Publication Details
Title: Finite Representations of Deformable Functions
Author: P. Perona
Group: ICSI Technical Reports
Date: July 1990
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-90-034.pdf
Overview:
Starting from a `template' function F(x) and composing it with a family of transformations T subscript 0 (e.g., rotations, scalings) of its domain one obtains a family of `deformations' of F, F0T(x) spanning an n-dimensional space; n is in general infinite. A technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of a finite number of `basis' functions; (2) to characterize those functions F generating finite-dimensional families. The technique applies to all cases where T subscript 0 belongs to a compact group of transformations. The results presented here have applications in early vision and signal processing for the computation of filters in a continuum of orientations and scales.
Bibliographic Information:
ICSI Technical Report TR-90-034
Bibliographic Reference:
P. Perona. Finite Representations of Deformable Functions. ICSI Technical Report TR-90-034, July 1990
Author: P. Perona
Group: ICSI Technical Reports
Date: July 1990
PDF: http://www.icsi.berkeley.edu/pubs/techreports/tr-90-034.pdf
Overview:
Starting from a `template' function F(x) and composing it with a family of transformations T subscript 0 (e.g., rotations, scalings) of its domain one obtains a family of `deformations' of F, F0T(x) spanning an n-dimensional space; n is in general infinite. A technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of a finite number of `basis' functions; (2) to characterize those functions F generating finite-dimensional families. The technique applies to all cases where T subscript 0 belongs to a compact group of transformations. The results presented here have applications in early vision and signal processing for the computation of filters in a continuum of orientations and scales.
Bibliographic Information:
ICSI Technical Report TR-90-034
Bibliographic Reference:
P. Perona. Finite Representations of Deformable Functions. ICSI Technical Report TR-90-034, July 1990