Scale space smoothing, image feature extraction and bessel filters

Authors:
Sasan Mahmoodi;Steve Gunn
Affiliations:
School of Electronics and Computer Science, Southampton University, Southampton, UK;School of Electronics and Computer Science, Southampton University, Southampton, UK
Venue:
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Year:
2011

Citing 3
Cited 1

A Computational Approach to Edge Detection

IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature Detection with Automatic Scale Selection

International Journal of Computer Vision
Edge Detection and Ridge Detection with Automatic Scale Selection

International Journal of Computer Vision

Edge Detection Filter based on Mumford-Shah Green Function

SIAM Journal on Imaging Sciences

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Abstract

The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian filters. The features extracted by the Bessel filter are therefore scale invariant. Edges, blobs, and junctions are features considered here to show that the extracted features remain unchanged by varying the scale of a Bessel filter. The scale invariance property of Bessel filters for edges is analytically proved here. We conjecture that Bessel filters also enjoy this scale invariance property for other kinds of features. The experimental results presented here confirm our conjecture of the scale invariance property of the Bessel filters.