Connecting Markov random fields and active contour models: application to gland segmentation and classification.

We introduce a Markov random field (MRF)-driven region-based active contour model (MaRACel) for histological image segmentation. This Bayesian segmentation method combines a region-based active contour (RAC) with an MRF. State-of-the-art RAC models assume that every spatial location in the image is statistically independent, thereby ignoring valuable contextual information among spatial locations. To address this shortcoming, we incorporate an MRF prior into energy term of the RAC. This requires a formulation of the Markov prior consistent with the continuous variational framework characteristic of active contours; consequently, we introduce a continuous analog to the discrete Potts model. Based on the automated segmentation boundary of glands by MaRACel model, explicit shape descriptors are then employed to distinguish prostate glands belonging to Gleason patterns 3 (G3) and 4 (G4). To demonstrate the effectiveness of MaRACel, we compare its performance to the popular models proposed by Chan and Vese (CV) and Rousson and Deriche (RD) with respect to the following tasks: (1) the segmentation of prostatic acini (glands) and (2) the differentiation of G3 and G4 glands. On almost 600 prostate biopsy needle images, MaRACel was shown to have higher average dice coefficients, overlap ratios, sensitivities, specificities, and positive predictive values both in terms of segmentation accuracy and ability to discriminate between G3 and G4 glands compared to the CV and RD models.

Image Analysis in Surgical Pathology.

Digitization of glass slides of surgical pathology samples facilitates a number of value-added capabilities beyond what a pathologist could previously do with a microscope. Image analysis is one of the most fundamental opportunities to leverage the advantages that digital pathology provides. The ability to quantify aspects of a digital image is an extraordinary opportunity to collect data with exquisite accuracy and reliability. In this review, we describe the history of image analysis in pathology and the present state of technology processes as well as examples of research and clinical use.

Class-specific weighting for Markov random field estimation: application to medical image segmentation.

Many estimation tasks require Bayesian classifiers capable of adjusting their performance (e.g. sensitivity/specificity). In situations where the optimal classification decision can be identified by an exhaustive search over all possible classes, means for adjusting classifier performance, such as probability thresholding or weighting the a posteriori probabilities, are well established. Unfortunately, analogous methods compatible with Markov random fields (i.e. large collections of dependent random variables) are noticeably absent from the literature. Consequently, most Markov random field (MRF) based classification systems typically restrict their performance to a single, static operating point (i.e. a paired sensitivity/specificity). To address this deficiency, we previously introduced an extension of maximum posterior marginals (MPM) estimation that allows certain classes to be weighted more heavily than others, thus providing a means for varying classifier performance. However, this extension is not appropriate for the more popular maximum a posteriori (MAP) estimation. Thus, a strategy for varying the performance of MAP estimators is still needed. Such a strategy is essential for several reasons: (1) the MAP cost function may be more appropriate in certain classification tasks than the MPM cost function, (2) the literature provides a surfeit of MAP estimation implementations, several of which are considerably faster than the typical Markov Chain Monte Carlo methods used for MPM, and (3) MAP estimation is used far more often than MPM. Consequently, in this paper we introduce multiplicative weighted MAP (MWMAP) estimation-achieved via the incorporation of multiplicative weights into the MAP cost function-which allows certain classes to be preferred over others. This creates a natural bias for specific classes, and consequently a means for adjusting classifier performance. Similarly, we show how this multiplicative weighting strategy can be applied to the MPM cost function (in place of the strategy we presented previously), yielding multiplicative weighted MPM (MWMPM) estimation. Furthermore, we describe how MWMAP and MWMPM can be implemented using adaptations of current estimation strategies such as iterated conditional modes and MPM Monte Carlo. To illustrate these implementations, we first integrate them into two separate MRF-based classification systems for detecting carcinoma of the prostate (CaP) on (1) digitized histological sections from radical prostatectomies and (2) T2-weighted 4 Tesla ex vivo prostate MRI. To highlight the extensibility of MWMAP and MWMPM to estimation tasks involving more than two classes, we also incorporate these estimation criteria into a MRF-based classifier used to segment synthetic brain MR images. In the context of these tasks, we show how our novel estimation criteria can be used to arbitrarily adjust the sensitivities of these systems, yielding receiver operator characteristic curves (and surfaces).

