, Cézanne finds a way to represent infinity in his paintings, which for him, like the Symbolists, was the essence of nature. In the synthesis of opposites, whether in color contrasts, spatial “near and far,” or “up and down,” Cézanne creates a “harmonious” painting.

Cézanne and Ingres

Certainly, Les Noces de Cana is not the sole model for Baigneuse debout, s’essuyant les cheveux . Relevant to our purposes here, a study of Cézanne’s Bathers, as a series, from their origin and into their development, Cézanne’s ambivalence toward French Neo-Classicism, and its arch-representative Dominique Ingres is well-documented. Cézanne would have seen La Source at the Louvre (Figure 6).⁴⁰ La Source , begun by Ingres in 1820, and completed in 1856, when Ingres was 76-years-old, was infamous to impressionist painters as its graceful lines and classicism represented the highest standard in Fine Art at the time. Cézanne did not care for the painting. He called it “system and false spirit” ²⁴. Applying axial lines and golden windows to La Source and Baigneuse debout, s’essuyant les cheveux , we can now see Cézanne copying and departing from his model in surprising ways.

As Michael Baxandall observes, “influence” works in reverse ⁴¹. Ingres’ La Source did not “influence” Cézanne. Instead, Cézanne drew a pattern from Veronese and subjected another model, Ingres’ La Source to the pattern, then dilated upon the results to suit his aims, the “harmonizing” of the youthful nude body. First, we notice that model and copy are mirror images. With arms raised, they form S shaped figures in classical contrapposto. They are symmetrical only in that, when a golden rectangle is formed over the rectangular plane of the canvasses, both figures’ left breasts are framed by the middle vertical line and the golden ratio vertical lines formed by the golden rectangle. The middle vertical axis also runs through both figures’ left eyes. The golden window in Ingres’ work frames the girl’s left thigh. In Cézanne, the golden window alludes to the girl’s thigh and hip by partially representing (yet with more convexity) her right hip through tonal modulation. Pointedly, Cézanne uses the subordinate horizontal line of the picture plane’s golden rectangle to “lower” his figure. In La Source the axial eye (picture center) is the sex of the young girl emptying the urn of water. The golden section runs across her legs above her knees. Clearly, in La Source , the picture center, as the “eye” of “god,” is Ingres’ visual pun on the source, water, and female genitalia. In Cézanne’s work, the exact center is the nude female’s hip swiveled in classical contrapposto, perhaps indicating that his “source” is “classical art,” while her sex is aligned with the golden section, making it “golden.” In Baigneuse debout, s’essuyant les cheveux , by aligning the female sex with the golden section, within a theme that involves washing the body, and in the case of Baigneuse debout, s’essuyant les cheveux , a woman drying her hair, Cézanne is harmonizing the studio erotism of Ingres’ young nude — he is bringing “the source” back to nature.⁴² He also “classicizes” the nude human form by posing his bathers in natural settings, and by associating them with the idealized friendships and homo-social eroticism of the Classical world. In his earliest male bathers as well, Cézanne aligns sex with the golden section of the left side of the frame (Figure 7).

In Figure 7, as in female nudes, Cézanne encloses the left breast of an early male bather (7.L.) in the golden rectangle and the vertical bisecting line of the painting. In the middle painting (7.M.) he centers or aligns the left male breast between the golden rectangle and the vertical bisecting line of the painting. In the right painting (7.R), the bather’s left breast aligns with the vertical bisecting line, while the bather’s left elbow aligns with the golden rectangle. In all three works, the golden window captures thigh and background. The navel aligns with the horizontal bisecting line and sex aligns with phi (the bottom side of the golden rectangle determined by the dimensions of the painting).

Golden Windows: Coming into Focus

Eighty Bather paintings exist in various states of completion out of Cézanne’s extant oeuvre of 1300 oil paintings and watercolors ⁴³. Of the 80 Bathers, 64 are available online for download for research and educational purposes. Using DDA, we identified the axis determined by the picture plane of each digital image, and identified the golden window. In Supplemental Table 2, we provide a snapshot image of all 64 golden windows we collected. Here we present twenty of these images that suggest the “lowering or descending effect” afforded by the golden window. All feature a head, breast or rear end. Most of the 64 paintings have a head, breast, thigh, or rear end framed by the golden window, but some frame the brightest point in the painting, or a faint structure in the far distance.

The Golden Strips

Adjacent to the golden window (Appendix IV) are the “golden strips” which elaborate on the point emphasized by the window. The “golden strip” in a bather painting is between the axial and golden ratio horizontal lines or vertical lines of the picture plane (Appendix IV). The golden strips allow for an alternation of frontal and rear nude forms with their sexes aligned with the golden section. As with Veronese’s Les Noces de Cana , Cézanne aligns the heads of the descended figures beneath the middle horizontal line bisecting the picture. For Andre Lohte, Cézanne’s genius is in his alternation of foreground and background figures. (What we call Cézanne’s “game,” he calls Cézanne’s “ruse” ). Lohte stated of Cézanne: “Genius consists in knowing how to compensate, through constant repetition of each phenomenon, for every thrust into depth, by an equal advance or return. Without this ruse the eye would immediately find the horizon, the distance, without being excited by the successive oppositions which retard its quest for space, and procure for it a subtle pleasure” ⁴⁴. We can now consider Veronese’s Les Noces de Cana a masterful example of this phenomenon in fine art painting, a strategy in painting with an endless “trajectory.” ⁴⁵ In Figure 9, we present the horizontal golden strip of Quatre Baigneuses (1888-1890) which shows Cézanne’s “alternation of foreground and background” described by Andre Lohte. In Figure 9, and in other Bathers, Cézanne’s “successive oppositions” have semantic meaning. For us, this signals Cézanne’s reconciliation of opposites in his windows and strips. Thematically, Cézanne reconciles body and mind into a third “noumenal” alliance. He aligns the attentive and communicative heads, hearts, and sexes of his descended and/or risen figures, along the golden section and the axial center of his Bather paintings. In Supplemental Table 3, we present the horizontal “golden strips” of the 64 bathers in this study.

