Top: External medialness processing on a humanoid object. The articulated movement of the left arm changes the location and orientation of the associated external dominant point near the concave curvature peak. We instead use the intersection of the main ridge orientation with the boundary i. Pairs of dark arrows along the contour illustrate the local support for concavity while the arrow along the medial ridge dark with white pointy head indicates the direction of flow of medialness away from the concavity.
Bottom: Similar illustration of interior medialness processing on a humanoid object to identify significant convexities in the vicinity of ends of medialness ridge trace. We have recently built systems on the basis of this tri-partite feature set to address problems of information retrieval with applications to environmental data sets biological shapes, static or in movement Aparajeya and Leymarie, , , movement computing Leymarie et al.
In Fig. This is to be compared with the use of primitives by a draughtsman, illustrated in Fig. The primitives recovered via hot spots are not exactly the same, but we claim are of similar type and illustrate a similar use of topology to connect these and of morphology to capture the main body parts and limbs and other features. Note that we do not here use the additional information provided by retrieved significant convex and concave features Fig. Middle: Our proposed shape representation in terms of a selection of internal dominant medial in light gray and contour convex and concave in dark gray points.
Bottom: A possible visualization of primitives obtained by connecting adjacent and overlapping interior medial annuli sausage-like regions. It is instructive to compare these object parts and relationships with the choices made by the artist who drew the originals Fig. We emphasize here the similarities and differences between the original ideas of Harry Blum and their continuing development and multiple applications since, and the concept of perception-based medialness or p - medialness.
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It also provides for uniqueness thanks to its precision: for a given set of abstract sources of propagation e. The MA offers a number of interesting additional features which explain in part its success in computational fields since its introduction in the s; we mention a few here for a more complete treatment of the subject, refer for example to the monograph edited by Siddiqi and Pizer Siddiqi and Pizer, : the topology of the object is reflected in the topology of the MA graph e.
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While the evidence for a medialness operation in the visual neural system is mounting, and its usefulness in cognition is also becoming apparent Sect. In particular, a series of similar dominant points can then be obtained for various, but sufficiently closely related line drawings. We have yet to perform such an analysis. We now explore in this penultimate section the application of medialness as a representation substrate for a class of works of visual art.
Our study is only meant as an entry into the subject and thus clearly not exhaustive. We focus on works from two important 20th century artists—Picasso and Matisse. For all our observations, we provide commentaries derived from a non-artist reading of medialness maps and features. We propose that such detailed analysis is made more explicit and obvious by using the information present in the medialness maps and recovered feature points. In c we show the medialness field in between the bounding canvas rectangular limits and the regions exterior to the female figures.
Such a medialness field can be used to study the spatial relations between the female figures. For example, an apparent first dichotomy is observed between two groups of figures: Demoiselles 1, 2 and 3 have very little medialness field left in-between them, in the form of elongated inroads; a similar situations with no intermediate space is observed for the second group of Demoiselles 4 and 5. However, the medialness region in between the two groups is wider and rich in its shape features with multiple hot spots and ridge ends Note Also the two groups are entirely separated by medialness from top to bottom , while within each group figures come in close contacts.
Indeed, Demoiselle 1 is almost entirely separated from Demoiselle 2 by a thin elongated region of exterior medialness. The central couple also share some strong pose features folded arms above head , which is made apparent when also considering the interior medialness. We also exploit the exterior medialness field for each figure individually, such as illustrated in Fig.
This field is used to retrieve significant concavities of the body; or by duality, significant convexities of the background located at the tip of medial ridges that end near the body. This process is repeated for each body individually. We propose that such feature maps and their underlying medialness fields can be used to conduct careful studies of artworks composed of distinct objects such as Les Demoiselles.
The five figures occupy similar amount of space in terms of retrieved medial disk areas. Some of the Demoiselles share similar parts indicated by local groupings of medial features: e. The convex and medial hot spots of the breasts of the Demoiselles 1, 2, 3 and 5, in profile or facing the observer, are also highlighted. We also approximate ridge following on the medialness field thick paths to link the various feature points.
We note that our choices of parameters and thresholds remain purely experimental and can only be used with care as a more in depth study over series of works will be required, to provide perhaps some systematic methods of parameter selection. Nevertheless, such visualization choices are useful we propose for at least some interactive modes of analysis of such an artwork. These three visualization modes are also juxtaposed in the next figure to illustrate their differences and similarities. Top: Selective feature points analysis, where interior ridge medialness following is also displayed vis.
