Guided search consensus: Large scale point cloud registration by convex optimization

In this paper we propose a point matching algorithm that computes correspondences between images and/or 3D objects in affine camera settings. We formulate the point correspondence problem by minimizing an error function over the set of all binary decisions. This function has two components: a geometric error (akin to retro-projection error) and an image dissimilarity component. Originally a combinatorial problem we obtain its exact solution through a convex relaxation. Hinging on a recent theorem, this solution is derived by carefully designing the minimizing function. The large scale optimization problem is handled by an extremely fast algorithm based on Nesterov´s projected gradient method. Experimental results show both computational efficiency and high robustness to large deviations and we demonstrate that it can cope with very hard real situations such as scenes with repetitive patterns. The methodology can be applied seamlessly to both 2D or/and 3D cameras.