Directional Lifting Wavelet Transform for Image Edge Analysis

TL;DR

This paper introduces a novel 2D directional discrete wavelet transform that decomposes images into 12 multiscale directional edges, enhancing edge detection and capturing image features more effectively.

Contribution

It presents a fully discrete, efficient lifting scheme-based transform with limited redundancy for improved image edge analysis.

Findings

Outperforms standard edge detection methods in accuracy.

Effectively captures directional and geometrical image features.

Demonstrates advantages in locating and orienting edges.

Abstract

In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is easy to implement in actual computations. The proposed transform is viewed as a category of redundant discrete wavelet transforms implemented by fast in-place computational algorithms by a lifting scheme that has been modified to incorporate redundancy. The redundancy is limited to $(N \times J+1)/4$, where $N=12$ is the directional selectivity and $J$ is a decomposition level of the multiscale transform. Numerical experiments in edge detection using various images demonstrate the advantages of the proposed method over some conventional standard methods. The proposed method outperforms several conventional edge detection methods in identifying both the location and orientation of edges, and well captures the directional and geometrical features of images.