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Different image processing techniques have recently been investigated for the characterization of complex porous media, such as bones, stones and soils. Among these techniques, 3D thinning algorithms are generally used to extract a one-voxel-thick skeleton from 3D porous objects while preserving the topological information. Models based on simplified skeletons have been shown to be efficient in retrieving morphological information from large scale disordered objects not only at a global level but also at a local level. In this paper, we present a series of 3D skeleton-based image processing techniques for evaluating the microarchitecture of large scale disordered porous media. The proposed skeleton method combines curve and surface thinning methods with the help of an enhanced shape classification algorithm. Results on two different porous objects demonstrate the ability of the proposed method to provide significant topological and morphological information.

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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.

Compared to curve-based or surface-based skeletons, the hybrid skeleton better matches the geometry of the data. Each rod is represented by a one-voxel-thick arc and each plate is represented by a one-voxel-thick surface. The hybrid skeleton as well as the proposed classification algorithm introduce relevant parameters linked to the presence of plates in the trabecular bone data, showing that rods and plates contain independent information about trabeculae. The hybrid skeleton offers a new opportunity for precise studies of porous media such as trabecular bone.

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Image registration is a valuable technique for medical diagnosis and treatment. In this paper, we present an enhanced implementation of the popular iterative closest point (ICP) algorithm developed for the registration of 3D free-form closed surfaces, based on the use of a look up matrix for finding the best correspondence pairs. The algorithm, called Comprehensive ICP (CICP) algorithm, is then successfully applied for comparing two sequences of 3D surfaces of the left ventricle of the heart, obtained from two different modalities: 4D Echography and Gated SPECT. The results show a good correspondence between the reconstructed sequence from 4D Echography and the reference Gated SPECT sequence. This study can be extended to comparing different medical reconstructions of sphere-like shaped organs collected from different modalities.