Optimal Transformation Estimation with Semantic Cues

This paper addresses the problem of estimating the geometric transformation relating two distinct visual modalities (e.g. an image and a map, or a projective structure and a Euclidean 3D model) while relying only on semantic cues, such as semantically segmented regions or object bounding boxes. The proposed approach differs from the traditional feature-to-feature correspondence reasoning: starting from semantic regions on one side, we seek their possible corresponding regions on the other, thus constraining the sought geometric transformation. This entails a simultaneous search for the transformation and for the region-to-region correspondences. This paper is the first to derive the conditions that must be satisfied for a convex region, defined by control points, to be transformed inside an ellipsoid. These conditions are formulated as Linear Matrix Inequalities and used within a Branch-and-Prune search to obtain the globally optimal transformation. We tested our approach, under mild initial bound conditions, on two challenging registration problems for aligning: (i) a semantically segmented image and a map via a 2D homography; (ii) a projective 3D structure and its Euclidean counterpart.