Comput Math Methods Med - Fitting C? continuous parametric surfaces to frontiers delimiting physiologic structures.

Tópicos

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Resumo

We present a technique to fit C(2) continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting of C(2) continuous parametric curves to scattered geometric data points is quite trivial, the fitting of C(2) continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that are C(2) continuous.

Resumo Limpo

present techniqu fit c continu parametr surfac scatter geometr data point form frontier delimit physiolog structur segment imag mathemat represent interest facilit larg number oper model fit c continu parametr curv scatter geometr data point quit trivial fit c continu parametr surfac difficulti come fact scatter data point assign uniqu parametr coordin fit quit sensit distribut parametr plane present new approach polygon quadrilater triangular surfac extract segment imag surfac subsequ project onto parametr plane manner ensur onetoon map result polygon mesh regular area edg length final point surfac fit relat trivial novelti approach lie regular polygon mesh process perform assess reconstruct geometr model mous heart ventricl computer tomographi scan result show excel reproduct geometr data surfac c continu

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