Multi-Object Analysis of Volume, Pose, and Shape Using Statistical Discrimination

One goal of statistical shape analysis is the discrimination between two populations of objects. Whereas traditional shape analysis was mostly concerned with studying single objects, analysis of multi-object complexes presents new challenges related to alignment and relative object pose. In this paper, we present a methodology for discriminant analysis of sets multiple shapes. Shapes are represented by sampled medial manifolds including normals to the boundary. Non-Euclidean metrics that describe geodesic distance between sets of sampled representations are used for shape alignment and discrimination. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Using an unbiased, soft discrimination score we can associate a statistical hypothesis test with the discrimination results. Furthermore, localization and nature significant differences between populations can be visualized via the average best discriminating axis

Elastic shape matching of parameterized surfaces using square root normal fields.

In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple \ensuremathL2\ensuremathL2 metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods

Baseline new bone formation does not predict bone loss in ankylosing spondylitis as assessed by quantitative computed tomography (QCT) - 10-year follow-up

<p>Abstract</p> <p>Background</p> <p>To evaluate the relationship between bone loss and new bone formation in ankylosing spondylitis (AS) using 10-year X-ray, dual-energy x-ray absorptiometry (DXA) and quantitative computed tomography (QCT) follow-up.</p> <p>Methods</p> <p>Fifteen AS patients free from medical conditions and drugs affecting bone metabolism underwent X-ray, DXA and QCT in 1999 and 2009.</p> <p>Results</p> <p>In spine QCT a statistically significant (p = 0,001) decrease of trabecular bone mineral content (BMC) was observed (change ± SD: 18.0 ± 7.3 mg/cm³). In contrast, spine DXA revealed a significant increase of bone mineral density (change ± SD: -0.15 ± 0.14 g/cm²). The mean BMC, both at baseline and follow-up was significantly lower (p = 0.02 and p = 0.005, respectively) in advanced radiological group as compared to early radiological group. However, in multiple regression model after adjustment for baseline BMC, the baseline radiological scoring did not influence the progression of bone loss as assessed with QCT (p = 0.22, p for BMC*X-ray syndesmophyte scoring interaction = 0.65, p for ANOVA-based X-ray syndesmophyte scoring*time interaction = 0.39). Baseline BMC was the only significant determinant of 10-year BMC change, to date the longest QCT follow-up data in AS.</p> <p>Conclusions</p> <p>In AS patients who were not using antiosteoporotic therapy spine trabecular bone density evaluated by QCT decreased over 10-year follow-up and was not related to baseline radiological severity of spine involvement.</p

Modeling Multi-object Configurations via Medial/Skeletal Linking Structures

We introduce a method for modeling a configuration of objects in 2D or 3D images using a mathematical "skeletal linking structure" which will simultaneously capture the individual shape features of the objects and their positional information relative to one another. The objects may either have smooth boundaries and be disjoint from the others or share common portions of their boundaries with other objects in a piecewise smooth manner. These structures include a special class of "Blum medial linking structures," which are intrinsically associated to the configuration and build upon the Blum medial axes of the individual objects. We give a classification of the properties of Blum linking structures for generic configurations. The skeletal linking structures add increased flexibility for modeling configurations of objects by relaxing the Blum conditions and they extend in a minimal way the individual "skeletal structures" which have been previously used for modeling individual objects and capturing their geometric properties. This allows for the mathematical methods introduced for single objects to be significantly extended to the entire configuration of objects. These methods not only capture the internal shape structures of the individual objects but also the external structure of the neighboring regions of the objects.Comment: This paper presents material relevant for two and three dimensional images that builds on and references a previous paper by the authors, arXiv:1402.551

Sparse approximation of currents for statistics on curves and surfaces

Computing, processing, visualizing statistics on shapes like curves or surfaces is a real challenge with many applications ranging from medical image analysis to computational geometry. Modelling such geometrical primitives with currents avoids feature-based approach as well as point-correspondence method. This framework has been proved to be powerful to register brain surfaces or to measure geometrical invariants. However, if the state-of-the-art methods perform efficiently pairwise registrations, new numerical schemes are required to process groupwise statistics due to an increasing complexity when the size of the database is growing. Statistics such as mean and principal modes of a set of shapes often have a heavy and highly redundant representation. We propose therefore to find an adapted basis on which mean and principal modes have a sparse decomposition. Besides the computational improvement, this sparse representation offers a way to visualize and interpret statistics on currents. Experiments show the relevance of the approach on 34 sets of 70 sulcal lines and on 50 sets of 10 meshes of deep brain structures

Quantification and visualization of variation in anatomical trees

This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers on subtree features. The second approach visualizes the global metric structure of datasets through low-distortion embedding into hyperbolic planes in the style of multidimensional scaling. A case study is made on a dataset of airway trees in relation to Chronic Obstructive Pulmonary Disease.Comment: 22 page