Trivariate Optimal Smoothing Splines with Dynamic Shape Modeling of Deforming Object
نویسندگان
چکیده
We develop a method of constructing trivariate optimal smoothing splines using normalized uniform B-spline as the basis functions. Such splines are useful particularly for modeling dynamic shape of 3-dimensional deformable object by using two variables for 3D shape and one for time evolution. The trivariate splines are constructed as a tensor product of three B-splines, and an optimal smoothing spline problem is solved together with typical examples of constraints as periodicity. The problem is formulated as convex quadratic programming (QP) problem in such a way that 3D array of control points is vectorized and a MATLAB QP solver is readily applicable for numerical solutions. We demonstrate usefulness of the method by dynamic shape modeling of red blood cell, where we will see that relatively small number of observation data yield satisfactory results.
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