Assadi 9707006 Visual perception of surfaces is crucial for 3D object recognition. All surfaces in natural scenes are endowed with texture. In this project, the investigator develops new algorithms to estimate shape (geometric characteristics of surfaces) from texture in natural and synthetic scenes. The new geometric models use piecewise Riemannian foliations, in the sense of differential topology, with additional structure. Given a 3D-textured surface, not necessarily piecewise smooth, one constructs a foliation whose leaves form a one-parameter family of 2D-textured and piecewise smooth mathematical surfaces approximating the given object. Together with an objective function defined on their leaves, such 2D-textured foliations are fundamental geometric objects that model 3D-textured surfaces in the world. One can use algorithms to recover shape from texture for the piecewise smooth leaves, e.g. curvature and slant. Several scene-based methods are explored to construct textured foliations, ranging from analytic (e.g. Hamilton-Jacobi equations) and topological techniques (e.g. integrable distributions) to statistical estimation methods. The psychophysical experiments to test the theory and compare different algorithms are explored with colleagues who are neuroscience experimentalists. In particular, the objective function can be numerically approximated based on psychophysical data. The new models are applied to perception of symmetry. The problem of modeling computational strategies employed by the visual cortex to estimate shape from texture, and their comparison with the new computational algorithms, is pursues. The investigator outlines a concrete training program and research collaboration with his senior colleagues in vision and neuroscience at UC Berkeley in order to achieve the cognitive and computational objectives of the project. How do we see? This simple question does not have a simple answer. Vision is a complex series of eve nts that begins when light enters the eyes and ends with perception. People are able to discriminate between objects of different size, contrast and color with precision. They can estimate curvature and orientation of surfaces with varying roughness and multitudes of texture, as well as describe within short time intervals properties of surfaces such as symmetry and similarity to other familiar objects. The human visual system easily outperforms any man-made machine. Decades of research in vision demonstrate the wisdom of the following approach: Key insights generally come from models that are well-suited for exploring a specific research question. Geometric models coupled with computational techniques have formed a cornerstone of modern theories of biological as well as robot vision, and of their diverse applications. In this project, the principal investigator and his colleagues establish a new link between advanced geometric theories in pure mathematics (theory of foliations from differential topology) and visual perception and estimation of shape of surfaces in natural and synthetic environments. Among applications of the theory, one could mention: robot motion planning and navigation of manless vehicles in rough terrain or unreachable environments; visual shape estimation of images of materials obtained by atomic force microscopy in scientific research and design of advanced materials; long-term computerized inspection of surfaces subject to ballistic deposition and erosion in environmental studies and ecology; and computational inspection of large databases of images from infrared radio astronomy in order to locate specific features. Just as the neurons in human visual system perform their tasks in parallel, the above-mentioned theory lends itself to parallel processing implementation.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9707006
Program Officer
Michael H. Steuerwalt
Project Start
Project End
Budget Start
1997-08-15
Budget End
1999-07-31
Support Year
Fiscal Year
1997
Total Cost
$50,000
Indirect Cost
Name
University of Wisconsin Madison
Department
Type
DUNS #
City
Madison
State
WI
Country
United States
Zip Code
53715