# Scale Space Semi-local Invariants

Scale space semi-local invariants.

Image Vision Comput., 15(5):335-344, 1997

## Online Version

A pdf version is available for download.

## Abstract

In this paper we discuss a new approach to invariant signatures for recognizing curves under viewing distortions and partial occlusion. The approach is intended to overcome the ill-posed problem of finding derivatives, on which local invariants usually depend. The basic idea is to use invariant finite differences, with a scale parameter that determines the size of the differencing interval. The scale parameter is allowed to vary so that we obtain a ‘scale space'-like invariant representation of the curve, with larger difference intervals corresponding to larger, coarser scales. In this new representation, each traditional local invariant is replaced by a scale-dependent range of invariants. Thus, instead of invariant signature curves we obtain invariant signature surfaces in a 3-D Invariant ‘scale space'.

## Keywords

## Co-authors

## Bibtex Entry

@article{BrucksteinRW97a,

title = {Scale space semi-local invariants.},

author = {Alfred M. Bruckstein and Ehud Rivlin and Isaac Weiss},

year = {1997},

journal = {Image Vision Comput.},

volume = {15},

number = {5},

pages = {335-344},

keywords = {Invariants; Object recognition; Scale space},

abstract = {In this paper we discuss a new approach to invariant signatures for recognizing curves under viewing distortions and partial occlusion. The approach is intended to overcome the ill-posed problem of finding derivatives, on which local invariants usually depend. The basic idea is to use invariant finite differences, with a scale parameter that determines the size of the differencing interval. The scale parameter is allowed to vary so that we obtain a ‘scale space'-like invariant representation of the curve, with larger difference intervals corresponding to larger, coarser scales. In this new representation, each traditional local invariant is replaced by a scale-dependent range of invariants. Thus, instead of invariant signature curves we obtain invariant signature surfaces in a 3-D Invariant ‘scale space'.}

}