Beyond the Church

Cézanne presents an affirmative and benedictory vision of youth and beauty in his Bathers. In Les Grandes Baigneuses , a 1906 painting left incomplete when he died, the church in the distance shows that his bathers exist in an intermediate space between the viewer outside the picture plane and the church (Figure 10). The bathers are in a space of their own, determined by the geometry that unites them. When we apply the geometric analysis of DDA to the painting, we see that the golden window frames a reality beyond the church. We feel this illustrates Cézanne’s Neoplatonic leanings, and fuels his concept of art as a religion. In his serial use of golden sections to structure his bather series, we see an interest in the infinite, and an understanding of the golden window as affording a glimpse of it.

Homage to the Classical World

Cézanne also uses sacred geometry to structure the imagined space of the image. In Baigneurs en Plein Air (Figure 11), an unfinished painting from 1890-1891, the ground of the five figures forms a Pentagon, below the horizontal line that bisects the painting.

As stated in Appendix IV, DDA will discriminate a variety of geometric shapes within a picture. The figure emerging in the golden window represents it triangular point. This implied pentagonal shape illustrates Cézanne’s advice to artists throughout his letters and conversations: “Interpret nature in terms of the cylinder, the sphere, the cone; put everything in perspective, so that each side of an object, a plane, recedes toward a central point” ” ²⁴. In addition to an implied pentagon, these bathers form an imaginary cone, a large triangle parallel to the surface plane whose tip coincides with the middle vertical axis of the paintings. This triangle provides vertical armature for the five bodies, linking them together in one unit with the armpits aligned at the diagonal lines. This compositional triangle both dynamically lifts the figures, and stabilizes the composition.

Cézanne suggests with a few blue and red strokes the figure whose breast is framed in the golden window of Figure 11. Cézanne repeated this particular composition in his search for a realization commensurate with his ideal. We can now think of a man lowering himself into a body of water as a compositional “problem” Cézanne was trying to solve in his Bather series. Painted in four-sided constructive strokes, and in Veronesian, “noumenal” blue and red color patches that resemble a harlequin’s costume, the figure is in motion, and not fully formed. He is an intermediate being, not yet concretized, nor fully translated between here and there within the noumenal square of the painting. Cézanne is clearly attuned to magical conceptions of the number four as representing the fourth element of earth in Platonic doctrine and inherent in the squares of the harlequin’s costume. He was also aware of the five-sided figure of the pentagon as representing the regenerative aspects of creation. The Harlequin’s checkerboard costume has been described as symbolizing “a chthonic force” ³⁹. If so, this chthonic force’s heart is framed in the golden window, a highly significant spot, charged with meaning, as we now see in Cézanne’s Bathers, and particularly in this painting (Figure 11) depicting five men in geometrical relationship to each other. In addition to a sacred understanding of numbers and shapes, three (triangle: divinity), four (square: earth) and five (pentagon: creation and regeneration), a means to create a harmony “parallel” to nature, this painting’s composition is Cézanne’s special homage to the pastoral poetry of Theocritus and Virgil, the classical literature he loved. It is well- known that Cézanne translated Theocritus and Virgil as a pastime in his youth ²⁴. The left side of Figure 11 appears to represent the sympotic aspects of male fraternity with the seated figure under the pine tree discoursing with the standing figure seen from behind. The right side of the painting pays homage to the erotic aspects of homo-sociality implied by Theocritus and developed in the bucolic poems of Virgil. In the poems, herdsmen gather to sing songs about “Daphnis,” a young man who drowns himself out of erotic frustration, or his cognates in the classical tradition who die: Hylas, Delphis, Adonis, and Narcissus, other beautiful boys, like the one in Figure 11 “posing” in the foreground. Theocritus and Virgil’s lost boys are the poets’ reflections on their own lost youth and/or the loss of specific male friends, or lovers ⁴⁶. For Cézanne, “Nature is not on the surface; it is in depth,” hence, the man in the water (in the depths) crying on the far right ²⁴. Cézanne’s effort to divinize the nude human body in company with other divinized bodies, whether “co-ed” or segregated by sex, and in the many paintings where difference in sex is not explicit, we see the artist’s engagement with Neoplatonism, in that his goal is to create a harmoniously simplified world with a playful, affirmative, benedictory vision of youthful nudity.

