Behavior of the Laplacian of Gaussian Extrema

This paper analyses the behavior in scale space of linear junction models (L, Y and X models), nonlinear junction models, and linear junction multi-models. The variation of the grey level is considered to be constant, linear or nonlinear in the case of linear models and constant for the other models. We are mainly interested in the extrema points provided by the Laplacian of the Gaussian function. Moreover, we show that for infinite models the Laplacian of the Gaussian at the corner point is not always equal to zero.Salvatore Tabbone received his Ph.D. in computer science from the Institut National Polytechnique de Lorraine (France) in 1994. He is currently an assistant professor at the University of Nancy2 (France) and a member of the QGAR research project on graphics recognition at the LORIA-INRIA research center. His research interests include computer vision, pattern recognition, content-based image retrieval, and document analysis and recognition.Laurent Alonso was a student of ENS Ulm from 1987 to 1991, he received the Ph.D. degree in Computer Science from the University of Paris XI, Orsay, France in 1992. From 1991 to 1995 he served as lecturer in the University of Nancy I (France). Actually, he is full researcher in INRIA (France). His research interests include realistic rendering, geometric algorithms and combinatorics.Djemel Ziou received the BEng Degree in Computer Science from the University of Annaba (Algeria) in 1984, and Ph.D. degree in Computer Science from the Institut National Polytechnique de Lorraine (INPL), France in 1991. From 1987 to 1993 he served as lecturer in several universities in France. During the same period, he was a researcher in the Centre de Recherche en Informatique de Nancy (CRIN) and the Institut National de Recherche en Informatique et Automatique (INRIA) in France. Presently, he is full Professor at the department of computer science at the University of Sherbrooke in Canada. He has served on numerous conference committees as member or chair. He heads the laboratory MOIVRE and the consortium CoRIMedia which he founded. His research interests include image processing, information retrieval, computer vision and pattern recognition.