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.

Fitting unbranching skeletal structures to objects.

Representing an object by a skeletal structure can be powerful for statistical shape analysis if there is good correspondence of the representations within a population. Many anatomic objects have a genus-zero boundary and can be represented by a smooth unbranching skeletal structure that can be discretely approximated. We describe how to compute such a discrete skeletal structure ("d-s-rep") for an individual 3D shape with the desired correspondence across cases.

A Novel Method for High-Dimensional Anatomical Mapping of Extra-Axial Cerebrospinal Fluid: Application to the Infant Brain.

Cerebrospinal fluid (CSF) plays an essential role in early postnatal brain development. Extra-axial CSF (EA-CSF) volume, which is characterized by CSF in the subarachnoid space surrounding the brain, is a promising marker in the early detection of young children at risk for neurodevelopmental disorders. Previous studies have focused on global EA-CSF volume across the entire dorsal extent of the brain, and not regionally-specific EA-CSF measurements, because no tools were previously available for extracting local EA-CSF measures suitable for localized cortical surface analysis.

SlicerSALT: Shape AnaLysis Toolbox.

SlicerSALT is an open-source platform for disseminating state-of-the-art methods for performing statistical shape analysis. These methods are developed as 3D Slicer extensions to take advantage of its powerful underlying libraries. SlicerSALT itself is a heavily customized 3D Slicer package that is designed to be easy to use for shape analysis researchers.

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.

Entropy-based Correspondence Improvement of Interpolated Skeletal Models.

Statistical analysis of shape representations relies on having good correspondence across a population. Improving correspondence yields improved statistics. Point distribution models (PDMs) are often used to represent object boundaries.

Non-Euclidean classification of medically imaged objects via s-reps.

Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging.

Fitting Skeletal Object Models Using Spherical Harmonics Based Template Warping.

We present a scheme that propagates a reference skeletal model (s-rep) into a particular case of an object, thereby propagating the initial shape-related layout of the skeleton-to-boundary vectors, called spokes. The scheme represents the surfaces of the template as well as the target objects by spherical harmonics and computes a warp between these via a thin plate spline. To form the propagated s-rep, it applies the warp to the spokes of the template s-rep and then statistically refines.

Skeletal shape correspondence via entropy minimization.

Purpose: Improving the shape statistics of medical image objects by generating correspondence of interior skeletal points.

Data: Synthetic objects and real world lateral ventricles segmented from MR images.

Methods: Each object's interior is modeled by a skeletal representation called the s-rep, which is a quadrilaterally sampled, folded 2-sided skeletal sheet with spoke vectors proceeding from the sheet to the boundary.

A SHAPE-NAVIGATED IMAGE DEFORMATION MODEL FOR 4D LUNG RESPIRATORY MOTION ESTIMATION.

Intensity modulated radiation therapy (IMRT) for cancers in the lung remains challenging due to the complicated respiratory dynamics. We propose a shape-navigated dense image deformation model to estimate the patient-specific breathing motion using 4D respiratory correlated CT (RCCT) images. The idea is to use the shape change of the lungs, the major motion feature in the thorax image, as a surrogate to predict the corresponding dense image deformation from training.

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 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.

Shape-correlated Deformation Statistics for Respiratory Motion Prediction in 4D Lung.

4D image-guided radiation therapy (IGRT) for free-breathing lungs is challenging due to the complicated respiratory dynamics. Effective modeling of respiratory motion is crucial to account for the motion affects on the dose to tumors. We propose a shape-correlated statistical model on dense image deformations for patient-specic respiratory motion estimation in 4D lung IGRT.

Automatic shape model building based on principal geodesic analysis bootstrapping.

We present a novel method for automatic shape model building from a collection of training shapes. The result is a shape model consisting of the mean model and the major modes of variation with a dense correspondence map between individual shapes. The framework consists of iterations where a medial shape representation is deformed into the training shapes followed by computation of the shape mean and modes of shape variation.

Automated finite-element analysis for deformable registration of prostate images.

Two major factors preventing the routine clinical use of finite-element analysis for image registration are: 1) the substantial labor required to construct a finite-element model for an individual patient's anatomy and 2) the difficulty of determining an appropriate set of finite-element boundary conditions. This paper addresses these issues by presenting algorithms that automatically generate a high quality hexahedral finite-element mesh and automatically calculate boundary conditions for an imaged patient. Medial shape models called m-reps are used to facilitate these tasks and reduce the effort required to apply finite-element analysis to image registration.

Geometrically proper models in statistical training.

In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of the training seriously affects the final results of segmentation or of significant difference finding between classes.

Population-based fitting of medial shape models with correspondence optimization.

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.

Regional appearance in deformable model segmentation.

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.

Multi-figure anatomical objects for shape statistics.

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.

A method and software for segmentation of anatomic object ensembles by deformable m-reps.

Deformable shape models (DSMs) comprise a general approach that shows great promise for automatic image segmentation. Published studies by others and our own research results strongly suggest that segmentation of a normal or near-normal object from 3D medical images will be most successful when the DSM approach uses (1) knowledge of the geometry of not only the target anatomic object but also the ensemble of objects providing context for the target object and (2) knowledge of the image intensities to be expected relative to the geometry of the target and contextual objects. The segmentation will be most efficient when the deformation operates at multiple object-related scales and uses deformations that include not just local translations but the biologically important transformations of bending and twisting, i.

Comparison of human and automatic segmentations of kidneys from CT images.

Purpose: A controlled observer study was conducted to compare a method for automatic image segmentation with conventional user-guided segmentation of right and left kidneys from planning computerized tomographic (CT) images.

Methods And Materials: Deformable shape models called m-reps were used to automatically segment right and left kidneys from 12 target CT images, and the results were compared with careful manual segmentations performed by two human experts. M-rep models were trained based on manual segmentations from a collection of images that did not include the targets.

Extracting branching tubular object geometry via cores.

Blood vessels and other anatomic objects in the human body can be described as trees of branching tubes. The focus of this paper is the extraction of the branching geometry in three-dimensional, as well as the extraction of the tubes themselves, via skeletons computed as cores. Cores are height ridges of a graded measure of medial strength called medialness, which measures how much a given location resembles the middle of an object as indicated by image intensities.

Feature selection for shape-based classification of biological objects.

This paper introduces a method for selecting subsets of relevant statistical features in biological shape-based classification problems. The method builds upon existing feature selection methodology by introducing a heuristic that favors the geometric locality of the selected features. This heuristic effectively reduces the combinatorial search space of the feature selection problem.

Principal geodesic analysis for the study of nonlinear statistics of shape.

A primary goal of statistical shape analysis is to describe the variability of a population of geometric objects. A standard technique for computing such descriptions is principal component analysis. However, principal component analysis is limited in that it only works for data lying in a Euclidean vector space.

Deformable M-Reps for 3D Medical Image Segmentation.

(formerly called DSLs) are a multiscale medial means for modeling and rendering 3D solid geometry. They are particularly well suited to model anatomic objects and in particular to capture prior geometric information effectively in deformable models segmentation approaches. The representation is based on , which define objects at coarse scale by a hierarchy of figures - each figure generally a slab representing a solid region and its boundary simultaneously.