Conclusion

In this paper, using the automated tools afforded by DDA, we have forged a connection in color, composition, geometry, and theme between Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux , and from this connection, we have brought to light unifying characteristics in Cézanne’s Bathers heretofore unidentified. We have identified the connection between Les Noces de Cana and Baigneuse debout s’essuyant le cheveux by producing dendrograms of Cézanne’s fifty- five 1895 Galerie Vollard Exhibition oil paintings compared to Veronese’s Les Noces de Cana , a painting we know Cézanne admired at the Louvre during his formative years as a painter and throughout his life. Using computer-assisted methods we generated dendrograms that clustered paintings related in color, saturation, brightness and complexity. After studying these parameters, we applied the geometric program of DDA to the study of Cézanne’s composition. Because Cézanne expressed Neoplatonic ideals regarding paintings in his conversations and letters, we programmed DDA to compute axial lines and golden rectangles according to the dimensions of the square, rectangle, and other geometric parameters to the painting under scrutiny. Using DDA we identified the golden rectangle for Les Noces de Cana , Baigneuse debout, s’essuyant les cheveux and Ingres’ La Source (another likely model for Baigneuse debout, s’essuyant les cheveux ). From the similarities and differences between the three paintings identified, based on axial symmetry and the golden section, we have formulated an approach to “seeing” Cézanne’s composition in his Bather series. Cézanne’s noumenal bodies, formerly perceived as “awkward” and composed with “baffling imbalance,” can now be viewed as “golden” ¹⁹. These are only the first parameters, customized to the study of paintings that we have introduced to DDA. As we continue to expand and use this computer program to compare influence between painters, we will add new parameters such as measurements for convexity, concavity, texture and composition, based on edge detection technology in the original DIAS program. These tools will assist us in investigating a variety of questions basic to art history.

Acknowledgments

This research began with an AAC&U TIDES (Teaching to Increase Diversity and Equity in the Classroom) grant that supported applying technology to the study of paintings from 2013-2017 at Lawrence Technological University. A Howard Hughes Medical Institute’s Inclusive Excellence Initiative grant (52008705) is sustaining LTU’s integration of computer-assisted analysis of art, music, and literature into its undergraduate curricula until 2021. The Developmental Studies Hybridoma Bank, an NIH National Resource, and the W.M. Keck Dynamic Image Analysis Facility housed at the University of Iowa provided the computational resources for this project. We thank LTU’s Research Support Services for providing a Faculty Seed Grant for travel, research assistants Liam Butler, Mary Cody, Irene Missler, and Neil Fraylick. We thank Dean Hsiao-Ping Moore and Prof. Lior Shamir for guidance and support, and LTU Provost Maria Vaz for approving a sabbatical leave Spring 2018, to conduct this work at the W.M. Keck Dynamic Image Analysis Facility at the University of Iowa.

Appendix I. Analyzing a collection of paintings using the customized DIAS/DENDRON-ART (DDA) program

The newly developed DIAS/DENDRON-ART (DDA) program integrates the 2D image analysis program DIAS (Soll et al., US patent #5655028; Soll, D.R. 1995. The use of computers in understanding how cell crawl. Int. Rev. Cytol. 163: 43-104; Soll, D.R. and Wessels, D. (eds.) 1998. Motion Analysis of Living Cells John Wiley, Ive., New York, 298 pages; Kuhl, S., Voss, E., Scherer, A., Lusche, D.F., Wessels, D., Soll, D.R. 2016. 4D tumorigenesis model for quantitation of coalescence, identification of unique cell behaviors and testing anti-cancer drugs. Chemotaxis Methods in Molec. Biol. 229-250), and the dendrography software program DENDRON. Schmid, Jan, Edward Voss and David R. Soll. “Computer-Assisted Methods for Assessing Strain Relatedness in Candida albicans by Fingerprinting with the Moderately Repetitive Sequence Ca3.” Journal of Clinical Microbiology. Vol 28.6 (June 1990). 1236-1243. Soll, D. R. “The ins and outs of DNA fingerprinting the infectious Fungi.” Clinical Microbiology Reviews . Vol.13.2 April 2000. P.332-370. The programs originally written in C++ have been converted to JAVA (Graphics Programming With Java, Second Edition. 2001. Steven’s Scott/Jones, Inc.). Images of paintings are scanned into a DDA folder, with borders equal to the inner edges of the frame and normalized for size. If a painting is faded, hue will not be significantly affected since DDA employs HSB (hue, saturation, brightness) color space (Oracle Java 7 documentation, online for “Class Color” ), as opposed to RGB (red, green, blue). DDA then automatically computes nine parameters that include brightness, saturation, complexity, redness, orangeness, yellowness, greenness, blueness and purpleness. Additional parameters based on DIAS edge detection programs are now under development and will be incrementally added. The “brightness” parameter is computed by converting the pixels of the entire image to HSB. A value of 0% is black and 100% is white. The average % for the entire picture is computed and the value converted to a range of 0.00 to 1.00. The “saturation” parameter is treated in a similar fashion. It represents the average richness of all colors assessed, is computed from 0 to 100%, then normalized to a value in the range of 0.00 to 1.00. For the “complexity” parameter, the image is first converted to grays with pixel intensities ranging from 0 to 255. The average value is then normalized to 0.00 to 1.00. The final parameters are six hues. On the color or “hue” wheel, they vary from 0 to 360°. The number of pixels with redness at 0° ± 5°, orange at 20 ± 5°, yellowness at 60 ± 5°, greenness at 120 ± 5°, blueness at 240 ± 5° and purpleness at 270 ± 5°, are computed and divided by the total number of pixels in the image. These individual pixel proportions are then converted to 0.00 to 1.00. The values of each parameter, all converted to a range of 0.00 to 1.00, were then used to generate a similarity coefficient (SAB) between every pair of paintings in a collection, using the following formula:

where ai and bi are the values of a parameter I for paintings A and B respectively, and k is the number of parameters. This formula was derived from that developed by Schmid, J., Voss, E. and Soll, D.R. 1990. (J. Clin Microbiol. 28, 1236-1243) for banding patterns of DNA fingerprints in which each band is a restrictive fragment length polymorphism (RFLP) pattern representing a parameter (Soll et. al. 1997 US Patent #5, 655, 028). An SAB of 0.00 represents complete dissimilarity, an SAB of 1.00 identicalness, and SABs of 0.01 to 0.99, increasing levels of similarity. For this study the average of the parameters of paintings are used to generate the SABs between all paintings in a collection, which are logged into a matrix, as presented for 18 pictures in Appendix I Table 1.

