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Abstract
Shadows provide perceptually important information about the shape of an illuminated three-dimensional (3D) surface. In this article, we present the topological properties of the shading problem in the Morse-theoretic framework, and we establish some key theoretical properties of the height function in the light direction of an illuminated 3D surface. We also describe a link between the shading problem and the height function in the light direction, and we derive the necessary and sufficient conditions for the shading function to be a Morse function.
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Notes on contributors
A. Ben Hamza
A. Ben Hamza received his Ph.D. degree in Electrical Engineering fromNorth CarolinaStateUniversity, USA. He is currently an assistant professor in the Information Systems Engineering Institute at Concordia University, Montreal, Canada. Prior to joining Concordia University, he was a postdoctoral research associate at Duke University in North Carolina, affiliated with both the Department of Electrical and Computer Engineering and the Fitz-patrick Center for Photonics and Communications Systems, where he worked on compressive sampling and human tracking using pyroelectric infrared sensors. His research interests include 3D graphics, nonlinear image processing, statistical quality control, and multimedia security. He is a member of the IASTED Technical Committee on Signal Processing for the term 2006–2009.