Shape Representation and Registration in Vector Implicit Spaces: Adopting a Closed-Form Solution in the Optimization Process
Issue No. 03 - March (2013 vol. 35)
Aly A. Farag , University of Louisville, Louisville
Hossam E. Abd El Munim , University of Louisville, Louisville
Amal A. Farag , University of Louisville, Louisville
In this paper, a novel method to solve the shape registration problem covering both global and local deformations is proposed. The vector distance function (VDF) is used to represent source and target shapes. The problem is formulated as an energy optimization process by matching the VDFs of the source and target shapes. The minimization process results in estimating the transformation parameters for the global and local deformation cases. Gradient descent optimization handles the computation of scaling, rotation, and translation matrices used to minimize the global differences between source and target shapes. Nonrigid deformations require a large number of parameters which make the use of the gradient descent minimization a very time-consuming process. We propose to compute the local deformation parameters using a closed-form solution as a linear system of equations derived from approximating an objective function. Extensive experimental validations and comparisons performed on generalized 2D shape data demonstrate the robustness and effectiveness of the method.
Shape, Vectors, Optimization, Lattices, Lungs, Closed-form solutions, Topology, optimization, Shape representation, shape alignment, distance transform, vector distance function, free form deformations
Aly A. Farag, Hossam E. Abd El Munim, Amal A. Farag, "Shape Representation and Registration in Vector Implicit Spaces: Adopting a Closed-Form Solution in the Optimization Process", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. , pp. 763-768, March 2013, doi:10.1109/TPAMI.2012.245