It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions.

https://www.math.uh.edu/~dlabate/shear_edges.pdf

A Shearlet Approach to Edge Analysis and Detection

http://www4.comp.polyu.edu.hk/~cslzhang/paper/PRL_02_Jan.pdf

Edge detection by scale multiplication in wavelet domain

In this paper, we propose a blind image watermarking algorithm based on the multiband wavelet transformation and the empirical mode decomposition. Unlike the watermark algorithms based on the traditional two-band wavelet transform, where the watermark bits are embedded directly on the wavelet coefficients, in the proposed scheme, we embed the watermark bits in the mean trend of some middle-frequency subimages in the wavelet domain. We further select appropriate dilation factor and filters in the multiband wavelet transform to achieve better performance in terms of perceptually invisibility and the robustness of the watermark. The experimental results show that the proposed blind watermarking scheme is robust against JPEG compression, Gaussian noise, salt and pepper noise, median filtering, and Con-vFilter attacks. The comparison analysis demonstrate that our scheme has better performance than the watermarking schemes reported recently.

Robust Image Watermarking Based on Multiband Wavelets and Empirical Mode Decomposition

System for screening objectionable images

https://www.cin.ufpe.br/~cabm/visao/artigos/A%20novel%20approach%20for%20edge%20detection%20based%20on%20the%20theory%20of%20universal%20gravity.pdf

A novel approach for edge detection based on the theory of universal gravity

In this correspondence, the problem of directional and multiscale edge detection is considered. Orthogonal and linear-phase M-band wavelet transform is used to decompose the image into M/spl times/M channels. These channels are then combined such that each combination, which we refer to as decomposition filter, results in zero-crossings at the locations of edges corresponding to different directions and resolutions, and inherently performs regularization against noise. By applying a zero-crossing detector on the outputs of the decomposition filters, edge maps of desired resolution and direction are obtained. In addition, with the application of the Teager's energy operator at the analysis stage, it is possible to obtain a reduction in unwanted zero-crossings. Final edge maps of images are obtained through simple combinations of directional edge maps.

Multidirectional and multiscale edge detection via M-band wavelet transform

The problem of directional and multiscale edge detection is considered. Orthogonal and linear-phase M-band wavelet transform is used to decompose the image into channels which correspond to different directions and resolution levels. "Meaningful" combinations of the synthesis filter outputs at the selected channels yield edge maps with desired properties. In addition, with the application of energy operators at the analysis stage, it is possible to obtain a reduction in unwanted zero-crossings. Final edge maps of images are obtained through simple combinations of directional edge maps. >

T. Aydin

Papers

Multidirectional and multiscale edge detection via M-band wavelet transform

Use of M-band wavelet transform for multidirectional and multiscale edge detection