On the Behavior of the Laplacian of Gaussian for Junction Models

This paper analyzes the behavior of diierent junction models in scale space. In this perspective, we study the behavior of linear models (L,Y and X models) and linear multi-models (two adjacent corners with innnite extent and a closed triangular model) with constant illumination, linear models with non-constant illumination and a non-linear model (curved junctions). The study shows under which conditions the Laplacian is zero or not at the junction point. Consequently, approaches based on the Laplacian of Gaussian to detect corners are not precise. Futher-more, all these models provide one or several extrema inside the junction sector. These extrema have nice scaling properties.