Setting priors and enforcing constraints on matches for nonlinear registration of meshes

Abstract

We show that a simple probabilistic modelling of the registration problem for surfaces allows to solve it by using standard clustering techniques. In this framework, point-to-point correspondences are hypothesized between the two free-form surfaces, and we show how to specify priors and to enforce global constraints on these matches with only minor changes to the optimisation algorithm. The purpose of these two modifications is to increase its capture range and to obtain more realistic geometrical transformations between the surfaces. We conclude with some validation experiments and results on synthetic and real data.

Fig. 1

Left: Mapping of descriptor values: From left to right: curvedness, shape index and total geodesic distance on two lateral ventricles. Homologous anatomical landmarks yield qualitatively the same descriptor values. Right: point-based matching (top) vs line-based matching performed by our algorithm (bottom).

Fig. 2. Experiments on synthetic data

From left to right: Experiments on two different structures: ventricles and caudate nuclei. a) and d) original and deformed; b) and e) mapping of registration error (mm) without using prior/constraint; c) and f) mapping of registration error using prior/constraint.

Fig. 3. Experiments on real data. Ventricles

From left to right: X (green) and A(Y) (red) before registration, position of the 8 anatomical landmarks of the 10 random experiments after registration without priors/constraints and with priors/constraints. Brain: From left to right and top to bottom: 1) brain 1 (top) and brain 2 (bottom); 2) brain 2 (with sulci shown in transparency) towards brain 1 without (top) and with (bottom) using priors/constraints. The four sulci are the central (red), lateral (blue), superior frontal (green) and inferior frontal (yellow) sulci.