Andrew Thall

Deformable M-Reps for 3D Medical Image Segmentation

M-reps (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 figural models, which define objects at coarse scale by a hierarchy of figures—each figure generally a slab representing a solid region and its boundary simultaneously. This paper focuses on the use of single figure models to segment objects of relatively simple structure.A single figure is a sheet of medial atoms, which is interpolated from the model formed by a net, i.e., a mesh or chain, of medial atoms (hence the name m-reps), each atom modeling a solid region via not only a position and a width but also a local figural frame giving figural directions and an object angle between opposing, corresponding positions on the boundary implied by the m-rep. The special capability of an m-rep is to provide spatial and orientational correspondence between an object in two different states of deformation. This ability is central to effective measurement of both geometric typicality and geometry to image match, the two terms of the objective function optimized in segmentation by deformable models. The other ability of m-reps central to effective segmentation is their ability to support segmentation at multiple levels of scale, with successively finer precision. Objects modeled by single figures are segmented first by a similarity transform augmented by object elongation, then by adjustment of each medial atom, and finally by displacing a dense sampling of the m-rep implied boundary. While these models and approaches also exist in 2D, we focus on 3D objects.The segmentation of the kidney from CT and the hippocampus from MRI serve as the major examples in this paper. The accuracy of segmentation as compared to manual, slice-by-slice segmentation is reported.

Multiscale deformable model segmentation and statistical shape analysis using medial descriptions

This paper presents a multiscale framework based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery. The segmentation procedure is based on a Bayesian deformable templates methodology in which the prior information about the geometry and shape of anatomical objects is incorporated via the construction of exemplary templates. The anatomical variability is accommodated in the Bayesian framework by defining probabilistic transformations on these templates. The transformations, thus, defined are parameterized directly in terms of natural shape operations, such as growth and bending, and their locations. A preliminary validation study of the segmentation procedure is presented. We also present a novel statistical shape analysis approach based on the medial descriptions that examines shape via separate intuitive categories, such as global variability at the coarse scale and localized variability at the fine scale. We show that the method can be used to statistically describe shape variability in intuitive terms such as growing and bending.

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.e., local rotation, and local magnification. In computer vision an important class of DSM methods uses explicit geometric models in a Bayesian statistical framework to provide a priori information used in posterior optimization to match the DSM against a target image. In this approach a DSM of the object to be segmented is placed in the target image data and undergoes a series of rigid and nonrigid transformations that deform the model to closely match the target object. The deformation process is driven by optimizing an objective function that has terms for the geometric typicality and model-to-image match for each instance of the deformed model. The success of this approach depends strongly on the object representation, i.e., the structural details and parameter set for the DSM, which in turn determines the analytic form of the objective function. This paper describes a form of DSM called m-reps that has or allows these properties, and a method of segmentation consisting of large to small scale posterior optimization of m-reps. Segmentation by deformable m-reps, together with the appropriate data representations, visualizations, and user interface, has been implemented in software that accomplishes 3D segmentations in a few minutes. Software for building and training models has also been developed. The methods underlying this software and its abilities are the subject of this paper.

Core-based portal image registration for automatic radiotherapy treatment verification

PURPOSE Portal imaging is the most important quality assurance procedure for monitoring the reproducibility of setup geometry in radiation therapy. The role of portal imaging has become even more critical in recent years due to the migration of three-dimensional (3D) treatment planning technology, including high-precision conformal therapy, from the research setting to routine clinical practice. Unfortunately, traditional methods for acquiring and interpreting portal images suffer from a number of deficiencies that contribute to the well-documented observation that many setup errors go undetected, and some persist for a clinically significant portion of the prescribed dose. Significant improvements in both accuracy and efficiency of detecting setup errors can, in principle, be achieved by using automatic image registration for on-line screening of images obtained from electronic portal imaging devices (EPIDs). METHODS AND MATERIALS This article presents recent developments in a method called core-based image analysis that shows great promise for achieving the desired improvements in error detection. Core-based image analysis is a fundamental computer vision method that is capable of exploiting the full power of EPIDs by providing for on-line detection of setup errors via automatic registration of user-selected anatomical structures. We describe a robust method for automatic portal image registration based on core analysis and demonstrate an approach for assessing both accuracy and precision of registration methods using realistic, digitally reconstructed portal radiographs (DRPRs) where truth is known. RESULTS Automatic core-based analysis of a set of 20 DRPRs containing known, random field positioning errors was performed for a patient undergoing treatment for prostate cancer. In all cases, the reported translation was within 1 mm of the actual translation with mean absolute errors of 0.3 mm and standard deviations of 0.3 mm. In all cases, the reported rotation was within 0.6 degree of the actual rotation with a mean absolute error of 0.18 degree and a standard deviation of 0.23 degree. CONCLUSION Our results, using digitally reconstructed portal radiographs that closely resemble clinical portal images, suggest that automatic core-based registration is suitable as an on-line screening tool for detecting and quantifying patient setup errors.

