Director of the Program in Applied Mathematics

Computational vision is at the heart of robotics and biomedicine, but it is primitive when compared with the human visual sense. Humans demonstrate, effortlessly, enormous visual flexibility and generality, unaware of human vision's staggering complexity. But more than one-third of the primate brain is dedicated to processing visual information.

How do we characterize the function of billions of neurons in algorithmic terms? I am putting the requirements of vision systems together with insights from neurophysiology and applied mathematics to develop an abstract theory of computational vision. Based on differential geometry, my approach leads to methods of curve detection, shading and texture analyses, stereo, color, and generic shape description. The key to studying and modeling vision is an interdisciplinary perspective, integrating computation, neuroscience, and mathematics.

Selected Publications

 
"Geometrical Computations Explain Projection Patterns of Long-range Horizontal Connections in Visual Cortex," O. Ben-Shahar and S.W. Zucker, Neural Computation, 16(3), 445–476 2003).

"Sketches with curvature: The curve indicator random field and Markov processes," J. August and S.W. Zucker, IEEE Trans. Pattern Analysis and Machine Intelligence, 25(4), 387–401 (2003).

"Hamilton-Jacobi Skeletons," K. Siddiqi, S. Bouix, A.R. Tannenbaum, and S.W. Zucker, Int'l. J. of Computer Vision, 48(3), 215–232 (2002).

"Complexity, Confusion, and Perceptual Grouping. Part I: The curve-like representation," B. Dubuc and S.W. Zucker, Int. J. of Computer Vision, 42(1/2), 55-82 (2001); reprinted in J. Math. Imaging and Vision, 15 (1/2), 55–82 (2001); Part II: Mapping Complexity, J. of Computer Vision, 42(1/2), 83-115 (2001); reprinted in J. Math. Imaging and Vision, 15(1/2), 83-115 (2001).

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