Adaptive Edge Detection with Directional Wavelet Transform Dusan Heric, Damjan Zazula Faculty of Electrical Engineering and Computer Science University of Maribor Smetanova 17, 2000 Maribor SLOVENIA Abstract: - This paper presents adaptive edge detector using a novel directional wavelet transform. The proposed algorithm has two stages: a) directional wavelet transform and b) edge detection on space–scale– directional plane with maximum entropy measure. Preliminary results with synthetic images show that directional wavelet transforms gives excellent results. The proposed method was tested on synthetic images at different signal-to-noise ratios (SNRs) and visually assessed on medical image. We assessed its reliability, accuracy and robustness using the mean absolute distance (MAD) metrics. Key-Words: - Wavelet transform, Directional filter, Edge detection 1 Introduction The process of edge detection is based on the hypothesis that the edge is a point where an image has sharp intensity transitions [1, 2, 3]. Important regions of interest (ROI) are separated by different level of pixel intensity value. Upon this assumption, many edge detectors have been proposed. Most of them depend on the local pixel intensity gradient, done by differencing [2] as a calculation of convolution of weighted matrix called local gradient mask. This group consists of well-known edge detectors, such as Sobel, Roberts, Prewitt, Robinson, Kirsch, Frei-Chen and Marr-Hildreth [3]. Their major drawbacks are high sensitivity to noise and disability of discrimination edges versus textures. Because of these limitations more advance edge detectors have been proposed which do not only detect edges but also try to connect neighbouring edge points into a contour. In this way, many authors have developed different edge detectors based on the scale space [6], active contours [5], and morphological operations [10]. Among all, the fundamental one is Canny edge detector [4], which is fast, reliable, robust and generic, but the accuracy is not satisfactory, because of the parameter σ which is the weakest point in the procedure [7]. The purpose of this paper is to present an edge detector based on directional wavelet transform. Analyzing a signal at different scales and directions increases the accuracy and reliability of edge detection. Focusing on localized signal structures, e.g. edges, with a zooming procedure enables simultaneous analysis from a rough to a fine shape [8]. Progressing between scales also simplifies the discrimination of edges versus textures [9]. Because of this ability the wavelets have also been used for edge detection in different applications. Wavelets are well adapted to singularities that are commonly found in real–life signals. In multidimensional cases, most often tensor product wavelets are employed. Therefore, wavelets are well adapted in higher dimensions for pointlike phenomena. But this is the only type of singularities that wavelets can efficiently represent. This problem was raised recently by Candes [12] who argued that in higher dimensions, there are many other kinds of intermittency such as singularities along lines and curves which wavelets do not deal with efficiently. In order to overcome this weakness, we have develop a new system of representations named directional wavelet transform which can effectively deal with linelike phenomena in 2-D. The paper is organized as follows: in Section 2 the directional wavelet transform is presented. Section 3 deals with the edge detector. Section 4 demonstrates the experimental results, while Section 5 concludes the paper. 2 Directional Wavelet Transform Natural images are not simply stacks of 1-D piecewise smooth scan–lines; discontinuity points (i.e. edges) are typically located along smooth curves (i.e. contours) owing to smooth boundaries of physical objects. Thus, natural images contain intrinsic geometrical structures that are key features in visual information [11]. The wavelet transform [8, 9] has a long and successful history as an efficient image processing Proceedings of the 5th WSEAS Int. Conf. on SIGNAL, SPEECH and IMAGE PROCESSING, Corfu, Greece, August 17-19, 2005 (pp1-4)