This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.
Shape modeling and analysis is an important problem in a variety of fields including biology, medical image analysis, and computer vision @cite_15 @cite_5 @cite_0 @cite_6 that has received considerable attention over the last few decades. Kendall @cite_6 defines ph shape as an equivalence class of pointsets under the similarities generated by translation, rotation, and scaling. Objects in biological images or anatomical structures in medical images often possess shape as the sole identifying characteristic instead of color or texture. Applications of shape analysis beyond natural contexts include handwriting analysis and character recognition. In the medical context, shapes of human anatomical structures can provide crucial cues in diagnosis of pathologies or disorders. The key problems in this context lie in the fitting of shape models to population image data followed by statistical analysis such as hypothesis testing to compare groups, classification of unseen shapes in one of the groups for which the shape models are learnt, or unsupervised clustering of shapes.
@cite_0 @cite_5 @cite_15 @cite_6
2116329629 2116663904 2165844313 2157375720
An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skelet al object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 subcortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations. Shape analysis has been a long standing problem in the literature. In this paper, we address the shape classification problem and make the following contributions: (1) We combine both contour and skeleton (also local and global) information for shape analysis, and we derive an effective classifier. (2) We collect a challenging shape database in which there are 20 categories of animals, with each having 100 shapes. All these shapes are obtained from real images with a large variation in pose, viewing angle, articulation, and self-occlusion. (3) We emphasize the importance of having good representation for shape classification to address the unique characteristics of shape. A thorough experimental study is conducted showing significant improvement by the proposed algorithm over many of the state-of-the-art shape matching and classification algorithms, on both our dataset and the well-known MPEG-7 dataset [19]. In addition, we applied our algorithm for recognizing and classifying objects from natural images and obtained very encouraging results. One goal of statistical shape analysis is the discrimination between two populations of objects. Whereas traditional shape analysis was mostly concerned with single objects, analysis of multi-object complexes presents new challenges related to alignment and pose. In this paper, we present a methodology for discriminant analysis of multiple objects represented by sampled medial manifolds. Non-Euclidean metrics that describe geodesic distances between sets of sampled representations are used for alignment and discrimination. Our choice of discriminant method is the distance-weighted discriminant because of its generalization ability in high-dimensional, low sample size settings. Using an unbiased, soft discrimination score, we associate a statistical hypothesis test with the discrimination results. We explore the effectiveness of different choices of features as input to the discriminant analysis, using measures like volume, pose, shape, and the combination of pose and shape. Our method is applied to a longitudinal pediatric autism study with 10 subcortical brain structures in a population of 70 subjects. It is shown that the choices of type of global alignment and of intrinsic versus extrinsic shape features, the latter being sensitive to relative pose, are crucial factors for group discrimination and also for explaining the nature of shape change in terms of the application domain. Shape is a significant visual clue for human perception and shape models show considerable promise as a basis for extracting objects from images. This paper proposes a novel approach for shape matching and modeling using the symmetry characterization of shape interior and the spatial relationships of shape structures. Based on the representative skelet al features, we develop a mechanism to generate a coarse segment matching between different instances of an object. Additionally, the natural correspondence of skelet al branches to sequential segments along the shape curves is employed in the matching process to avoid false correspondences across different segments. Point matches within the corresponding segments are then obtained by solving a constrained assignment problem. The validation of the proposed approach is illustrated on various data sets in the presence of considerable deformation and occlusion and the results are compared with those of popular approaches. We also demonstrate the performance of our method on biological objects for shape modeling, showing better models than those obtained by the state-of-the-art shape modeling approaches.