Improved VSF Algorithm for Smooth Surface Reconstruction From Sparse Medical Data

Abstract

This paper presents a Modified Variational Splines Fitting (MVSF) algorithm for surface reconstruction using thin plate splines on scattered patches or points of originally smooth surfaces. In particular, a more accurate derivation of the discrete equations for the energy corresponding to the thin plate model is introduced. The results obtained on simulated data show that the proposed algorithm converges faster than the original VSF algorithm. Additionally, we discuss an approach for choosing the algorithm's parameters using a cross validation technique. Results obtained with the modified algorithm are compared to those using a Frequency Fourier-based 3D Harmonic modelling (3DHM) algorithm and show that the proposed algorithm gives an improved performance under the small sample size condition. The developed model has been successfully applied for real biomedical data; in particular for the reconstruction of left ventricle of human heart.

The comprehensive ICP (CICP) algorithm and its application to the multidmoal registration of 3D surfaces of the heart

“…Each closed surface is developed in a rectangular domain by transforming data form Cartesian to special coordinates, starting from the centre of gravity of each surface. Developed surfaces are then interpolated by a modified variation splines fitting (MVSF) algorithm [6] (based on a method previously presented by Szeliski [7]) for the reconstruction of the LV surfaces, and the signed difference is calculated between each pair of corresponding samples within the two surfaces. A color matrix, proportional to the range of the radial differences, is determined and projected on the reference gated SPECT surfaces.…”