Gray-scale image edge detection based on directional beamlet transform

Traditional edge detectors based on pixel processing one by one have poor ability to detect edge in noisy images. The beamlet transform is a method of linear feature detection but fail to detect edge. The directional beamlet transform is proposed in this paper. The DBT transfer the linear singularity to point-singularity, and reduce the influence to edge of noise. Experiment results prove the efficiency of the method proposed even in noisy images.

1. Introduction

Edge in an image may be defined as a rapid photometric change in the registered intensity values. From a pixel level perspective, edge can be viewed as the regions of an image where the image values undergo a sharp variation. In discrete 2-D image edge is detected as linear combination of the point's singularities between pixels. Noise is among the most significant obstacles of edge detection. Most of edge detectors only produce points at the positions of edges of images. The popular edge detectors like those of Canny, Sobel, etc. did just that [1]. Nevertheless, the applications of these detectors are limited especially in noisy image. As we know, besides pixels, there still are curves and other patterns in image. To exact curves and patterns, high dimensional singularities processing ability is demanded, which is strikingly similar to physiological peculiarity of human eyes. Beamlet tansform[2] is a new tool of detecting linear feature target in image, but the traditional beamlet transform is absent the ability of detecting edge. So we improve the traditional beamlet transform and present the directional beamlet transform.