Deformable kernels for early vision
Perona, P.
Pattern Analysis and Machine Intelligence, IEEE Transactions on
Volume 17, Issue 5, May 1995 Page(s):488 - 499
Digital Object Identifier 10.1109/34.391394
Summary: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
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