Projective analysis of 2-D images

Recently, the use of the heatlike equation was 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 here an alternative. Roughly speaking, it is a kind of decomposition of the heatlike formulation with well-posed second-order PDE's. 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 x 3 matrix.