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Deformable kernels for early vision
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. This discretization produces
anisotropies due to a loss of traslation-, rotation- scaling- invariance that makes early vision algorithms less precise and
more difficult to design. This need not be so: one can compute
and store efficiently the response of families of linear
filters defined on a continuum of orientations and scales. A
technique is presented that allows (1) to compute the best approximation of a given family using linear combinations of
a small number of 'basis' functions; (2) to describe all finite-dimensional families, i.e. the families of filters for which a
finite dimensional representation is possible with no error.
The technique is general and can be applied to generating
filters in arbitrary dimensions. Experimental results are presented that demonstrate the applicability of the technique to
generating multi-orientation multi-scale 20 edge-detection
kernels. The implementation issues are also discussed
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