The matrix is then used to generate a dendrogram using the unweighted pair group method based on arithmetic averages (UPGMA), first employed by Rohlf ,1963 Classification of Aedes by numerical taxonomic methods [Diptera, Culcidae]. (Ann. Entomal. Soc. Am. 56, 798-804) and discussed in more detail for application by Snesth and Sokel (1973. Numerical Taxonomy W.H. Freeman and Co., San Francisco, CA). In generating a dendrogram, connections are identified in descending values. The matrix is first scanned for the SAB with the highest value. The first two are joined by a vertical node at that SAB. If two or more pairs have the same highest SAB, one is picked randomly to initiate the process of generating a tree. The system then grows the tree of relatedness, connecting pairs, individual paintings and groups of two or more, or groups. The node involving more than two paintings is computed as the arithmetic mean of the SABs between the pictures connected. This process continues until all pictures are connected to form a relatedness tree (dendrogram). The accuracy of the dendrogram has been assessed by goodness of fit (i.e., whether the distance in the dendrogram approximates the SABs in the matrix (Avis, J.C. 1994. Molecular numbers, natural history and evolution. Chapraon and Hull, New York, NY). By using completely different methods to assess genetic relatedness between the same collection of strains of an infectious fungus, the accuracy of the DENDRON program was previously verified (Pujol, C., joly, S., Lockhart, S.R., Sebastian, N., Tibayrenc, M., and Soll, D.R. 1977. J. Clin Microbiol, 2348-2358; Soll D.R. 2000. Clin Microbiol Rev 13, 332-370). The robustness of DIAS/DENDRON ART (DDA) in clustering was also verified by the addition of the restored Les Noces de Cana to the Cézanne collection and the unrestored Les Noces de Cana , as described in Appendix II.

Appendix II

A comparison of the Cézanne Galerie Vollard collection with the unrestored (Appendix II A) and restored (Appendix II B) versions of Veronese’s Les Noces de Cana , using all parameters but green. Greenness was removed because in the restored version, a man’s cloak, which was red, was converted by restoration to green. Both Cézanne’s Baigneuse debout, s’essuyant les cheveux and Veronese’s Les Noces de Cana reside in the same cluster with the restored and unrestored Les Noces de Cana . It should be noted that the alternative clusters in the three dendrograms share a majority of other related Cézanne pictures, as is evident in lists of the paintings in the alternative clusters, presented in Appendix II D. These results also demonstrate the accuracy of the clustering method of DIAS/Dendron, given that the addition of different versions, in this case the unrestored and restored Les Noces de Cana , or the addition of both, does not disrupt relationships, even though each dendrogram is generated independently, using the unweighted pair-group method employing arithmetic averages, as described in Appendix I.

Appendix II. A

Appendix II. B

Appendix II. C

Appendix II. D

Comparison of pictures in the resident clusters of Cézanne’s  _Baigneuse debout, s’essuyant les cheveux_  and either the unrestored or restored versions of Veronese’s  _Les Noces de Cana_ . Only the first word of the titles of the paintings are included.    Unrestored (Louvre)  _Cana_   Restored (Venice)  _Cana_   Unrestored and Restored  _Cana_       Baigneuse  Baigneuse  Baigneuse      Les Bégonias  Les Bégonias  Les Bégonias      La Baignade  La Baignade  La Baignade      Pommes  Pommes  Pommes      Nature Morte  Nature Morte  Nature Morte      Esquisse de M. Cézanne  Esquisse de M. Cézanne  Esquisse de M. Cézanne        La Jas de Bouffan  La Jas de Bouffan      

Appendix III. Further demonstration of clustering Veronese’s Les Noces de Cana and Cézanne’s Baigneuse debout, s’essuyant les cheveux

To further demonstrate the similarity of Veronese’s Les Noces de Cana and Cézanne’s Baigneuse debout, s’essuyant les cheveux , we generated a dendrogram based on the SABs between these two paintings and nineteen paintings Cézanne would have viewed in the Louvre between 1861 and 1906. The artists include Delacroix (green), Rubens (black), and Tintoretto (blue). Les Noces de Cana and Baigneuse debout, s’essuyant les cheveux again clustered, supporting the relationship and accuracy of the dendrography program.

