Joshua H. Levy

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.

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. However, the lack of shape priors in the training stage itself makes it difficult to enforce shape legality, i.e., making the model free of local self-intersection or creases. Shape legality not only yields proper shape statistics but also increases the consistency of parameterization of the object volume and thus proper appearance statistics. In this paper we propose a method incorporating explicit legality constraints in training process. The method is mathematically sound and has proved in practice to lead to shape probability distributions over only proper objects and most importantly to better segmentation results.

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.

Rotational flows for interpolation between sampled surfaces

We introduce a locally defined shape-maintaining method for interpolating between corresponding oriented samples (vertices) from a pair of surfaces. We have applied this method to interpolate synthetic data sets in two and three dimensions and to interpolate medially represented shape models of anatomical objects in three dimensions. In the plane, each oriented vertex follows a circular arc as if it was rotating to its destination. In three dimensions, each oriented vertex moves along a helical path that combines in-plane rotation with translation along the axis of rotation. We show that our planar method provides shape-maintaining interpolations when the reference and target objects are similar. Moreover, the interpolations are size maintaining when the reference and target objects are congruent. In three dimensions, similar objects are interpolated by an affine transformation. We use measurements of the fractional anisotropy of such global affine transformations to demonstrate that our method is generally more-shape preserving than the alternative of interpolating vertices along linear paths irrespective of changes in orientation. In both two and three dimensions we have experimental evidence that when non-shape-preserving deformations are applied to template shapes, the interpolation tends to be visually satisfying with each intermediate object appearing to belong to the same class of objects as the end points.

P2E-3 Blind Source Separation and K-Means Clustering for Vascular ARFI Image Segmentation, In Vivo and Ex Vivo

Blind source separation (BSS) is a time domain method for signal decomposition previously demonstrated in medical ultrasound for adaptive regression filtering. Just as BSS is relevant to clutter rejection by differentiating RF signals from moving blood versus arterial wall tissue, BSS is useful for distinguishing displacement profiles measured in tissue exhibiting different mechanical responses to radiation force. In concert with K-means clustering, an algorithm for partitioning N data points into K subsets, BSS can be employed for automated image segmentation via mechanical property in acoustic radiation force impulse (ARFI) ultrasound. We present BSS-based ARFI image segmentation in application to the peripheral vasculature. First, our segmentation method is validated using a synthetic data set with additive noise. Second, our method is demonstrated in an excised atherosclerotic familial hypercholesterolemic (FH) pig iliac artery with confirmation by matched immunohistochemistry. Finally, the method is applied to segmenting in vivo ARFI images in an atherosclerotic FH pig iliac artery as well as a human popliteal vein with no known disease. This work substantiates additional applications of BSS-based ARFI image segmentation

Image estimation from marker locations for dose calculation in prostate radiation therapy

Tracking implanted markers in the prostate during each radiation treatment delivery provides an accurate approximation of prostate location, which enables the use of higher daily doses with tighter margins of the treatment beams and thus improves the efficiency of the radiotherapy. However, the lack of 3D image data with such a technique prevents calculation of delivered dose as required for adaptive planning. We propose to use a reference statistical shape model generated from the planning image and a deformed version of the reference model fitted to the implanted marker locations during treatment to estimate a regionally dense deformation from the planning space to the treatment space. Our method provides a means of estimating the treatment image by mapping planning image data to treatment space via the deformation field and therefore enables the calculation of dose distributions with marker tracking techniques during each treatment delivery.

A large-to-fine-scale shape prior for probabilistic segmentations using a deformable m-rep

Training a shape prior has been potent scheme for anatomical object segmentations, especially for images with noisy or weak intensity patterns. When the shape representation lives in a high dimensional space, principal component analysis is often used to calculate a low dimensional variation subspace from frequently limited number of training samples. However, the eigenmodes of the sub-space tend to keep the large-scale variation of the shape only, losing the detailed localized variability which is crucial to accurate segmentations. In this paper, we propose a large-to-fine-scale shape prior for probabilistic segmentation to enable local refinement, using a deformable medial representation, called the m-rep. Tests on the goodness of the shape prior are carried out on large simulated data sets of (a) 1000 deformed ellipsoids with mixed global deformations and local perturbation; (b) 500 simulated hippocampus models. The predictability of the shape priors are evaluated and compared by a squared correlations metric and the volume overlap measurement against different training sample sizes. The improved robustness achieved by the large-to-fine-scale strategy is demonstrated, especially for low sample size applications. Finally, posterior 3D segmentations of the bladder from CT images from multiple patients in day-to-day adaptive radiation therapy demonstrate that the local residual statistics introduced by this method improve the segmentation accuracy.