Edge detection using G-lets based on matrix factorization by group representations

Abstract

A new edge detection technique using transformation groups based G-lets filters is proposed in this paper. Discretizing gradients seem to produce discontinuity in classic edge detectors. No particular filter is capable of identifying meaningful edges at all scales and it increases computations with a multiscale approach. It is a challenge to get localized edges without spurious ones due to noise and integrate the obtained edges into meaningful object boundaries. Without breaking edge continuity and strictly localizing edges requires that filters do not blur the image during preprocessing. G-lets filters are found to be capable of performing well in most type of images including natural, noisy, low resolution and synthetic. In this paper, an edge detection algorithm using G-lets filters which are built by direct factorization of linear transformation matrices using irreducible representations is proposed. A multiresolution approach is shown to enhance the possibility of detecting faint edges. An edge tracing algorithm is presented to produce the edge image. The computational cost involved is comparatively lesser than existing filters. It is found that the geometries in the original image are preserved in the edge image. The edge tracing algorithm is capable of constructing object boundaries without the inner textures in a way that is not completely dependent on intensity thresholding. G-lets filters and the edge operator is found to be a promising algorithm for drastically bringing down the computations needed for realtime applications. The results are compared with BSDS500 boundary detection dataset using pb and global pb detectors.