Fitting Coupled Geometric Objects for Metric Vision

A new approach to fitting coupled geometric objects, such as concentric circles, is presented. The objects can be coupled via common Grassmannian coefficients or through a correlation constraint on their coefficients. The implicit partitioning and partial block diagonal structure of the design matrix enables an efficient orthogonal residualization based on a generalized Eckart-Young-Mirsky matrix approximation. The residualization prior to eigenor singular-value decomposition improves the numerical efficiency and makes the result invariant to the residuals of the independent portions. Analysis is performed for the generalized case of coupled implicit equations and examples of parallel lines, concentric circles and coupled conics are given. Furthermore, numerical tests and applications in image processing are presented.