ZYGMUNT PIZLO

Personal Information:

    Zygmunt Pizlo  CV

    Professor
    Department of Psychological Sciences,
    School of Electrical and Computer Engineering (by courtesy)
    Purdue University
    West Lafayette, IN 47907-2081

    email: pizlo at psych dot purdue dot edu
    tel. (765) 494 6930
    FAX: (765) 496 1264
    Room #: PRCE 194

Pizlo's Lab

Graduate Seminar: Perception of 3D shape (Psy 606, Fall 2008)

     - Definition of 3D shape

     - History of shape in art and psychology

     - Affine and projective geometry

     - Biology of natural form

     - Symmetry, groups, invariants and Curie principle

     - Computational models

     - Shape recovery, veridicality and constancy

New:

Z. Pizlo (2008) "3D shape: its unique place in visual perception." Cambridge, MA: MIT Press. 

Errata

Li, Y. & Pizlo, Z. (2007) Reconstruction of shapes of 3D symmetric objects by using planarity and compactness constraints. Proceedings of IS&T/SPIE Conference on Vision Geometry, vol. 6499 (computational model - preliminary version)

Li, Y., Pizlo, Z. & Steinman, R.M. (2008) A computational model that recovers the 3D shape of an object from a single 2D retinal representation. Vision Research (in press) (computational model - elaborated version; US patent - pending)

Pizlo, Z., Li, Y. & Steinman, R.M. (2008) Binocular disparity only comes into play when everything else fails; a finding with broader implications than one might suppose. Spatial Vision (in press).

Demos

 1. Shape Recovery Demo - Synthetic Objects and Images - Start this demo by right-clicking on "Demo 1" : Hit the "return" key or use the mouse to rotate the original and the recovered shapes. Right click to see the next example when you are satisfied that you have seen how well the model recovered the 3D shape from the specific 2D image used.  Press ESC to exit this demo. The first six examples in this demo make use of the same "original" shape. Its recovery was made from different 2D images of this "original" shape."  The 3D shape recovered was almost the same for all of the 2D images that were used to recover it. Note also that the entire 3D shape is recovered, namely, both the visible surfaces in front and the invisible surfaces in back were recovered despite the fact that the model was given 2D images from which hidden edges were removed. This demo includes three different 3D shapes, with six 2D images for each. The last 3D shape shown in this demo represents a chair. This 3D chair was represented by 3D points and recovered from the 2D images of these points. In all of the examples shown in this demo, the model was given the contours or points, as well as the information about which features are symmetric in 3D space and which contours are planar in 3D space. In other words, figure-ground organization was provided to the model to make it possible for the 3D shape to be recovered from its 2D images.

    This demo showed that once figure-ground organization is provided to the model, it can recover the shape of a 3D object, represented by a line drawing, from a variety of the 2D images that would be produced if the object was viewed from almost any viewing direction. Now, consider whether this model can be applied to real images of real objects? It can because most real images of real objects can be represented quite well by line drawings. In other words, this model will be able to recover the 3D structure of real objects as well as it can recover their representations in line drawings.

    Note that even though 3D properties of individual points and features, such as depth and surface orientation, are always ambiguous in a single 2D image, shape is almost never ambiguous because shape, unlike other perceptual properties, such as color, is complex. This fact explains why it is easier to recover 3D shape than to recover the depths of points and the orientations of surfaces.

    This claim, which would have been considered paradoxical in 1709 (Berkeley) or even in 1912 (Wertheimer), does not  seem paradoxical today because a computational model can recover 3D shape from 2D shape, something that cannot be done if one tries to do this by working with points. We like to think that the success of our computational model is a good example of what Gestalt Psychologists had in mind when they said that "the whole is different from the sum of its parts."

2. Shape Recovery Demo - Real Images Segmented by Hand - see Demo 1 to find out how to start and run this demo. In this demo, the contours in the 2D image, given to the model, were extracted by an unskilled human hand. The model was also given information about which features were symmetric in 3D space and which contours were planar in 3D space. Press "c" to toggle the contours and "i" to toggle the 2D image. Press "pause" to stop the rotation, and "s" to synchronize the rotation, after you changed the 3D orientation of one of the 3D shapes by using mouse. The "chair" was recovered from six different 2D images.

    Note that the 3D shape could be recovered very well from a 2D image even when the 2D information about the contours in the image, which was provided to the model, was very crude. This means that our model's recovery of 3D shape is quite robust in the presence of the noise and errors in the 2D image. The human visual system does a much better job "extracting contours" than the unskilled human, who drew the contours used for 3D recovery in this demo.

 
    The important message illustrated by this demo is that the spatially global aspects of the 2D image (its 2D shape) is the important determinant of 3D shape recovery. Spatial details, such as exact positions of points and magnitudes of curvatures of contours, are irrelevant.  We can now claim that "the whole is not only different from its parts, it is also more important than its parts."

3. Shape Recovery Demo - Real Images Segmented Automatically* - instructions are the same as for Demo 2. Again, the model was given information about which features were symmetric in 3D space and which contours were planar in 3D space. In this demo, our symmetry constraint was applied to more contours than in Demo 2.

