Computing & the Arts



Giuseppe Arcimboldo (1527-1593),
L'Estate ("Summer"), 1573, Le Louvre Museum.



1. Computational theories of Visual Perception

 Part-based Representation of Visual Shape

and Implications for Visual Cognition

Sing, M., & Hoffman, D.

Chapter 9 in From Fragments to Objects: Grouping and Segmentation in Vision, T. F. Shipley & P. J. Kellman (Eds.), pp. 401-459. Elsevier Science. 2001.

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"Human vision organizes object shapes in terms of parts and their spatial relationships."


N.B.: This is direct line with the Gestalt school ideas.

Introduction


Objects as perceptual units.

Parts of objects as perceptual units.

Parts are perceived for 2D shapes, topographic surfaces (2.5D), as well as 3D objects.


Why?
Phenomenology

Valleys vs. Hills

Fig.1. Hills vs. Valleys
Similarity

Fig.2. Same parts?
Which is more similar on the right to the one on the left?
Figure-ground





Transparency

Fig. 4. One disk looks transparent.
Symmetry

Fig. 5. Symmetry is easier than repetition.
Pop out (pre-attentive processing)

Fig.6. Concavity pops-out amongst convex distractors.


Boundaries of Parts



Computational theories:
Geons (after Biederman) from Shimon Edelman's Experimental Epistemology Project.










Problem: Each class of primitives only captures a finite (and relatively small) set of shapes (and parts).




Transversality principle

Two shapes intersect and (in general) create a concave crease at the locus of intersection.


The Transversality Principle leads to the Rule of Concave Creases:


Partition a 3D shape at concave creases.

Generalize this rule to smoother boundaries: Partition at loci of "negative minima of curvature."

Figure & ground reverses the sign of curvature.


Minima rule for (2D) silhouettes:


Similar parts?


Minima rule for (3D) shapes:





Height direction defines negative curvature for an oriented surface.



Assumes we can give an orientation to surface patches.
Assumes an inside versus outside (figure vs ground) for silhouettes.

If the parts are similar (here the same) repetition can become easier...

After Attneave, Biederman, etc.:
(more) information is encoded in "corners" (or concave elements).
If this information can be spatially related (paired), parts can be recovered.

N.B.: Information is not directly to the amount of "stuff" we draw (the trace), but instead to where we draw (at loci carrying more geometric meaning intrinsic to the shape).



Limitations


Concavities, yes, .... but how to pair them to define "cuts" ?




Issue of Scale


Shorter cuts (and smaller parts) are preferred.


Curvature strength (value) orients the cuts.


Gestalt principles come into play: Good continuation




Besides curvature .... what else?

Axial symmetries are another intrinsic geometric representation of shapes which can support meaningful partitioning.







N.B.: The original definition of Symmetry Axis Transform (SAT), i.e., the process by which one computes the representation of a shape in terms of its axial symmetries, also applies to the outside (the ground), not just the inside (figure) of the "scene" (the objects). We will cover this topic in depth in another paper.


Saliency of figure vs ground


"Other things being equal, the choice of figure and ground is preferred which leads to the most salient parts for the figure."

"a" is more likely seen as leading to the figure in "c" than "b".
This saliency rule may lead to inconsistency (such as in "d").

Relative salience of parts by changing the sharpness of curvature at "corners."
Issue of Transparency








Issue of Pre-attentive processing & Parts

Fact:

Target among distractors. (a) leads to a pop-out, not (b).
Issue of Occlusion / Overlapping



(a), (b), (c) tend to be seen as two overlapping objects even though
these figures lack any T-junctions to signal occlusion.
Smoothing the negative minima (d), or disrupting the good-continuation between one set of contours (e),
switches the percept to that of a single object with multiple parts.




References

Attneave:Similarity:1950
Attneave, F., "Dimensions of Similarity," American Journal of Psychology, vol. 63, pp. 516--556, 1950.

Attneave:Visual:1954
Attneave, F., "Some Informational Aspects of Visual Perception," Psychological Review, vol. 61, pp. 183-193, 1954.

Biederman:Components:1987
Biederman, I., "Recognition-by-components: A theory of human image understanding," Psychological Review, vol. 94, no. 2, pp. 115-117, 1987.

Blum:Shape:1973
Blum, H., "Biological Shape and Visual Science," Journal of Theoretical Biology, vol. 38, pp. 205-287, 1973.

Siddiqi:Parts:1995
Siddiqi, K., & Kimia, B., "Parts of visual form: Computational aspects," IEEE Transactions on PAMI, vol. 17, no.3, pp. 239-251, March 1995.

Siddiqi:Triangle:2001
Siddiqi, K., Kimia, B., Tannenbaum, A., & Zucker, S., "On the psychophysics of the shape triangle," Vision Research, vol. 41, no. 9, pp. 1153-1178, 2001.

Sing:Part:2001
Sing, M., & Hoffman, D., "Part-Based Representations of Visual Shape and implications for visual cognition,"  Chapter 9 in From Fragments to Objects: Grouping and Segmentation in Vision, T. F. Shipley & P. J. Kellman (Eds.), pp. 401-459. Elsevier Science. 2001.
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Last update: Oct. 31, 2006