A Metric for genus-zero surfaces
This provides a theoretically grounded metric for shape comparison of genus-zero surfaces, which is fundamental for applications in computer graphics and medical imaging.
The authors introduce a symmetric distortion energy to compare genus-zero surfaces, prove the existence of a conformal diffeomorphism minimizing this energy, and show that the resulting energies define a metric on the space of such surfaces.
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing diffeomorphisms give a metric on the space of genus-zero Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms are shown to have properties that are highly desirable for applications.