Appendix IV. How to identify a golden window

Supplementary Table I: List of Works

  Name of Artist  Title of Work  Medium  Size  Year  Location  Link to artwork used for analysis      Paul Cézanne  La Maison abandonnée  Oil on Canvas  19 5/16 x 23 in  1878-79  Private Collection, New York  https://uploads7.wikiart.org/images/paul-cezanne/      Paul Cézanne  La Baie de Marseille, avec vue sur le village  Oil on Canvas  26 3/16 x 32 11/16 in.  1877-79  Vollard Archives, Photo No. 604  https://www.moma.org/collection/works/80302?locale=en      Paul Cézanne  L'Estaque  Oil on Canvas  31 1/2 x 39 1/16 in.  1879-83  The Museum of Modern Art, New York  https://www.moma.org/meetme/artwork/index      Paul Cézanne  La Campagne à Pontoise, près du Valhermeil  Oil on Canvas  36 3/8 x 28 7/8 in.  1881-82  Fondation Sirina, Vaduz  http://www.cezannecatalogue.com/catalogue_images/main      Paul Cézanne  Marronniers et ferme du Jas de Bouffan  Oil on Canvas  25 13/16 x 32 in.  1885  Private Collection, New York  https://uploads1.wikiart.org/images/paul-cezanne/      Paul Cézanne  Gardanne (vue verticale)  Oil on Canvas  31 1/2 x 25 5/16 in.  1886  The Metropolitan Museum of Art, New York  http://images.metmuseum.org/CRDImages/ep/original/DT1941.jpg      Paul Cézanne  Gardanne (vue horizontale)  Oil on Canvas  25 X 39 in.  1885  Barnes Foundation, Philadelphia (BF917)  http://www.cezannecatalogue.com/catalogue_images/      Paul Cézanne  Le Grand Pin  Oil on Canvas  33 1/16 x 36 3/16 in.  1887-89  Museu de Arte de São Paulo Assis  https://uploads2.wikiart.org/images/paul-cezanne/the-great-pine-1889.jpg      Paul Cézanne  Maison au bord de la Marne (l'Île Machefer)  Oil on Canvas  28 11/16 x 35 13/16 in.  1888-94  White House Collection, Washington, D.C.  http://www.cezannecatalogue.com/catalogue_images/      Paul Cézanne  Le Chemin de halage sur les bords de la  Oil on Canvas  24 13/16 x 31 1/8 in.  1888  Art Gallery of New South Wales, Sydney  https://www.artgallery.nsw.gov.au/media/collection      Paul Cézanne  Le Jas de Bouffan  Oil on Canvas  29 3/8 x 21 1/2 in.  1890-94  Private Collection, Japan  https://uploads2.wikiart.org/images/paul-cezanne/jas-de-bouffan-1887.jpg      Paul Cézanne  Au bord de l'eau  Oil on Canvas  28 11/16 x 36 3/16 in  1890-92  National Gallery of Art, Washington, D.C.  https://images.nga.gov/en/search/do_quick_search.html?q=%221972.9.1%22      Paul Cézanne  Le Pont sur la Marne à Créteil  Oil on Canvas  28 x 35 3/8 in.  1894  Pushkin Museum, Moscow  https://uploads0.wikiart.org/images/paul-cezanne/bridge-over-the-marne-      Paul Cézanne  Sous-bois  Oil on Canvas  45 11/16 x 31 7/8 in.  1893-94  Los Angeles County Museum of Art  https://collections.lacma.org/node/172409      Paul Cézanne  Le Nègre Scipion  Oil on Canvas  42 1/8 x 32 11/16 in.  1867  Museu de Arte de São Paulo Assis  https://uploads4.wikiart.org/images/paul-cezanne/the-negro-scipio-1867.jpg      Paul Cézanne  Portrait de Victor Chocquet (buste)  Oil on Canvas  13 13/16 x 10 11/16 in  1877  Virginia Museum of Fine Arts, Richmond  https://uploads6.wikiart.org/images/paul-cezanne/      Paul Cézanne  Portrait de l'artiste  Oil on Canvas  10 3/16 x 5 7/8 in.  1877  Musée d'Orsay, Paris  https://uploads7.wikiart.org/images/paul-cezanne/self-portrait-3.jpg      Paul Cézanne  Portrait de Louis Guillaume  Oil on Canvas  22 x 18 1/5 in.  1879-80  National Gallery of Art, Washington, D.C.  https://images.nga.gov/en/search/do_quick_search.html?q=%221963.10.101      Paul Cézanne  Portrait de l'artiste  Oil on Canvas  18 1/8 x 15 in.  1882  Pushkin Museum, Moscow  http://www.arts-museum.ru/data/fonds/europe_and_america      Paul Cézanne  Madame Cézanne en robe rayée  Oil on Canvas  22 3/16 x 18 1/5 in.  1883-85  Yokohama Museum of Art  https://uploads5.wikiart.org/images/paul-cezanne/      Paul Cézanne  Esquisse d'un portrait de madame Cézanne  Oil on Canvas  8 x 5 1/2 in.  1883  Richard Gray, Chicago  https://uploads5.wikiart.org/images/paul-cezanne/      Paul Cézanne  Esquisse d'un portrait du fils de l'artiste  Oil on Canvas  7 11/16 x 4 1/2 in.  1883-85  Von der Heydt Museum, Wuppertal  http://www.cezannecatalogue.com/catalogue_images/main_lg/R534.jpg      Paul Cézanne  Madame Cézanne au chapeau vert  Oil on Canvas  38 1/2 x 31 1/2 in.  1891-92  Barnes Foundation, Philadelphia (BF141)  https://uploads8.wikiart.org/images/paul-cezanne/      Paul Cézanne  Le Garçon au gilet rouge  Oil on Canvas  31 7/8 x 25 5/8 in.  1888-90  The Museum of Modern Art, New York  https://www.moma.org/collection/works/79086?locale=en      Paul Cézanne  Le Garçon au gilet rouge  Oil on Canvas  31 5/16 x 25 3/16 in.  1888-90  Foundation E.G. Bührle Collection, Zürich  https://uploads5.wikiart.org/images/paul-cezanne/boy-in-a-red-vest-1889.jpg      Paul Cézanne  Le Garçon au gilet rouge  Oil on Canvas  36 3/16 x 28 11/16 in.  1888-90  National Gallery of Art, Washington, D.C.  https://images.nga.gov/en/search/do_quick_search.html?q=%221995.47.5%2      Paul Cézanne  Madame Cézanne dans la serre  Oil on Canvas  36 3/16 x 28 11/16 in.  1891-92  The Metropolitan Museum of Art, New York  http://images.metmuseum.org/CRDImages/ep/original/DP317780.jpg      Paul Cézanne  Cézanne coiffé d'un chapeau mou  Oil on Canvas  23 5/8 x 19 5/16 in.  1894  Bridgestone Museum of Art, Tokyo  https://uploads0.wikiart.org/images/paul-cezanne/      Paul Cézanne  Jeune fille à la poupée  Oil on Canvas  36 3/16 x 28 11/16 in.  1895  Private Collection, New York  https://uploads5.wikiart.org/images/paul-cezanne/young-girl-with-a-doll.jpg      Paul Cézanne  Le Festin – L'Orgie; Le Banquet de  Oil on Canvas  51 3/16 x 31 7/8 in.  1867  Private Collection, France  https://uploads4.wikiart.org/images/paul-cezanne/the-feast-the-banquet-of      Paul Cézanne  Le Pêcheur à la ligne  Oil on Canvas  10 5/8 x 14 3/16 in.  1868-70  ?  