Illusory Surfaces

This work is supported by the NSF CAREER Award and by the Sloan Foundation.
(a)                   (b)                  

(c)                   (d)  

Figures (a) and (c) are known as Kanizsa figures. I study the formation of illusory contours (the boundary of objects that humans perceive, but where intensity gradient information is not present) via the formation of salient surfaces. The ouput of the algorithms proposed by us (collaborators and I) are salient surfaces as shown in (b) and (d).


Here, at the Center for Neural Sciences, professors Nava Rubin and Robert Shapley are also working on the perceptual/computational issues related to these phenomena.

There are interesting phenomena relating illusory contours to stereo vision and in particular the phenomena gets a much stronger perception.


Paper and Abstracts:

Salient and Multiple Illusory Surfaces

D. Geiger and H. Pao and N. Rubin

Conference on Computer Vision and Pattern Recognition, Santa Barbara, 1998.

All illusory surface figures yield a perception of a surface occluding another one or the background. Occluded surfaces yield completion, a phenomena known as amodal completions. It is intriguing that for some images we do see illusory surfaces, but not for others (see figure~\ref{fig:kanizsa_square_cross_fish}). Also, illusory surfaces may have portions occluded. We aim to understand these phenomena.

Our approach detects junctions and intensity edges. From these junctions we seek to find an optimal image organization, i.e., multiple ordered surfaces with the ordering accounting for salience. The most salient being the figure, while the other surfaces are classified as background. A decision of which surface is the visible one (on top) is made locally, at each pixel, allowing the salient surface (figure) to have portions occluded, i.e., with amodal completions. We account for a variety of imagery not explained before.A common factor in all illusory contour figures is the perception of a surface occluding part of a background. We show that by diffusing a proper set of junction hypothesis (salient X background) we obtain salient surfaces with boundaries representing illusory contours. Amodal completions emerge at the overlapping surfaces.

A Computational View of Visual Organization for Figure/Ground Separation

D. Geiger and K. Kumaran and L. Parida

Conference on Computer Vision and Pattern Recognition, San Francisco, 1996.

A common factor in all illusory contour figures is the perception of a surface occluding part of a background. We show that by diffusing a proper set of junction hypothesis (salient X background) we obtain salient surfaces with boundaries representing illusory contours. Amodal completions emerge at the overlapping surfaces.

We address the problem of selecting the best image organization (set of hypothesis). Within a Bayes rational we propose an optimization criteria based on (i) a coherence measure between pairs of junctions (correlation between the diffusion of each pair); (ii) a bias towards smoother junctions; (iii) a bias towards salient surfaces ``that explain'' more junctions. A statistical physics approach to select the best organization is applied. The experiments suggest that despite the large number of possible organizations our approach may take only a few steps (in organization space) to select the best one.

Illusory surface perception and visual Organization

K. Kumaran and D. Geiger and L. Gurvits

Network journal

Illusory contours occur in a wide variety of circumstances in nature. A striking man made example is the Kanizsa triangle. A common factor in all such figures is the perception of a surface occluding part of a background, i.e. illusory contours are always accompanied by illusory surfaces. The detection of occlusion cues suggest various different local surface configurations, leading to a large combinatorial set of global surface configurations, each one constituting an image organization.

We address the problems of why and how the image organizations that yield illusory contours arise. Our approach is to (i) detect occlusions; (ii) assign surface-states at these locations that reflect the presence of a particular surface configuration; (iii) apply a Bayesian model to diffuse this local surface information; (iv) define an entropy measure for each image organization to select the best one(s) as the one(s) giving the lowest entropy values. We note that (a) the illusory contours arise from the surface boundaries and hence, we do not propagate/extend intensity edges; (b) the overlapping surfaces provide explanation for the amodal completions. The model reproduces various qualitative and quantitative aspects of illusory contour perception and has been supported by a series of experiments.