Alessio Del Bue
Large-scale optimisation of bilinear models with manifold constraints in Computer Vision
I will present a unified approach to solve different bilinear factorisation problems in the presence of high percentages of missing data in the measurements. This framework deals with two common problems in Computer Vision: the sensor cannot measure the whole extension of the observed event (missing data) and high-dimensional data lies on specific manifolds. The problem of fitting such data is formulated as a constrained optimisation problem where one of the factors is constrained to lie on the given manifold. To achieve this, I will introduce an equivalent reformulation of the bilinear factorisation problem. The proposed reformulation decouples the core bilinear aspect from the manifold specificity creating a flexible approach for dealing with a large set of problems. I will then present results on two classical Computer Vision problems: Structure from Motion and Photometric Stereo.