Bottom: equivalent analysis for the exterior medialness field. Below is shown the use of vis. In the Rites of Spring we see two human figures with similar arm structures while the horns of the goat mimic or respond to these arms in extension and general orientation pointing upward and curving.
Also, the leg and knee of the dancing human figure appear also repeated mirrored in the front leg structures of the goat. In the Bullfight , the horns of the bull respond in medialness structure to the spades of the toreador. Such ambiguity creates a tension that may augment the interest of the observer in the overall art piece.
Top row: Rites of Spring and Bullfight , lithographs by Picasso, circa , with superimposed feature points vis.
Middle row: alternate visualization of medialness features vis. Bottom row: Visualization of the sausage regions derived from sufficiently overlapping hot spot domains. The human faces have very similar medialness structures and recovered feature points descriptions, with protuberances highlighting the nose, mouth and chin which are used to emphasize a sense of orientation in space: crying towards the sky, gaping towards the massacre.
In our analysis of the same series, Fig. A similar simplification process occurs with the legs noticeable in terms of medialness as the legs are eventually reduced to simple curves. The tail is eventually made clearly separated from the main body rather than overlapping as in the initial sketches , and it too is simplified into an elongated curve; this is made more explicit in the analysis of the exterior medialness Fig.
From the exterior medialness we also can observe how the backbone and overall dorsal region is made smoother rounder, upwards, with no concavities left. The artist finally converges on an ultimate version January 17, which appears to represent a compromise by combining elements of the two penultimate stages January 5 and 10, , preserving the simplest structures for the legs and tail January 10 and head and main body January 5 , while deciding to go for the more elaborate reproductive system and inner body lines of January Bull series processed: Visualization of interior medialness and feature points vis.
Bull series processed: Visualization of exterior medialness and feature points vis. These three drawings were used by Koenderink, Van Doorn and Wagemans in their extensive study on cartoon-style line drawings Koenderink et al. One of their analyses is based on contour fitting of drawn strokes and further analyses of curvature and pairings indicating strong MA cues and significant circular primitives such as associated to the buttocks of the female bodies, Fig.
We provide finer detailed analyses as we compute medialness for a larger set of line traces since we do not require to carefully represent drawn strokes our medialness can be computed from partial data, points or line segments. In these drawings, the long linear structures of the arms are made explicit by the ridges of medialness, while important body parts e. Top row: Three s Picasso drawings of the female form adapted from Koenderink et al.
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A2 —originals in color. Bottom row: Visualization of the sausage regions derived from overlapping hot spot domains in p-medialness. Women Drawn series processed; top row: vis. Starting with Fig. Matisse was part of the same group as Picasso of visual artists who emerged on the art scene of Paris in the early s and had a major impact throughout their lifetime, often re-inventing their style and practice, all the while influencing each other as well as their contemporaries. In this figure, we have three examples of the famous series of blue cuts in which Matisse explored the female form.
In terms of medialness structures, we can observe very similar limbs and body descriptions alike generalized cylinders ; breasts are singled out, the head plays a dominant role with one or very few hot spots but its pose varies. The foldings of the arms and legs are similar, and represent an exploration of various possible solutions in terms of occlusions, orientations and foldings of hand and foot , which is made more apparent in the visualization of sausage regions bottom row of Fig.
Women Cut-Outs series, Matisse, Top row: Our medialness analysis is shown, superimposed vis. Bottom row: Visualization of the sausage regions derived from overlapping hot spot domains. This series was photographed by Matisse during a period of six months in when he explored various changes in pose and parts, which lead to a finished piece, the Large Reclining Nude or Pink Nude , Fig.
We study 16 of the original 22 photographs in the series here the original photographs are part of the Baltimore Museum of Art collection. If we consider the interior medialness information Figs A10 to A13 , the final version represents a more symmetric pause legs versus arms and head ; the dorsal line is smoother, the large buttocks lead towards a finer waist line creating an approximate triangular flow as a generalized cylinder, oriented from the buttocks towards the breasts. The legs are more neatly aligned, one the left leading to the end of the other right which is otherwise largely occluded.
The knee is folding in response to the right arm over the head creating a mirrored symmetrical pause left legs vs. Also, one hand leads to the bottom of the canvas in response to one foot a possibility explored in a few previous frames. In this last iteration, the head is re-oriented straight up alike the breasts main convexities closely aligned in orientation.
A15 , bottom right , which underlines the smooth way the buttocks link to the back line up to the rest of the body on one side, and to the folded leg on the other side.
