Correspondence evaluation in local shape analysis and structural subdivision

journal articleRegional volumetric and local shape analysis has become of increasing interest to the neuroimaging community due to the potential to locate morphological changes. In this paper we compare three common correspondence methods applied to two studies of hippocampal shape in schizophrenia: correspondence via deformable registration, spherical harmonics (SPHARM) and Minimum Description Length (MDL) optimization. These correspondence methods are evaluated in respect to local statistical shape analysis and structural subdivision analysis. Results show a non-negligible influence of the choice of correspondence especially in studies with low numbers of subjects. The differences are especially striking in the structural subdivision analysis and hints at a possible source for the diverging findings in many subdivision studies. Our comparative study is not meant to be exhaustive, but rather raises awareness of the issue and shows that assessing the validity of the correspondence is an important step

Population-based fitting of medial shape models with correspondence optimization

pre-printA crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3-D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system.We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size

Entropy-based particle correspondence for shape populations

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies

Linear and Nonlinear Generative Probabilistic Class Models for Shape Contours

We introduce a robust probabilistic approach to modeling shape contours based on a low- dimensional, nonlinear latent variable model. In contrast to existing techniques that use objective functions in data space without ex- plicit noise models, we are able to extract complex shape variation from noisy data. Most approaches to learning shape models slide observed data points around fixed con- tours and hence, require a correctly labeled ‘reference shape’ to prevent degenerate so- lutions. In our method, unobserved curves are reparameterized to explain the fixed data points, so this problem does not arise. The proposed algorithms are suitable for use with arbitrary basis functions and are applicable to both open and closed shapes; their effec- tiveness is demonstrated through illustrative examples, quantitative assessment on bench- mark data sets and a visualization task

Skeletal Shape Correspondence Through Entropy

We present a novel approach for improving the shape statistics of medical image objects by generating correspondence of skeletal points. Each object's interior is modeled by an s-rep, i.e., by a sampled, folded, two-sided skeletal sheet with spoke vectors proceeding from the skeletal sheet to the boundary. The skeleton is divided into three parts: the up side, the down side, and the fold curve. The spokes on each part are treated separately and, using spoke interpolation, are shifted along that skeleton in each training sample so as to tighten the probability distribution on those spokes' geometric properties while sampling the object interior regularly. As with the surface/boundary-based correspondence method of Cates et al., entropy is used to measure both the probability distribution tightness and the sampling regularity, here of the spokes' geometric properties. Evaluation on synthetic and real world lateral ventricle and hippocampus data sets demonstrate improvement in the performance of statistics using the resulting probability distributions. This improvement is greater than that achieved by an entropy-based correspondence method on the boundary points