On corner and vertex detection

A formal representation of corner and vertex detection is presented. In particular, an analytical study is presented which allows one to know exactly what the behavior is of a detector around trihedral vertices. It is shown that near three surfaces, two elliptic maxima of DET exist, and their location is inside extremal contrast surface. The intermediate surface always shows a hyperbolic minima. It is shown that the detector allows to find the exact position of vertex. The approach proposed has been tested on many noisy synthetic data and real images and its robustness seems promising.<>