Multiscale medial shape-based analysis of image objects

pre-printMedial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an object-intrinsic coordinate system and thus provides correspondence between instances of the object in and near the object(s); 2) it captures the object interior and is, thus, very suitable for deformation; and 3) it provides the basis for an intuitive object-based multiscale sequence leading to efficiency of segmentation algorithms and trainability of statistical characterizations with limited training sets. As a result of these properties, medial representation is particularly suitable for the following image analysis tasks; how each operates will be described and will be illustrated by results: 1) segmentation of objects and object complexes via deformable models; 2) segmentation of tubular trees, e.g., of blood vessels, by following height ridges of measures of fit of medial atoms to target images; 3) object-based image registration via medial loci of such blood vessel trees; 4) statistical characterization of shape differences between control and pathological classes of structures. These analysis tasks are made possible by a new form of medial representation called m-reps, which is described

Discrimination analysis using Multi-object statistics of shape and pose

journal articleA main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper, we present work towards modeling the shape and pose variability of sets of multiple objects. Principal geodesic analysis (PGA) is the extension of the standard technique of principal component analysis (PCA) into the nonlinear Riemannian symmetric space of pose and our medial m-rep shape description, a space in which use of PCA would be incorrect. In this paper, we discuss the decoupling of pose and shape in multi-object sets using different normalization settings. Further, we introduce methods of describing the statistics of object pose and object shape, both separately and simultaneously using a novel extension of PGA. We demonstrate our methods in an application to a longitudinal pediatric autism study with object sets of 10 subcortical structures in a population of 47 subjects. The results show that global scale accounts for most of the major mode of variation across time. Furthermore, the PGA components and the corresponding distribution of different subject groups vary significantly depending on the choice of normalization, which illustrates the importance of global and local pose alignment in multi-object shape analysis. Finally, we present results of using distance weighted discrimination analysis (DWD) in an attempt to use pose and shape features to separate subjects according to diagnosis, as well as visualize discriminating differences

Statistical shape analysis of Multi-Object complexes

journal articleAn 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 skeletal 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 sub-cortical 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

Patient-specific anatomical illustration via model-guided texture synthesis

Medical illustrations can make powerful use of textures to attractively, effectively, and efficiently visualize the appearance of the surface or cut surface of anatomic structures. It can do this by implying the anatomic structure's physical composition and clarifying its identity and 3-D shape. Current visualization methods are only capable of conveying detailed information about the orientation, internal structure, and other local properties of the anatomical objects for a typical individual, not for a particular patient. Although one can derive the shape of the individual patient's object from CT or MRI, it is important to apply these illustrative techniques to those particular shapes. In this research patient-specific anatomical illustrations are created by model-guided texture synthesis (MGTS). Given 2D exemplar textures and model-based guidance information as input, MGTS uses exemplar-based texture synthesis techniques to create patient-specific surface and solid textures. It consists of three main components. The first component includes a novel texture metamorphosis approach for creating interpolated exemplar textures given two exemplar textures. This component uses an energy optimization scheme derived from optimal control principles that utilizes intensity and structure information in obtaining the transformation. The second component consists of creating the model-based guidance information, such as directions and layers, for that specific model. This component uses coordinates implied by discrete medial 3D anatomical models (m-reps). The last component accomplishes exemplar-based texture synthesis by textures whose characteristics are spatially variant on and inside the 3D models. It considers the exemplar textures from the first component and guidance information from the second component in synthesizing high-quality, high-resolution solid and surface textures. Patient-specific illustrations with a variety of textures for different anatomical models, such as muscles and bones, are shown to be useful for our clinician to comprehend the shape of the models under radiation dose and to distinguish the models from one another

Multi-object analysis of volume, pose, and shape using statistical discrimination

pre-printOne 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

Skeletons, Object Shape, Statistics

Objects and object complexes in 3D, as well as those in 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called “s-reps,” these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here we will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for measuring the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here

Constructing 3D faces from natural language interface

This thesis presents a system by which 3D images of human faces can be constructed using a natural language interface. The driving force behind the project was the need to create a system whereby a machine could produce artistic images from verbal or composed descriptions. This research is the first to look at constructing and modifying facial image artwork using a natural language interface. Specialised modules have been developed to control geometry of 3D polygonal head models in a commercial modeller from natural language descriptions. These modules were produced from research on human physiognomy, 3D modelling techniques and tools, facial modelling and natural language processing. [Continues.

Training models of anatomic shape variability: Training models of anatomic shape variability

Learning probability distributions of the shape of anatomic structures requires fitting shape representations to human expert segmentations from training sets of medical images. The quality of statistical segmentation and registration methods is directly related to the quality of this initial shape fitting, yet the subject is largely overlooked or described in an ad hoc way. This article presents a set of general principles to guide such training. Our novel method is to jointly estimate both the best geometric model for any given image and the shape distribution for the entire population of training images by iteratively relaxing purely geometric constraints in favor of the converging shape probabilities as the fitted objects converge to their target segmentations. The geometric constraints are carefully crafted both to obtain legal, nonself-interpenetrating shapes and to impose the model-to-model correspondences required for useful statistical analysis. The paper closes with example applications of the method to synthetic and real patient CT image sets, including same patient male pelvis and head and neck images, and cross patient kidney and brain images. Finally, we outline how this shape training serves as the basis for our approach to IGRT∕ART

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments