Search

Automated medical image segmentation is a challenging task that benefits from the use of effective image appearance models. In this paper, we compare appearance models at three regional scales for statistically characterizing image intensity near object boundaries in the context of segmentation via deformable models. The three models capture appearance in the form of regional intensity quantile functions. These distribution-based regional image descriptors are amenable to Euclidean methods such as principal component analysis, which we use to build the statistical appearance models. The first model uses two regions, the interior and exterior of the organ of interest. The second model accounts for exterior inhomogeneity by clustering on object-relative local intensity quantile functions to determine tissue-consistent regions relative to the organ boundary. The third model analyzes these image descriptors per geometrically defined local region. To evaluate the three models, we present segmentation results on bladders and prostates in CT in the context of day-to-day adaptive radiotherapy for the treatment of prostate cancer. Results show improved segmentations with more local regions, probably because smaller regions better represent local inhomogeneity in the intensity distribution near the organ boundary. [ABSTRACT FROM AUTHOR]

A 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. [ABSTRACT FROM AUTHOR]

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications. For instance, shape statistics are useful in understanding the structural changes in anatomy that are caused by growth and disease. Classical statistical techniques can be applied to study shape representations that are parameterized by a linear space, such as landmark data or boundary meshes, but they cannot handle more complex representations of shape. We have been developing representations of geometry based on the medial axis description or m-rep. While the medial representation provides a rich language for variability in terms of bending, twisting, and widening, the medial parameters are elements of a nonlinear Riemannian symmetric space. Therefore, linear statistical methods are not applicable in the m-rep setting, and statistical methods for analyzing manifold data are needed. This chapter presents a general method called principal geodesic analysis (PGA) for computing the variability of manifold-valued data. PGA is a direct generalization of principal component analysis (PCA) and is based solely on intrinsic properties of the underlying manifold, such as the notion of geodesic curves and distance. We demonstrate the use of PGA to describe the shape variability of medial representations, and results are shown on a hippocampus data set. The applicability of PGA is also shown within a 3D image segmentation framework based on a Bayesian posterior optimization of deformable medial models. [ABSTRACT FROM AUTHOR]

A main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper, we present work in progress 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 new methods of describing the statistics of object pose using a novel extension of PGA, which previously has been used for global shape statistics. These new pose statistics are then combined with shape statistics to form a more complete description of multi-object complexes. We demonstrate our methods in an application to a longitudinal pediatric autism study with object sets of 10 subcortical structures in a population of 20 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. [ABSTRACT FROM AUTHOR]

We present a novel approach to statistically characterize histograms of model-relative image regions. A multiscale model is used as an aperture to define image regions at multiple scales. We use this image description to define an appearance model for deformable model segmentation. Appearance models measure the likelihood of an object given a target image. To determine this likelihood we compute pixel intensity histograms of local model-relative image regions from a 3D image volume near the object boundary. We use a Gaussian model to statistically characterize the variation of non-parametric histograms mapped to Euclidean space using the Earth Mover's distance. The new method is illustrated and evaluated in a deformable model segmentation study on CT images of the human bladder, prostate, and rectum. Results show improvement over a previous profile based appearance model, out-performance of statistically modeled histograms over simple histogram measurements, and advantages of regional histograms at a fixed local scale over a fixed global scale. [ABSTRACT FROM AUTHOR]

We present a methodology for estimating the probability of multi-object anatomic complexes that reflects both the individual objects' variability and the variability of the inter-relationships between objects. The method is based on m-reps and the idea of augmenting medial atoms from one object's m-rep to the set of atoms of an object being described. We describe the training of these probabilities, and we present an example of calculating the statistics of the bladder, prostate, rectum complex in the male pelvis. Via examples from the real world and from Monte-Carlo simulation, we show that this means of representing multi-object statistics yields samples that are nearly geometrically proper and means and principal modes of variations that are intuitively reasonable. [ABSTRACT FROM AUTHOR]

We face the question of how to produce a scale space of image intensities relative to a scale space of objects or other characteristic image regions filling up the image space, when both images and objects are understood to come from a population. We argue for a schema combining a multi-scale image representation with a multi-scale representation of objects or regions. The objects or regions at one scale level are produced using soft-edged apertures, which are subdivided into sub-regions. The intensities in the regions are represented using histograms. Relevant probabilities of region shape and inter-relations between region geometry and of histograms are described, and the means is given of inter-relating the intensity probabilities and geometric probabilities by producing the probabilities of intensities conditioned on geometry. [ABSTRACT FROM AUTHOR]

Multi-figure m-reps allow us to represent and analyze a complex anatomical object by its parts, by relations among its parts, and by the object itself as a whole entity. This representation also enables us to gather either global or hierarchical statistics from a population of such objects. We propose a framework to train the statistics of multi-figure anatomical objects from real patient data. This training requires fitting multi-figure m-reps to binary characteristic images of training objects. To evaluate the fitting approach, we propose a Monte Carlo method sampling the trained statistics. It shows that our methods generate geometrically proper models that are close to the set of Monte Carlo generated target models and thus can be expected to yield similar statistics to that used for the Monte Carlo generation. [ABSTRACT FROM AUTHOR]

With a mind towards achieving means of image comprehension by computer, we intend to convey the benefits of (1) characterizing the geometry of object complexes in the real world as contrasted with the geometric conformation of their images, and (2) describing populations of object complexes probabilistically. We show how a multi-scale description of inter-scale residues of geometric features provides a set of efficiently trainable probability distributions via a Markov random field approach, and specifies the location and scale of geometric differences between populations. These ideas and methods are illustrated using medial representations for 3D objects, depending on their properties (1) that local descriptors have an associated coordinate frame and distance metric, and (2) that continuous geometric random variables can be used to describe all members of a population of object complexes with a common structure and the variation among those members. We demonstrate with respect to the following object-complex-relative discrete scale levels: a whole object complex, individual objects, various object parts and sections, and fine boundary details. Using this illustrative framework, we show how to build Markov random field (MRF) models on the geometry scale space based on the statistics of shape residues across scales and between neighboring geometric entities at the level of locality given by its scale. In this paper, we present how to design and estimate MRF models on two scale levels, namely boundary displacement and object sections. [ABSTRACT FROM AUTHOR]

We present a method of 3D/2D image registration. The algorithm is based on the property of near projective invariance in tubular objects. The skeletons of tubular anatomical structures (e.g., intracerebral blood vessels) are used as registration primitives. Experiments with Magnetic Resonance Angiogram (MRA) patient studies and both simulated and actual X-ray angiograms suggest that the algorithm is very accurate and robust. The algorithm requires only a small number of primitives. In addition, the algorithm is relatively insensitive to the choice of tubular structures used. Experimental results justifying these claims are included. [ABSTRACT FROM AUTHOR]

This paper presents a method for identifying image loci that can be used as a basis for object segmentation and image registration. The focus is on 1D and 2D shape loci in 3D images. This method, called marching ridges, uses generalized height ridges, oriented medialness measures and a marching cubes like algorithm to extract optimal scale-orientation cores. This algorithm can can also be used for other image processing tasks such as finding intensity skeletons of objects and identifying object boundaries. [ABSTRACT FROM AUTHOR]