A vectorial Color Edge detector using spatiocolorimetric neighborhood hypergraph and perceptual color distance S. Rital * , H. Cherifi * and D. Aboutajdine ** (IEEE Senior member) * LIRSA, University of Burgundy, Faculty of Sciences Mirande Dijon, France email: soufiane.rital, hocine.cherifi@u-bourgogne.fr ** GSCM, department of physics, B. P. 1014 Science Faculty of Rabat Rabat, Morocco. email: aboutaj@fsr.ac.ma. ABSTRACT In this paper, we present an edge detection approach in color image using neighborhood hypergraph. The edge struc- ture is detected by a structural model. The Color Image Neighborhood Hypergraph (CINH) representation is first computed using a perceptual color distance, then the hy- peredges of CINH are classified into noise, edge or others based on hypergraph properties. To evaluate the algorithm performance, experiments were carried out on synthetic and real color images corrupted by α-stable noise. The results show that the proposed edge detector finds the edges prop- erly from color images. KEY WORDS Graph, Hypergraph, Color space, Neighborhood hyper- graph, noise detection, color distance 1 Introduction Edge detection is a front-end processing step in most com- puter vision and image understanding systems. The accu- racy and reliability of edge detection is critical to the over- all performance of these systems. Earlier developments of edge detection are mostly based on direct application of the difference operation and could encounter difficulties when images are corrupted by noise. Much research has been car- ried out in the effort to detect edge structures in the presence of noise. One type of edge detector employs smoothing be- fore using the difference operator, so as to offset the effects of noise. The use of color in edge detection increases the amount of information needed for processing which complicates the definition of the problem. A number of approaches have been proposed from processing individual planes to true vector-based approaches. Multidimensionality adds one important step, image recombination, which can be inserted at different places. This insertion translates into performing some sets of operations on each color component. The in- termediate results are then combined into a single output. The point at which recombination occurs is key to under- standing the different categories of color edge detection al- gorithms: output fusion methods, multidimensional gradi- ent methods, and vector methods. In output fusion methods, gray-scale edge detection is carried out independently in each color component; com- bining these results yields the final edge map. Multidimen- sional gradient methods are characterized by a single esti- mate of the orientation and strength of an edge at a point. The first such method belongs to Robinson [6], who also appears to have published the first paper on color edge de- tection. He computed 24 directional derivatives (8 neigh- bors × 3 components) and choose the one with the largest magnitude as the gradient. However, it was Di Zenzo [11] who wrote the classic paper on multidimensional gradients. His method was derived algebraically, but it is perhaps bet- ter explained in terms of matrices. A 2 × 2 matrix is formed from the outer product of the gradient vector in each compo- nent. These matrices are summed over all components, and the square root of the principal eigenvalue (i.e., the princi- pal singular value) becomes the magnitude of the gradient. The corresponding eigenvector yields the gradient direc- tion. This approach was used in various forms by Cumani [4]. In vector methods, the decomposition and recombina- tion steps nullify each other; the vector nature of color is preserved throughout the computation. How to represent and use these vectors has varied greatly. Perhaps the most compelling work in vector methods so far has been that of Trahanias and Venetsanopoulos [10]. Their method used the median of a set of vectors, which is the vector in that set whose distance to all other vectors is minimized. Once the vector median has been determined, vectors in a neigh- borhood are sorted by their distances from the vector me- dian, and various statistics are measured and used for edge detection. The algorithms that incorporate more vector op-