Robert E. Broadhurst

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. 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.

Histogram statistics of local model-relative image regions

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 Movers 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.

A statistical appearance model based on intensity quantile histograms

We present a novel histogram method for statistically characterizing the appearance of deformable models. In deformable model segmentation, appearance models measure the likelihood of an object given a target image. To determine this likelihood we compute pixel intensity quantile histograms of object-relative image regions from a weighted 3D image volume near the object boundary. We use a Gaussian model to statistically characterize the variation of histograms understood in Euclidean space via the Mallows distance. The probability of gas and bone tissue intensities are separately modeled to leverage a priori information on their expected distributions. The method is illustrated and evaluated in a segmentation study on CT images of the human left kidney. Results show improvement over a profile based appearance model and that the global maximum of the MAP estimate gives clinically acceptable segmentations in almost all of the cases studied

CLUSTERING ON LOCAL APPEARANCE FOR DEFORMABLE MODEL SEGMENTATION

We present a novel local region approach for statistically characterizing appearance in the context of medical image segmentation via deformable models. Our appearance model reflects the inhomogeneity of tissue mixtures around the exterior of the object of interest by determining mixture-consistent local region types relative to the object boundary. The region types are formed by clustering local regional image descriptors. We partition the object boundary according to region type and apply principal component analysis on the cluster populations to acquire a statistical model of object appearance that accounts for local variability in the object exterior. We present results using this approach to segment bladders and prostates in CT in the context of day-to-day adaptive radiotherapy for prostate cancer. Results show improved fits versus those obtained with a previously developed method

Signaling local non-credibility in an automatic segmentation pipeline

The advancing technology for automatic segmentation of medical images should be accompanied by techniques to inform the user of the local credibility of results. To the extent that this technology produces clinically acceptable segmentations for a significant fraction of cases, there is a risk that the clinician will assume every result is acceptable. In the less frequent case where segmentation fails, we are concerned that unless the user is alerted by the computer, she would still put the result to clinical use. By alerting the user to the location of a likely segmentation failure, we allow her to apply limited validation and editing resources where they are most needed. We propose an automated method to signal suspected non-credible regions of the segmentation, triggered by statistical outliers of the local image match function. We apply this test to m-rep segmentations of the bladder and prostate in CT images using a local image match computed by PCA on regional intensity quantile functions. We validate these results by correlating the non-credible regions with regions that have surface distance greater than 5.5mm to a reference segmentation for the bladder. A 6mm surface distance was used to validate the prostate results. Varying the outlier threshold level produced a receiver operating characteristic with area under the curve of 0.89 for the bladder and 0.92 for the prostate. Based on this preliminary result, our method has been able to predict local segmentation failures and shows potential for validation in an automatic segmentation pipeline.

Deep structure of images in populations via geometric models in populations

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.

Statistical Applications with Deformable M-Reps

There are many uses of the means of representing objects by discrete m-reps and of estimating probability distributions on them by extensions of linear statistical techniques to nonlinear manifolds describing the associated nonlinear transformations that were detailed in Chapter 8. Two important ones are described in this chapter: segmentation by posterior optimization and determining the significant shape distinctions that can be found in two different probability distributions on an m-rep with the same topology but from two different classes. Both uses require facing issues of probabilities on geometry at multiple levels of spatial scale. The segmentation problem requires the estimation of the probability of image intensity distributions given the object description; we describe a way of doing that by an extension of principal component analysis to regional intensity summaries produced using the object-relative coordinates provided by m-reps. Applications of both segmentation and determination of shape distinctions to anatomic objects in medical images are described. Also described is a variant on the segmentation program used in estimating the probability density on an m-rep; this program fits an m-rep to a binary image in a way that is intended to achieve correspondence of medial atoms across the training population.

WE‐C‐I‐609‐07: On Constructing Priors and Likelihoods for Deformable Shape Models

Purpose: Explicit deformable shape models (DSMs) can be used in a Bayesian statistical framework to provide a prioriinformation for posterior optimization to match the DSM against a target image for automatic segmentation. In this approach a DSM is initialized in the target image and undergoes a series of deformations to closely match the target object. Deformation is driven by optimizing an objective function with terms for geometric typicality (prior) and model‐to‐image match (likelihood). The purpose of this work was to develop strategy, methodology, and tools for constructing the geometric prior and intensity likelihood for a particular form of DSM called m‐reps. Method and Materials: Geometric truth is defined for an object of interest by a statistically significant collection of expert human segmentations of training images. M‐reps are fit to the human drawn contours by minimizing the distance between the surfaces of the m‐rep and the contours under added conditions that lead to positional correspondence across training cases. The geometry of the resulting set of training m‐reps is analyzed in non‐Euclidean space using an approach called principal geodesic analysis (PGA) to yield a set of eigenmodes that define the geometric prior. The intensity likelihood is constructed by registering each training m‐rep with the corresponding gray scale image and collecting regional intensity information that is statistically characterized over all training cases. The intensity information can be in several forms including linear profiles and regional histograms. Results: PGA produces modes that include natural deformations such as local twisting, bending, bulging, and constricting. Unlike analysis in Euclidean space, improper shapes are avoided. The form of the intensity prior can be customized to each object of interest for optimal performance. Conclusion: These methods are powerful, robust and generalizable to other DSMs. Conflict of Interest: The presenting author has a financial interest in Morphormics, Inc.