Approximation Models for Dynamic Vision

Amitabha Mukerjee
Center for Robotics and Dept of Mechanical Engineering
I.I.T. Kanpur, Kanpur 208016, INDIA
(e-mail: amit@iitk.ernet.in)

Abstract

The models used for visual recognition of an object must reflect the accuracy available to the task. This is particularly important for dynamic vision models, with resolution levels changing depending on focus variations. Currently, different models for different resolutions are usually pre-chosen by the programmer, but computational approaches to approximation modeling is beginning to emerge, both for general reasoning models as well as for geometric objects [1,2]. Approximating geometric models of spatial information is particularly difficult since such models typically use metric information such as distance, and also derivative concepts such as size, angles, area, volume, which are non-qualitative in nature

In this work, we present a representation for obtaining different levels of geometric approximation that offers several levels of model abstraction, provides for visual feedback, and degrades smoothly between resolutions. The basic approach models three-dimensional objects using the generalized cylinder paradigm. Instead of representing the cross-sections of the objects as line boundaries, we model these using an axial representation based on line-set voronoi diagrams, which are represented using relative angles, length ratios and axis velocities. The model representing angle and length is a hybrid derivative of a qualitative approach to modeling two-dimensional space [3], and the resolution of the model is widely variable. The hybrid models used in this approach have the property that for a given class of operations, the result data be limited to k data fields. We use such "k-proper" discretizations for the real line and the circle to model the axes of the 2D shapes. The 3D axes of deformation are also represented using qualitative hybrid quadrants. Models at any given level of resolution are then capable of reconstruction and visualization by identifying a sample from the valid object space. Any visual model can now be tested to determine if it is a member of this object class.

The model has been implemented and evaluated using computational similarity measures (moments and inertias), and also by psychological testing on a group of subjects to evaluate the "recognizability" at various resolutions.

References

  • King, Joseph Scott, and Amitabha Mukerjee, 1990 Inexact Visualization, Proceedings of the IEEE Conference on Biomedical Visualization, Atlanta GA, May 22-25, 1990, p.136-143.
  • Weld, Daniel S., 1988 Theories of comparative analysis, PhD Thesis, MIT AI TR 1035, May 1988, 174 pages.
  • Mukerjee, Amitabha, and Gene Joe, 1990 A qualitative model for space, AAAI-90, July 29-Aug 3, Boston, p.721-727.
  • Mukerjee, Amitabha, 1990 Accidental alignments: an approach to qualitative vision, IEEE Conference on Robotics and Automation, Sacramento, April 1991, p. 1096-1101.