Projective Evolution of Plane Curves
International Journal of Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
The Use of Size Functions for Comparison of Shapes Through Differential Invariants
Journal of Mathematical Imaging and Vision
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The use of the heatlike equation has been extended to the projective case in order to find a projective analysis of curves and images; unfortunately, this formulation leads to a fifth-order partial differential equation (PDE) that is not easy to implement. Thanks to the use of a three-dimensional (3-D) homogeneous representation of a picture, we present an alternative. Roughly speaking, it is a kind of decomposition of the heatlike formulation with well-posed second-order PDEs. The number of parameters goes from one to three (the scale parameter and two direction parameters). Moreover, this study allows us to propose a simplified multiscale analysis, which is given by an unique PDE (one parameter), for the subgroup of the projective transformations associated, up to a nonzero scalar factor, to an orthogonal 3×3 matrix