Unable to locate color version      Paul Cézanne  Le Déjeuner sur l'herbe  Oil on Canvas  23 5/8 x 31 7/8 in.  1870  Private Collection, New York  https://uploads0.wikiart.org/images/paul-cezanne/luncheon-on-the-grass-      Paul Cézanne  Au bord de l'étang  Oil on Canvas  17 1/2 x 21 1/16 in.  1876-77  Museum of Fine Arts, Boston  http://www.mfa.org/collections/object/download/50439      Paul Cézanne  Le Déjeuner sur l'herbe  Oil on Canvas  13 3/8 x 15 3/8 in.  1878-80  ?  Unable to locate color version      Paul Cézanne  La Lutte d'amour  Oil on Canvas  14 7/8 x 18 5/16 in.  1880  National Gallery of Art, Washington, D.C.  https://images.nga.gov/en/search/do_quick_search.html?q=%221972.9.2%22      Paul Cézanne  Les Moissonneurs  Oil on Canvas  10 3/16 x 16 1/8 in.  1880  Private Collection, Switzerland  http://www.cezannecatalogue.com/catalogue_images/main_lg/454.jpg      Paul Cézanne  Léda au cygne  Oil on Canvas  23 x 28 7/8 in.  1880  Barnes Foundation, Philadelphia (BF36)  https://uploads0.wikiart.org/images/paul-cezanne/leda-and-the-swan.jpg      Paul Cézanne  Le Vase rococo  Oil on Canvas  28 11/16 x 23 5/8 in.  1875-77  National Gallery of Art, Washington, D.C.  https://images.nga.gov/en/search/do_quick_search.htm      Paul Cézanne  Deux poires  Oil on Canvas  6 1/2 x 9 3/8 in.  1875  Christie's, New York  https://www.ecosia.org/images?addon=chrome&addonversion=      Paul Cézanne  Cinq pommes  Oil on Canvas  5 x 10 in.  1877-78  Mr. and Mrs. Eugene V. Thaw, New York  https://www.ecosia.org/images?addon=chrome&addonversion      Paul Cézanne  Pommes  Oil on Canvas  7 1/2 x 10 1/2 in.  1878  The Fitzwilliam Museum, Cambridge  https://uploads3.wikiart.org/images/paul-cezanne/apples-1878.jpg      Paul Cézanne  Pommes et linge  Oil on Canvas  9 13/16 x 17 5/16 in.  1879-80  Private Collection, Japan  http://www.cezannecatalogue.com/catalogue/entry.php?id=335      Paul Cézanne  Bol et boîte à lait  Oil on Canvas  7 7/8 x 7 1/16 in.  1879  Bridgestone Museum of Art, Tokyo  https://uploads2.wikiart.org/images/paul-cezanne/still-life-bowl-and-milk-      Paul Cézanne  Verre et pommes  Oil on Canvas  12 3/8 x 15 11/16 in.  1879-80  Collection Rudolf Staechelin, Basel  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Les Bégonias   Oil on Canvas  18 1/8 x 21 1/4 in.  1879-80  Private Collection  http://www.cezannecatalogue.com/catalogue_images/      Paul Cézanne  Deux fruits  Oil on Canvas  7 1/2 x 9 1/8 in.  1885  Private Collection, Japan  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Grenade et poires dans une assiette  Oil on Canvas  10 5/8 x 14 3/16 in.  1885  Private Collection, New York  https://uploads7.wikiart.org/images/paul-cezanne/      Paul Cézanne  Nature morte  Oil on Canvas  13 13/16 x 18 1/8 in.  1890  The State Hermitage Museum, St. Petersburg  https://uploads7.wikiart.org/images/paul-cezanne/still-life-with-apples-1.jpg      Paul Cézanne  Fruits et cruchon  Oil on Canvas  13 x 16 1/8 in.  1893-94  Museum of Fine Arts, Boston  http://www.mfa.org/collections/object/fruit-and-a-jug-on-a-table-33253       Paul Cézanne  La Corbeille de pommes  Oil on Canvas  25 5/8 x 31 1/2 in.  1893  The Art Institute of Chicago  https://uploads0.wikiart.org/images/paul-cezanne/       Paul Cézanne  Nature morte  Oil on Canvas  17 5/16 x 24 in.  1895  Sammlung Esther Grether, Basel  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  La Baigneuse debout, s'essuyant les cheveux  Oil on Canvas  11 3/8 x 5 1/8 in.  1869  Private Collection  https://uploads1.wikiart.org/images/paul-cezanne/      Paul Cézanne  La Baignade  Oil on Canvas  7 1/2 x 10 5/8 in.  1875-77  Private Collection, New York  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur aux bras écartés  Oil on Canvas  13 x 9 3/8 in.  1877-78  Jasper Johns, Sharon, Conn.  https://uploads2.wikiart.org/images/paul-cezanne/      Paul Cézanne  Les Baigneurs au repos  Oil on Canvas  31 1/8 x 38 3/16 in.  1876-77  Barnes Foundation, Philadelphia (BF906)  https://uploads3.wikiart.org/images/paul-cezanne/bathers-at-rest-1877.jpg      Paul Cézanne  Quatre Baigneuses  Oil on Canvas  13 13/16 x 15 5/8 in.  1880  Private Collection  https://uploads0.wikiart.org/images/paul-cezanne/four-bathers-1878.jpg       Paul Cézanne  Baigneuses devant une tente  Oil on Canvas  24 13/16 x 33 1/16 in.  1883-85  Staatsgalerie, Stuttgart  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Le Baigneur au Rocher  Oil on Canvas  66 x 44 1/2 in. (part  1867-1869  Chrysler Art Museum Norfolk, VA  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneuses  Oil on Canvas  13 x 15 11/16 in.  1870  Private Collection  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Homme Etendu et Baigneuses  Oil on Canvas  10 1/2 x 13 3/4 in.  1868-1870  Private Collection  Private Collection.      