Continuous model of irregular sampled data using multilevel B-splines

The present work deals with the problem of obtaining a continuous multivariate function based on B-splines, which approximates irregular sampled data. A multiresolution pyramidal approach is proposed, giving robustness and speed at the time of determining the coefficients that define the surface. The resulting pyramid of functions having different resolutions may reduce subsequent calculation when manipulating the image by utilizing hierarchical algorithms. The B-spline surface is calculated by adjusting the coefficients through the least squares criteria, which is implemented in an iterative gradient algorithm. Simulations in 2-D and approximations with real ultrasound data are carried out to test the performance of the algorithm.