Continuous Medial Representations for Geometric Object Modeling in 2D and 3D

We describe a novel continuous medial repre- sentation for describing object geometry and a deformable templates method for tting the representation to images. Our representation simultaneously describes the boundary and medial loci of geometrical objects, always maintaining Blums symmetric axis transform (SAT) relationship. Cu- bic b-splines dene the continuous medial locus and the as- sociated thickness eld, which in turn generate the object boundary. We present geometrical properties of the rep- resentation and derive a set of constraints on the b-spline parameters. The 2D representation encompasses branching medial loci; the 3D version can model objects with a sin- gle medial surface, and the extension to branching medial surfaces is a subject of ongoing research. We present prelim- inary results of segmenting 2D and 3D medical images. The representation is ultimately intended for use in statistical shape analysis.

Extended-precision floating-point numbers for GPU computation

Double-float (df64) and quad-float (qf128) numeric types can be implemented on current GPU hardware and used efficiently and effectively for extended-precision computational arithmetic. Using unevaluated sums of paired or quadrupled f32 single-precision values, these numeric types provide approximately 48 and 96 bits of mantissa respectively at singleprecision exponent ranges for computer graphics, numerical, and general-purpose GPU programming. This paper surveys current art, presents algorithms and Cg implementation for arithmetic, exponential and trigonometric functions, and presents data on numerical accuracy on several different GPUs. It concludes with an in-depth discussion of the application of extended precision primitives to performing fast Fourier transforms on the GPU for real and complex data. [Addendum (July 2009): the presence of IEEE compliant double-precision hardware in modern GPUs from NVidia and other manufacturers has reduced the need for these techniques. The double-precision capabilities can be accessed using CUDA or other GPGPU software, but are not (as of this writing) exposed in the graphics pipeline for use in Cg-based shader code. Shader writers or those still using a graphics API for their numerical computing may still find the methods described herein to be of interest.]

Towards the prioritization of regression test suites with data flow information

Regression test prioritization techniques re-order the execution of a test suite in an attempt to ensure that defects are revealed earlier in the test execution phase. In prior work, test suites were prioritized with respect to their ability to satisfy control flow-based and mutation-based test adequacy criteria. In this paper, we propose an approach to regression test prioritization that leverages the all-DUs test adequacy criterion that focuses on the definition and use of variables within the program under test. Our prioritization scheme is motivated by empirical studies that have shown that (i) tests fulfilling the all-DUs test adequacy criteria are more likely to reveal defects than those that meet the control flow-based criteria, (ii) there is an unclear relationship between all-DUs and mutation-based criteria, and (iii) mutation-based testing is significantly more expensive than testing that relies upon all-DUs.In support of our prioritization technique, we provide a formal statement of the algorithms and equations that we use to instrument the program under test, perform test suite coverage monitoring, and calculate test adequacy. Furthermore, we examine the architecture of a tool that implements our novel prioritization scheme and facilitates experimentation. The use of this tool in a preliminary experimental evaluation indicates that, for three case study applications, our prioritization can be performed with acceptable time and space overheads. Finally, these experiments also demonstrate that the prioritized test suite can have an improved potential to identify defects earlier during the process of test execution.

Multi-scale 3-D Deformable Model Segmentation Based on Medial Description

This paper presents a Bayesian multi-scale three dimensional deformable template approach based on a medial representation for the segmentation and shape characterization of anatomical objects in medical imagery. Prior information about the geometry and shape of the anatomical objects under study is incorporated via the construction of exemplary templates. The anatomical variability is accommodated in the Bayesian framework by defining probabilistic transformations on these templates. The modeling approach taken in this paper for building exemplary templates and associated transformations is based on a multi-scale medial representation. The transformations defined in this framework are parameterized directly in terms of natural shape operations, such as thickening and bending, and their location. Quantitative validation results are presented on the automatic segmentation procedure developed for the extraction of the kidney parenchyma-including the renal pelvis-in subjects undergoing radiation treatment for cancer. We show that the segmentation procedure developed in this paper is efficient and accurate to within the voxel resolution of the imaging modality.

Representing multifigure anatomical objects

We use multifigure m-reps to represent anatomical objects, such as human livers, with named components. Each component is represented as a single figure m-rep. These figures of the object are connected via hinge geometry. A smooth object surface is then computed using our technique based on the subdivision method applied to a single figure m-rep. This novel representation allows us to represent and analyze a complex anatomical object by its individual components, by relations among its components, and by the object itself as a whole entity. Using our representation, some preliminary results on statistical analysis of multifigure anatomical objects are presented.

Object models in multiscale intrinsic coordinates via m-reps

Abstract Object descriptions used for 3D segmentation by deformable models and for statistical characterization of 3D object classes benefit from having intrinsic correspondences over deformation of the objects or multiple instances in the same object class. These correspondences apply over a variety of spatial scale levels and consequently lead to efficient segmentation and probability distributions of geometry that are trainable with an achievable number of training instances. This paper describes a figural coordinate system provided by m-reps models and shows how such coordinates not only provide the required positional correspondences, but also are intuitive and provide orientational and metric correspondences. Examples are given for the segmentation of kidneys from CT and for the statistical characterization of schizophrenia and control classes of cerebral ventricles and of hippocampus pairs.