Colour transfer and shape registration using functional data representations

Abstract

In this thesis we propose new colour transfer and shape registration methods based on the robust L2 distance. For colour transfer, we present an approach inspired by techniques recently proposed in shape registration. We model the colour distribution of a palette and target image using Gaussian Mixture Models and register them using the L2 distance. We estimate a parametric transfer function which can be easily stored in memory for later use and allows for the interpolation of several colour transfer functions which can create interesting special effects. We also show that pixel correspondences can be easily incorporated into our method to enhance the colour transfer result. We show that our method compares well both qualitatively and quantitatively to other colour transfer approaches and that our recolouring step is computationally the fastest. We also propose a new shape registration technique which extends previous registration methods that model shapes as probability density functions and estimate the registration parameters by minimising a divergence between them. Our proposed technique models the point positions and directional information of a shape, and we investigate mixture models with Dirac, Gaussian and von Mises-Fisher kernels. We validate our framework experimentally on shapes differing by both a rotation and non-rigid deformation and show that in general using both point and normal vector information allows for better registration of shapes. Finally, we present a short exploration of the results generated when two optimal transport techniques are applied to the 3D shape registration problem.