The Construction of 2d Rotationally Invariant Wavelets and Their Application in Image Edge Detection

Abstract

Construction of rotationally invariant 2D wavelets is important in image processing, but is difficult. In this paper, the discrete form of a 2D rotationally invariant wavelet is constructed by back-projection from a 1D symmetrical wavelet. Such rotationally invariant 2D wavelets allow effective edge detection in any direction. These wavelets are combined with the 2D directional wavelets for the use in non-maximum suppression edge detection. The resulting binary edges are characterized by finer contours, differential detection characteristics and noise robustness compared to other edge detectors in various test images. In particular, where fine binary edges in noisy images are required, this novel approach compares favorably to the classical methods of Canny and Mallat with detection of more edges thanks to the implicit denoising properties and the full rotational invariance of the method.

Symmetric Multivariate Wavelets

“…35,36 Nonseparable FBs have better characteristics than their separable counterparts (which consist of products of 1D FBs along each dimension). The number of degrees of freedom is also much bigger for nonseparable FBs.…”