Paul Cézanne  Baigneur et Baigneuses  Oil on Canvas  7 7/8 x 15 3/4 in.  1870-1871  Travis Hanson, Fine Art, New York  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneuse au bord de la mer  Oil on Canvas  9 1/4 x 8 5/8 in.  1875  Barnes Foundation, Philadelphia  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneuse assise  Oil on Canvas  7 5/8 x 4 3/4 in.  1875  Columbus Museum of Art  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  La Baignade  Oil on Canvas  7 1/2 x 10 5/8 in.  1875-1877  Private Collection, New York  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur aux bras écartés  Oil on Canvas  9 1/2 x 5 1/2 in.  1876  Rose Art Museum, Brandeis University  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur aux bras écartés  Oil on Canvas  9 x 6 in.  1876-1877  Private Collection, France  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Cinq Baigneurs  Oil on Canvas  9 3/8 x 9 13/16 in.  1876  Musee d'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur aux bras écartés  Oil on Canvas  9 3/8 in. x 6 5/16 in.  1875-1876  Private Collection  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneuses  Oil on Canvas  15 x 18 1/8 in.  1875  The Metropolitan Museum of Art  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Cinq Baigneuses sous des arbre  Oil on Canvas  23 5/8 x 28 11/16 in.  1875  Private Collection  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Trois Baigneuses  Oil on Canvas  7 1/2 x 8 11/16 in.  1874-1875  Musee d'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneurs au repose I  Oil on Canvas  15 x 18 in.  1875-1876  Musee d'Art et d'Histoire, Geneva  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneurs au repose II  Oil on Canvas  15 x 18 1/8 in.  1875-1876  Location Unknown  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur debout  Oil on Canvas  11 13/16 in. x 6 11/16 in.  1876  Sotheby's New York  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Baigneur assis au bord de l'eau  Oil on Canvas  11 3/8 x 8 5/16 in.  1876  Obersteg Collection, Basel  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Trois Baigneuses  Oil on Canvas  9 3/8 x 12 1/2 in.  1876-1877  Barnes Foundation, Philadelphia  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Trois Baigneuses  Oil on Canvas  9 13/16 x 13 1/5 in.  1876-1877  Elliott Wolk, Scarsdale  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Trois Baigneuses  Oil on Canvas  20 1/2 x 21 3/8 in.  1876-1877  Private Collection  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Trois Baigneuses  Oil on Canvas  12 x 13 in.  1875  Private Collections  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Quatre Baigneuses  Oil on Canvas  10 5/8 x 13 5/8 in.  1876-1877  Barnes Foundation, Philadephia  http://www.cezannecatalogue.com/exhibitions/entry.php?id=52      Paul Cézanne  Quatre Baigneuses  Oil on Canvas  15 x 18 1/8 in.  1877-1878  Pola Museum of Art, Kanagawa  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneuses  Oil on Canvas  15 1/2 x 16 1/2 in.  1877-1878  Barnes Foundation, Philadephia  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneuses  Oil on Canvas  17 7/8 x 21 5/8 in.  1877-1878  Musee Picasso, Paris  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneuses  Oil on Canvas  15 x 16 1/8 in.  1877-1878  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuse  Oil on Canvas  8 5/8 x 5 1/2 in  1877-1878  Kuboso Memorial Museum of Arts  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneur vu de dos  Oil on Canvas  9 3/8 in. x 7 1/2 in.  1877-1878  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneur aux bras écartés  Oil on Canvas  28 3/4 x 23 5/8 in.  1877-1878  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneurs  Oil on Canvas  13 5/8 x 15 in.  1879-1880  The Detroit Institute of Art  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneurs  Oil on Canvas  23 5/8 x 28 3/4 in.  1880-1882  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneur  Oil on Canvas  12 5/8 x 8 5/8 in.  1877-1878  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Le Bain  Oil on Canvas  13 13/16 in. x 8 11/16 in.  1880-1882  Staatsgalerie, Stuttgart  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneur debout vu de dos  Oil on Canvas  13 in. x 8 11/16 in.  1879-1882  The Art Institute of Chicago  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneur debout vu de dos  Oil on Canvas  10 13/16 in. x 6 13/16 in.  1879-1882  Henry and Rose Pearlman Foundation  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Quatre Baigneuses  Oil on Canvas  13 13/16 in. x 15 5/8 in.  1880  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs et Baigneuses  Oil on Canvas  7 1/2 in. x 8 5/16 in.  1880  Ohara Museum, Kurashiki  