B-spline Surface Approximation Using Hierarchical Genetic Algorithm

Surface approximation using splines has been widely used in geometric modeling and image analysis. One of the main problems associated with surface approximation by splines is the adequate selection of the number and location of the knots, as well as, the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation problem. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension, and the B-spline coefficients simultaneously. Our approach is able to find solutions with fewest parameters within of the B-spline basis functions. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces have been included.

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