Improved VSF algorithm for smooth surface reconstruction from sparse medical data

Ahmad Almhdie (1) , Christophe Léger (1) , Maïtine Bergounioux (2) , Mohamed Deriche (3) , Roger Lédée

1 LESI - Laboratoire d'électronique, signaux, images
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 KFUPM - King Fahd University of Petroleum and Minerals

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.

Mots clés: sparse or scattered data; medical data; surface reconstruction; thin plate model; smooth surface

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Imagerie médicale

Ahmad Almhdie, Christophe Léger, Maïtine Bergounioux, Mohamed Deriche, Roger Lédée. Improved VSF algorithm for smooth surface reconstruction from sparse medical data. Journal of Computing and Information Technology, 2007, 15 (2), pp.123-130. ⟨10.2498/cit.1000820⟩. ⟨hal-00607885⟩