By comparing the evolution of the main negative space above the reclining female body, we discover that it has become more rectangular in form and that various options were explored by the artist, with slight changes in relative positions of legs and arms and breasts. Finally, in the last frame by observing either the interior or exterior medialness, we see the final solution selected by the artist, where the body occupies space in a more rectangular format, where the arms and top parts of the legs are nearly parallel and oriented vertically.
Medialness description of exteriors with respect to each female nude figure vis. Matisse explored various possibilities of the female reclining nude over a period of half a year in For our final experiment, in Fig. Both illustrate the use of long cylindrical parts to convey movement on a static canvas.
From the interior medialness depictions we see a similar use of sausage regions. The head is given more details convexities and concavities for the Acrobat , while the breasts are made explicit for the female figure in Flowing Hair. From the exterior medialness depictions, we see that Matisse uses parallelism repetitively, with the arms, hair strokes, and neatly aligned legs, while Picasso, instead forces the extruding body parts of his Acrobat to explore a rectangular frame at various angles and folds, where no two parts is in parallel.
Picasso and Matisse. Left: Acrobat by Pablo Picasso, oil on canvas, Top row: Vis. Middle row: Visualization of the sausage regions derived from overlapping hot spot domains. Bottom row: Vis. Medialness is shown to have deep roots in perception and cognition, the arts as well as computational models of shape understanding.
More recently, evidence is mounting in the literature that parts of the visual cortex are likely involved in some forms of medialness computations and uses. Much remains to be explored however before we have a clear understanding of the various layers of representations and processing involved, in particular as complex feedback loops are integrated by our nervous system. Our combination of these two apparently different representations one of regions, the other of contours can be unified—a concept we refer to as p-medialness for perception-based medialness —as shown in our recent work Aparajeya and Leymarie, ; Leymarie et al.
As indicated by recent studies in perception and cognition models, such extrema are better thought of as combining significant curvature peaks with regional support De Winter and Wagemans, , rather than referring to the traditional mathematical definition biased towards a purely local concept and analysis. All rights reserved.
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Remember me on this computer. Cancel Forgot your password? Showing all editions for 'Visual Thought : the depictive space of perception'. Year Language English. Displaying Editions 1 - 10 out of Visual thought : the depictive space of perception by Liliana Albertazzi;. Print book. Koenderink and Andrea J. In this case, the authors advance the idea that it is critical that we distinguish spatial perspectives and analyze the work of the German sculptor Adolf Hildebrand to delineate their point.
Hildebrand became interested in perceptual spaces due to his interactions with the painter Hans von Mareesand and the philosopher and theoretician of art and aesthetics Konrad Fiedler. Surprisingly, although Hildebrand was a sculptor, his influential treatise The Problem of Form treats aesthetic perception as largely pictorial perception.
Graphic illustrations, references to experimental work, and some discussion that personalized Hildebrand as an artist allowed these authors to effectively use him as a starting point in distinguishing the structure of pictorial space from that of visual space, while also showing where they intersect. Gert J. In it, van Tonder showed his knack for combining solid scientific analysis with qualities often seen as "outside" of the scientific domain.
Titled "Order and complexity in naturalistic landscapes: on creation, depiction, and perception of Japanese dry rock gardens," he opens with the comment that he knows that what he intuits as order and complexity is closely related to his subjective experience when looking into a classical Japanese dry rock garden karesansui design. Yet, as he further explains, he also knows that no specific grid, ratio, clearly identifiable fractal dimension or other measure reveals why he experiences the garden as a calming space innervated by a subtle balance of tensions.
The qualitative and quantitative tension are addressed through experimental work that uses a computational model for image segmentation using forward-inverse medial axis transformation, nicely supplemented by his training with the Ueoto gardening school and studies of classical gardening history. This allows van Tonder to convincingly show that there is substantial overlap between the visual features that classical gardeners manipulated and the perceptual grouping factors used by the Gestalt school to describe the process of figure-ground segmentation.
In addition, van Tonder points out that investigations suggest that karesansui design focusing primarily on rocks and trees simplifies the segmentation process, equalizes the salience of parts and wholes over a range of spatial scales, and balances the salience of figure and ground. Karesansui design seems to "recruit" mechanisms of perceptual completion to reconstruct visual features that are otherwise too complex to present in their totality, thereby achieving even more perceptually complex results with sparse design compositions of interest.
If there is a downside to the van Tonder essay, it is its length. Informative and packed with information, each paragraph covered so much ground that I am certain I failed to entirely digest the depth of the article and the structure and complexity of the details he presented. Equally compelling is Timothy L. Hubbard and Jon R.