Perona, Pietro (1995) Deformable kernels for early vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17 (5). pp. 488-499. ISSN 0162-8828. http://resolver.caltech.edu/CaltechAUTHORS:PERieeetpami95
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Early vision algorithms often have a first stage of linear-filtering that `extracts' from the image information at multiple scales of resolution and multiple orientations. A common difficulty in the design and implementation of such schemes is that one feels compelled to discretize coarsely the space of scales and orientations in order to reduce computation and storage costs. A technique is presented that allows: 1) computing the best approximation of a given family using linear combinations of a small number of `basis' functions; and 2) describing all finite-dimensional families, i.e., the families of filters for which a finite dimensional representation is possible with no error. The technique is based on singular value decomposition and may be applied to generating filters in arbitrary dimensions and subject to arbitrary deformations. The relevant functional analysis results are reviewed and precise conditions for the decomposition to be feasible are stated. Experimental results are presented that demonstrate the applicability of the technique to generating multiorientation multi-scale 2D edge-detection kernels. The implementation issues are also discussed.
|Additional Information:||© Copyright 1995 IEEE. Reprinted with permission. Manuscript received Oct. 28, 1991; revised Jan. 24, 1994. I am very grateful to Massimo Porrati, Alberto Grunbaum, David Donoho, Federico Girosi, Mohammad Naraghi, and Frank Ade for giving me good advice and useful references. I would also like to acknowledge useful conversations with Ted Adelson, Josef Bigiin, Stefano Casadei, Rachid Deriche, Charles Desoer, Peter Falb, Bill Freeman, Milan Jovovic, Takis Konstantopoulos, Olaf Kubler, Paul Kube, Reiner Lenz, Jitendra Malik, Stephane Mallat, Sanjoy Mitter, Richard Murray, Shankar Sastry, and Doug Shy. The comments of one anonymous reviewer are also gratefully acknowledged. The simulations in this work have been carried out using Paul Kube’s “viz” image-manipulation package, and would have taken much longer without Paul’s very friendly support. The images in this paper have been printed with software kindly provided by Eero Simoncelli. Some of the simulations have been run on a computer generously loaned to the author by Prof. Canali of the Universiti di Padova. This work was in part carried out while the author was with the International Computer Science Institute at Berkeley and at the Laboratory for Information and Decision Systems of M.I.T. with the Center for Intelligent Control Systems sponsored by U.S. Army Research Office grant number DAAL 03-86-K-0171. This research was in part sponsored by National Science Foundation Research Initiation grant IRI 9211651.|
|Subject Keywords:||Steerable filters, wavelets, early vision, multiresolution image analysis, multirate filtering, deformable filters, scale-space|
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|Deposited On:||11 Dec 2006|
|Last Modified:||26 Dec 2012 09:21|
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