Sparse Decomposition and Modeling of Anatomical Shape Variation

Recent advances in statistics have spawned powerful methods for regression and data decomposition that promote sparsity, a property that facilitates interpretation of the results. Sparse models use a small subset of the available variables and may perform as well or better than their full counterparts if constructed carefully. In most medical applications, models are required to have both good statistical performance and a relevant clinical interpretation to be of value. Morphometry of the corpus callosum is one illustrative example. This paper presents a method for relating spatial features to clinical outcome data. A set of parsimonious variables is extracted using sparse principal component analysis, producing simple yet characteristic features. The relation of these variables with clinical data is then established using a regression model. The result may be visualized as patterns of anatomical variation related to clinical outcome. In the present application, landmark-based shape data of the corpus callosum is analyzed in relation to age, gender, and clinical tests of walking speed and verbal fluency. To put the data-driven sparse principal component method into perspective, we consider two alternative techniques, one where features are derived using a model-based wavelet approach, and one where the original variables are regressed directly on the outcome

Linear Shape Deformation Models with Local Support Using Graph-based Structured Matrix Factorisation

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. In this paper, a method to obtain deformation factors with local support is presented. The benefits of such models include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. For that, based on a well-grounded theoretical motivation, we formulate a matrix factorisation problem employing sparsity and graph-based regularisation terms. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation ability and sparse shape reconstruction, whereas for human body shapes our method gives more realistic deformations.Comment: Please cite CVPR 2016 versio

Posterior shape models

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness

Sparse Modeling of Landmark and Texture Variability using the Orthomax Criterion

In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach