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Two Problems in Computer Vision and Graphics.

October 19, 2004

Lance Williams <williams@cs.unm.edu>

I will discuss my work on two problems in computer vision and graphics. Computer vision: A visual computation is Euclidean invariant if every rotation and translation of its input produces an equal rotation and translation of its output. Is it possible for a network built from a finite number of discrete components (such as the human visual cortex) to implement visual computations which are invariant to continuous rotations and translations of its input? I will show that the answer to this problem is yes for an important problem in human visual information processing. Computer graphics: The power of wavelet transforms derives from their ability to compactly represent discrete periodic functions defined on rectangular domains. We describe a wavelet transform suitable for functions defined on surfaces modeled as meshes. We demonstrate analysis and synthesis of functions of a sphere, and then apply our transform to a problem in computer graphics, namely, synthesizing texture on surfaces without distortion or discontinuity.