Construction of a 3D Physically-Based Multi-Object Deformable Model

This paper addresses the problem of describing the significant intra and inter variability of 3D deformable structures within 3D image data sets. In pursuing it, a 3D probabilistic physically based deformable model is defined. The statistically learned deformable model captures the spatial relationships between the different objects surfaces, together with their shape variations. The structures of interest in each volume are parameterized by the amplitudes of the vibration modes of a deformable spherical mesh. For a given 3D image in the training set, a vector containing the largest vibration modes describing the desired object is created. This random vector is statistically constrained by retaining the most significant variation modes of its Karhunen-Loeve (KL) expansion on the considered population. The surfaces of the modeled structures thus deform according to the variability observed in the training set. A preliminary application of a 3D multi-object model for the segmentation of 3D brain structures from MR images is presented.