Some recent results on the projective evolution of 2-D curves

In this paper, we begin to explore the evolution of curves of the projective plane according to a family of intrinsic equations generalizing a “projective heat equation”. This is motivated by previous work for the Euclidean and the affine case, as well as by applications in the perception of two-dimensional shapes. We establish the projective arclength evolution and the projective curvature evolution. Among this family of equations, we point out the ones preserving an important property of the Euclidean and affine heat equations that was not preserved in the projective case: a curve with constant curvature should remain such a curve during its evolution