    The contours, extracted automatically, and used for the recoveries shown is this demo, were obviously more accurate than those extracted by hand (Demo 2), and as one might expect, the 3D shapes recovered are more accurate, too. The recovered 3D shapes are more accurate primarily because the symmetry constraint was applied to more edges than in Demo 2, where it was only applied to pairs of symmetric edges (i.e. edges that are on the opposite sides of the symmetry plane). In this demo, it was also applied to edges that are, in themselves, symmetric (e.g., straight-line edges that are orthogonal to the plane of symmetry).

    Symmetry (mirror, rotational and translational) is probably the most important shape constraint ("prior") because it restricts the family of possible 3D interpretations dramatically. A 3D interpretation of a 2D image of N unrelated points is characterized by N degrees of freedom. The free parameters are the depths of the points. But, when the points form a mirror-symmetric configuration in 3D space, and the skewed (distorted) symmetry is detected in the 2D image, the 3D interpretation is characterized by only one degree of freedom (see the description of the symmetry constraint in our computational model, linked above).

    Note that the symmetry constraint is used in our model to make up for the information that is missing from the 2D image, not to compress the 2D image, as others have done. Our use of symmetry is better because the primary task of the visual system is to see 3D shapes not to code 2D images.

    When all is said and done, it seems likely that our main contribution consists of pointing out that most, if not all objects "out there" are characterized by at least one type of symmetry. This is almost surely the case with respect to many of the objects that are important to us. Symmetry of objects "out there" is almost never perfect. This is the case either because the objects are not exactly symmetrical or because parts of symmetrical objects can move independently (for example, human and animal bodies). But, the human observer can easily detect partial and/or approximate symmetry. Even a little bit of symmetry goes a very long way. Without 3D symmetry there is no 3D shape, no percept of 3D shape and no shape constancy. The fundamental importance of symmetry cannot be overstated.

*  (Additional examples of 3D shape recovery with variety of natural 3D shapes, such as cars, planes, boats, bicycles, insects, and birds will be shown at our posters, as well as at the Demo Night, at the VSS 2008 Meeting in Naples, FL).

Acknowledgment: The demos were prepared by Yunfeng Li.

 

Course Information:

Research Topics:

Selected publications (Complete list is here):

    Zygmunt Pizlo, Emil Stefanov, John Saalweachter, Zheng Li, Yll Haxhimusa, Walter G. Kropatsch. (2006) Traveling Salesman Problem: a Foveating Pyramid Model. Journal of Problem Solving, 1, 83-101.
    Purdue TSP Application.

    Pizlo, Z., Li Y., Francis, G. (2005) A new look at binocular stereopsis. Vision Research, 45, 2244-2255.
    Related demo: Cubes Demo

    Pizlo, Z. (2001) Perception viewed as an inverse problem. Vision Research, 41, 3145-3161.
    Related demos: shape from binocular disparity, shape constancy demo, and shape constancy experiment (coming shortly)

    Steinman, R.M., Pizlo, Z. & Pizlo, F.J. (2000) Phi is not beta, and why Wertheimer's discovery launched the Gestalt revolution: a minireview. Vision Research, 40, 2257-2264.
    Check out the Java-Applet Demo!

    S.M.Graham, A.Joshi & Z. Pizlo (2000) The Traveling Salesman Problem: a hierarchical model. Memory & Cognition 28, 1191-1204.
    To see a real-life application of traveling salesman problem, click here

    Chan, M.W., Pizlo, Z. & Chelberg, D.M. (1999) "Binocular Shape Reconstruction: Psychological Plausibility of the 8 Point Algorithm". Computer Vision & Image Understanding 74, 121-137.
    Check out the images illustrating the fixation constraint!

    Pizlo, Z. & Stevenson, A. (1999) "Shape constancy from novel views". Perception & Psychophysics 61, 1299-1307.
    Check out the Java-Applet Demo!

    Z. Pizlo & M.R. Scheessele (1998) Perception of 3D scenes from pictures. Proceedings of IS&T/SPIE Conference on Human Vision and Electronic Imaging, vol. 3299 (pp. 410-423).
    Check out the Java-Applet Demo!

Interdisciplinary Graduate Programs:

    Computational Science and Engineering

      The Computational Science and Engineering Program at Purdue provides students with the opportunity to study a specific science or engineering discipline along with computing in a multidisciplinary environment. This program involves currently 16 departments (including the Department of Psychological Sciences).

    Interdisciplinary Program in Video and Image Systems Engineering

      This program is comprised of three parts: a new curriculum centered around a degree option in VISE to be earned as part of the Masters or Ph.D. degrees; a state-of-the-art lecture/laboratory facility for instruction, laboratory experiments, and project and homework activities in VISE courses; and enhancement of existing courses and development of new courses in the VISE area. This program involves currently the School of Electrical and Computer Engineering and the Department of Psychological Sciences at Purdue University.

  • Personal Information
  • Course Information
  • Research Topics
  • Publications/demos
  • Interdisciplinary Graduate Programs

    Links:

  • Workshop on Human Problem Solving
  • Psychophysics
  • Demos @ ViPer
  • VIPER (ECE)
  • CS&E
  • VISE
  • Quantitative Psychology Homepage
  • Psychological Sciences @ Purdue
  • Purdue University

    • Page maintained by: Filip Pizlo filip@psych.purdue.edu