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Cinq Baigneuses  Oil on Canvas  25 5/8 x 25 5/8 in  1885  Kunst Musuem, Basel  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Le Grand Baigneur  Oil on Canvas  50 x 38 1/8 in.  1885  The Museum of Modern Art, New York  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Six Baigneuses also known as Les Ondines  Oil on Canvas  13 x 17 3/8 in  1887  Private Collection, Geneva  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  23 5/8 x 31 7/8 in.  1890  Musee d'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  20 11/16 in. x 25 5/16 in.  1890-1892  Saint Louis Art Museum  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Quatre Baigneuses  Oil on Canvas  28 3/8 x 36 1/4 in.  1888-1890  Ny Carlsberg Glyptotek, Copenhagen  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  11 in. x 17 5/16 in.  1890  Musee D'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  11 1/4 x 20 in.  1890-1895  Stiftung Langmatt Sidney and Jenny Brown  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  15 3/8 x20 7/8 in  1890  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs en plein air   Oil on Canvas  21 1/4 x 25 5/8 in.  1890-1891  The State Hermitage Museum, St. Petersburg  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  8 5/8 x 13 in.  1892  Musee de Beaux-Arts, Lyon  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs et Baigneuses  Oil on Canvas  8 7/8 x 13 15/16 in  1890  The Art Institute of Chicago  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Groupe de Baigneuses  Oil on Canvas  18 1/2 x 30 1/4 in.  1895  Ordrupgaard Collection, Copenhagen  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  7 1/2 x 10 1/4 in.  1890-1895  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Groupe de Baigneurs  Oil on Canvas  11 1/2 x 15 1/2 in.  1892-1894  Barnes Foundation, Philadelphia  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Le Bain  Oil on Canvas  10 1/4 x 15 3/4 in.  1892-1894  Pushkin Museum, Moscow  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Groupe de Baigneurs  Oil on Canvas  8 1/2 x 12 1/8 in.  1895  Philadelphia Museum of Art  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Les Grandes Baigneuses  Oil on Canvas  53 1/2 x 75 1/4 in.  1894-1905  National Gallery, London  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Les Grandes Baigneuses  Oil on Canvas  52 3/8 x 81 1/2 in.  1895-1906  Barnes Foundation, Philadelphia  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Les Grandes Baigneuses  Oil on Canvas  82 x 98 in.  1906  Philadelphia Museum of Art  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  11 x 14 1/4 in.  1900-1904  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  20 1/8 x 24 1/4 in  1899-1904  The Art Institute of Chicago  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Groupe de Sept Baigneurs  Oil on Canvas  14 5/8 x 17 3/4 in.  1900  Fondation Beyeler, Riehen, Basel  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  10 5/8 x 18 1/4 in.  1898-1900  The Baltimore Museum of Art  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  8 5/8 x 13 in.  1899-1900  Musee d'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  10 5/8 x 8 5/8 in  1900  Location Unknown  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  16 5/8 x 21 5/8 in.  1900-1904  Musee d'Orsay, Paris France  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  11 7/8 x 17 3/8 in.  1900  Location Uknown  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Esquisse deBaigneurs  Oil on Canvas  7 7/8 x 13 in.  1900-1902  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  11 1/2 x 9 1/4 in.  1902-1906  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Esquisse de Baigneurs  Oil on Canvas  12 5/8 x 15 3/4 in.  1902-1906  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Esquisse de Baigneurs  Oil on Canvas  25 5/8 x 31 7/8 in.  1900-1906  Fondazione Magnani-Rocca, Parma  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  13 3/4 x 8 5/8 in.  1900  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Esquisse de Baigneuses  Oil on Canvas  9 x 6 5/8 in.  1900  Becon Collection, Greenwich  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneurs  Oil on Canvas  9 x 10 1/2 in.  1902-1904  Barnes Foundation, Philadelphia  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Etude de Baigneuses  Oil on Canvas  8 3/8 x 12 3/4 in.  1900-1906  Museum Rosengart, Lucerne  http://www.cezannecatalogue.com/exhibitions      Paul Cézanne  Baigneuses  Oil on Canvas  29 x 36 3/8 in.  1902-1906  Private Collection  http://www.cezannecatalogue.com/exhibitions      Paolo Veronese  Les Noces de Cana (before conservation)  Oil on Canvas  22 ft.3 in. x 32 ft  1563  Louvre (unrestored)  https://www.wikiart.org/en/paol o-veronese/the-marriage-at-cana-      Paolo Veronese  Les Noces de Cana (digital facsimile)  Digital Reproduction  22 ft. 3 in. x 32 ft.  2006  Fondazione Giorgio Cini, Venice  https://www.cineclubdecaen.com/peinture/peintres/veronese/nocesdecana.jpg      

SUPPLEMENTARY TABLE II: Golden Windows

SUPPLEMENTARY TABLE III: Golden Strips