Perona, Pietro (1998) Orientation diffusions. IEEE Transactions on Image Processing, 7 (3). pp. 457-467. ISSN 1057-7149 http://resolver.caltech.edu/CaltechAUTHORS:PERieeetip98
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Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing images at multiple scales, and enhancing discontinuities. A number of diffusions of image brightness have been defined and studied so far; they may be applied to scalar and vector-valued quantities that are naturally associated with intervals of either the real line, or other flat manifolds. Some quantities of interest in computer vision, and other areas of engineering that deal with images, are defined on curved manifolds; typical examples are orientation and hue that are defined on the circle. Generalizing brightness diffusions to orientation is not straightforward, especially in the case where a discrete implementation is sought. An example of what may go wrong is presented. A method is proposed to define diffusions of orientation-like quantities. First a definition in the continuum is discussed, then a discrete orientation diffusion is proposed. The behavior of such diffusions is explored both analytically and experimentally. It is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge-process and anisotropic diffusion. A number of open questions are proposed.
|Additional Information:||© Copyright 1998 IEEE. Reprinted with permission. Manuscript received November 1, 1996; revised March 21, 1997. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Guillermo Sapiro. The second proof was derived in collaboration with A. Salden. Conversations with S. Belongie, J. Weichert, S. Mitter, and F. Fagnani are gratefully acknowledged. Comments from the anonymous reviewers were very helpful in improving a previous version of the paper.|
|Subject Keywords:||Orientation analysis, texture analysis, diffusions, scale-space|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||12 Mar 2006|
|Last Modified:||26 Dec 2012 08:47|
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