Shape-aware surface reconstruction from sparse 3D point-clouds.

The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose the use of a statistical shape model (SSM) as a prior for surface reconstruction. The SSM is represented by a point distribution model (PDM), which is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we formulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given points are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are "oriented" according to the surface normals at the PDM points, a surface-based fitting is accomplished. Estimating the parameters of the GMM in a maximum a posteriori manner yields the reconstruction of the surface from the given data points. We compare our method to the extensively used Iterative Closest Points method on several different anatomical datasets/SSMs (brain, femur, tibia, hip, liver) and demonstrate superior accuracy and robustness on sparse data

A Bayesian Approach to Sparse Model Selection in Statistical Shape Models

Groupwise registration of point sets is the fundamental step in creating statistical shape models (SSMs). When the number of points on the sets varies across the population, each point set is often regarded as a spatially transformed Gaussian mixture model (GMM) sample, and the registration problem is formulated as the estimation of the underlying GMM from the training samples. Thus, each Gaussian in the mixture specifies a landmark (or model point), which is probabilistically corresponded to a training point. The Gaussian components, transformations, and probabilistic matches are often computed by an expectation-maximization (EM) algorithm. To avoid over- and under-fitting errors, the SSM should be optimized by tuning the required number of components. In this paper, rather than manually setting the number of components before training, we start from a maximal model and prune out the negligible points during the registration by a sparsity criterion. We show that by searching over the continuous space for optimal sparsity level, we can reduce the fitting errors (generalization and specificities), and thereby help the search process for a discrete number of model points. We propose an EM framework, adopting a symmetric Dirichlet distribution as a prior, to enforce sparsity on the mixture weights of Gaussians. The negligible model points are pruned by a quadratic programming technique during EM iterations. The proposed EM framework also iteratively updates the estimates of the rigid registration parameters of the point sets to the mean model. Next, we apply the principal component analysis to the registered and equal-length training point sets and construct the SSMs. This method is evaluated by learning of sparse SSMs from 15 manually segmented caudate nuclei, 24 hippocampal, and 20 prostate data sets. The generalization, specificity, and compactness of the proposed model favorably compare to a traditional EM based model

A system for unsupervised extraction of orthopedic parameters from CT data

The request for software assistance is increasingly gaining importance in the field of orthopedic surgery. In the near future more people will need implants, which have to last longer. New developments in computer assisted therapy planning promise to significantly reduce the number of revisions and increase the longevity of an implant. For example the computation of the functional outcome of a total knee replacement by prediction of kinematics may provide important guidance during surgery. Speed, accuracy and as little manual interaction as possible are the key factors to make those new developments available to the clinical routine. To reach this goal we present a software assistant for the reconstruction of individual anatomical models (e.g. geometry and landmarks) from medical image data, which is an essential step in this effort. We will present and discuss present and future application scenarios

An articulated statistical shape model for accurate hip joint segmentation

In this paper we propose a framework for fully automatic, robust and accurate segmentation of the human pelvis and proximal femur in CT data. We propose a composite statistical shape model of femur and pelvis with a flexible hip joint, for which we extend the common definition of statistical shape models as well as the common strategy for their adaptation. We do not analyze the joint flexibility statistically, but model it explicitly by rotational parameters describing the bent in a ball-and-socket joint. A leave-one-out evaluation on 50 CT volumes shows that image driven adaptation of our composite shape model robustly produces accurate segmentations of both proximal femur and pelvis. As a second contribution, we evaluate a fine grain multi-object segmentation method based on graph optimization. It relies on accurate initializations of femur and pelvis, which our composite shape model can generate. Simultaneous optimization of both femur and pelvis yields more accurate results than separate optimizations of each structure. Shape model adaptation and graph based optimization are embedded in a fully automatic framework

Automatic detection and classification of teeth in CT data

We propose a fully automatic method for tooth detection and classification in CT or cone-beam CT image data. First we compute an accurate segmentation of the maxilla bone. Based on this segmentation, our method computes a complete and optimal separation of the row of teeth into 16 subregions and classifies the resulting regions as existing or missing teeth. This serves as a prerequisite for further individual tooth segmentation. We show the robustness of our approach by providing extensive validation on 43 clinical head CT scans

Improving deformable surface meshes through omni-directional displacements and MRFs

Deformable surface models are often represented as triangular meshes in image segmentation applications. For a fast and easily regularized deformation onto the target object boundary, the vertices of the mesh are commonly moved along line segments (typically surface normals). However, in case of high mesh curvature, these lines may intersect with the target boundary at "non-corresponding" positions, or even not at all. Consequently, certain deformations cannot be achieved. We propose an approach that allows each vertex to move not only along a line segment, but within a surrounding sphere. We achieve globally regularized deformations via Markov Random Field optimization. We demonstrate the potential of our approach with experiments on synthetic data, as well as an evaluation on 2 x 106 coronoid processes of the mandible in Cone-Beam CTs, and 56 coccyxes (tailbones) in low-resolution CTs