Closed-form solutions for polygon-based node motion estimation

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Abstract
Motion compensation using 2-D mesh models requires computation of the parameters of a spatial transformation within each mesh element (patch). It is well known that the parameters of an affine (bilinear or perspective) mapping can be uniquely estimated from three (four) node-point motion estimates. This paper presents closed-form overdetermined solutions for least squares estimation of the motion parameters, which also preserve mesh-connectivity using node-based connectivity constraints. In particular, two new algorithms are presented: The first method, based on the dense motion estimates, can be viewed as post processing of the dense motion field for best compact representation in terms of irregularly spaced samples, while the second one, which is based on spatio-temporal intensity gradients, offers closed- form solutions for direct estimation of the best node-point motion vectors. We show that the performance of the proposed closed-form solutions are comparable to those of the alternative search-based solutions at a fraction of the computational cost.

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