<title>Hierarchical edge detector using the first- and second-derivative operators</title>

Abstract

ABSTRACT This paper presents a new method for edge detection by combining the Sobel operator and the Lapla-cian of Gaussian (LoG) operator. The underlying idea is to combine the advantages of both operatorsand eliminate their disadvantages. Different methods of combining the two operators are considered. Onemethod yields promising results in precise and blur free edge detection, and good stability versus imagenoise. A method for designing the LoG kernel is also presented. 1. INTRODUCTION Many theories and algorithms applied to high-level vision tasks assume that the pictures are already segmented, i.e., the desired features (lines, edges etc.) of the picture are already given. Hence, edge detection is an important segmentation task in Image Processing and Computer Vision.We can distinguish between first derivative operators (Gradient operators) and second derivativeoperators (Laplacian operators). Both types of operators have been studied extensively, and their advan-tages and drawbacks are well known (see References 1-3 for a good overview). The underlying idea ofthis approach to edge detection is to combine the advantages of both types of operators, and eliminate