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Summary: IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 6, NO. 9, SEPTEMBER 1997 1255
Closed-Form Connectivity-Preserving Solutions
for Motion Compensation Using 2-D Meshes
Yucel Altunbasak and A. Murat Tekalp, Senior Member, IEEE
Abstract-- Motion compensation using two-dimensional (2-D)
mesh models requires computation of the parameters of a
spatial transformation for 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) point correspondences (at the vertices of a triangular or
quadrilateral mesh element). On the other hand, overdetermined
solutions using more than the required minimum number of
point correspondences provide increased robustness against
correspondence-estimation errors; however, this necessitates
special consideration to preserve mesh-connectivity. This
paper presents closed-form, overdetermined solutions for least
squares estimation of affine motion parameters for a triangular
mesh, which preserve mesh-connectivity using patch-based or
node-based connectivity constraints. In particular, four new
algorithms are presented: patch-constrained methods using
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