Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

3D medical volume segmentation using hybrid multiresolution statistical approaches

This article is available through the Brunel Open Access Publishing Fund. Copyright © 2010 S AlZu’bi and A Amira.3D volume segmentation is the process of partitioning voxels into 3D regions (subvolumes) that represent meaningful physical entities which are more meaningful and easier to analyze and usable in future applications. Multiresolution Analysis (MRA) enables the preservation of an image according to certain levels of resolution or blurring. Because of multiresolution quality, wavelets have been deployed in image compression, denoising, and classification. This paper focuses on the implementation of efficient medical volume segmentation techniques. Multiresolution analysis including 3D wavelet and ridgelet has been used for feature extraction which can be modeled using Hidden Markov Models (HMMs) to segment the volume slices. A comparison study has been carried out to evaluate 2D and 3D techniques which reveals that 3D methodologies can accurately detect the Region Of Interest (ROI). Automatic segmentation has been achieved using HMMs where the ROI is detected accurately but suffers a long computation time for its calculations

Conserved but flexible modularity in the zebrafish skull: implications for craniofacial evolvability

Morphological variation is the outward manifestation of development and provides fodder for adaptive evolution. Because of this contingency, evolution is often thought to be biased by developmental processes and functional interactions among structures, which are statistically detectable through forms of covariance among traits. This can take the form of substructures of integrated traits, termed modules, which together comprise patterns of variational modularity. While modularity is essential to an understanding of evolutionary potential, biologists currently have little understanding of its genetic basis and its temporal dynamics over generations. To address these open questions, we compared patterns of craniofacial modularity among laboratory strains, defined mutant lines and a wild population of zebrafish ( ). Our findings suggest that relatively simple genetic changes can have profound effects on covariance, without greatly affecting craniofacial shape. Moreover, we show that instead of completely deconstructing the covariance structure among sets of traits, mutations cause shifts among seemingly latent patterns of modularity suggesting that the skull may be predisposed towards a limited number of phenotypes. This new insight may serve to greatly increase the evolvability of a population by providing a range of 'preset' patterns of modularity that can appear readily and allow for rapid evolution

Quantum Tetrahedra

We discuss in details the role of Wigner 6j symbol as the basic building block unifying such different fields as state sum models for quantum geometry, topological quantum field theory, statistical lattice models and quantum computing. The apparent twofold nature of the 6j symbol displayed in quantum field theory and quantum computing -a quantum tetrahedron and a computational gate- is shown to merge together in a unified quantum-computational SU(2)-state sum framework