Detection of prostate cancer on histopathology using color fractals and Probabilistic Pairwise Markov models.

In this paper we present a system for detecting regions of carcinoma of the prostate (CaP) in H&E stained radical prostatectomy specimens using the color fractal dimension. Color textural information is known to be a valuable characteristic to distinguish CaP from benign tissue. In addition to color information, we know that cancer tends to form contiguous regions. Our system leverages the color staining information of histology as well as spatial dependencies. The color and textural information is first captured using color fractal dimension. To incorporate spatial dependencies, we combine the probability map constructed via color fractal dimension with a novel Markov prior called the Probabilistic Pairwise Markov Model (PPMM). To demonstrate the capability of this CaP detection system, we applied the algorithm to 27 radical prostatectomy specimens from 10 patients. A per pixel evaluation was conducted with ground truth provided by an expert pathologist using only the color fractal feature first, yielding an area under the receiver operator characteristic curve (AUC) curve of 0.790. In conjunction with a Markov prior, the resultant color fractal dimension + Markov random field (MRF) classifier yielded an AUC of 0.831.

Markov random field driven region-based active contour model (MaRACel): application to medical image segmentation.

In this paper we present a Markov random field (MRF) driven region-based active contour model (MaRACel) for medical image segmentation. State-of-the-art region-based active contour (RAC) models assume that every spatial location in the image is statistically independent of the others, thereby ignoring valuable contextual information. To address this shortcoming we incorporate a MRF prior into the AC model, further generalizing Chan & Vese's (CV) and Rousson and Deriche's (RD) AC models. This incorporation requires a Markov prior that is consistent with the continuous variational framework characteristic of active contours; consequently, we introduce a continuous analogue to the discrete Potts model. To demonstrate the effectiveness of MaRACel, we compare its performance to those of the CV and RD AC models in the following scenarios: (1) the qualitative segmentation of a cancerous lesion in a breast DCE-MR image and (2) the qualitative and quantitative segmentations of prostatic acini (glands) in 200 histopathology images. Across the 200 prostate needle core biopsy histology images, MaRACel yielded an average sensitivity, specificity, and positive predictive value of 71%, 95%, 74% with respect to the segmented gland boundaries; the CV and RD models have corresponding values of 19%, 81%, 20% and 53%, 88%, 56%, respectively.

High-throughput detection of prostate cancer in histological sections using probabilistic pairwise Markov models.

In this paper we present a high-throughput system for detecting regions of carcinoma of the prostate (CaP) in HSs from radical prostatectomies (RPs) using probabilistic pairwise Markov models (PPMMs), a novel type of Markov random field (MRF). At diagnostic resolution a digitized HS can contain 80Kx70K pixels - far too many for current automated Gleason grading algorithms to process. However, grading can be separated into two distinct steps: (1) detecting cancerous regions and (2) then grading these regions. The detection step does not require diagnostic resolution and can be performed much more quickly. Thus, we introduce a CaP detection system capable of analyzing an entire digitized whole-mount HS (2x1.75cm(2)) in under three minutes (on a desktop computer) while achieving a CaP detection sensitivity and specificity of 0.87 and 0.90, respectively. We obtain this high-throughput by tailoring the system to analyze the HSs at low resolution (8microm per pixel). This motivates the following algorithm: (Step 1) glands are segmented, (Step 2) the segmented glands are classified as malignant or benign, and (Step 3) the malignant glands are consolidated into continuous regions. The classification of individual glands leverages two features: gland size and the tendency for proximate glands to share the same class. The latter feature describes a spatial dependency which we model using a Markov prior. Typically, Markov priors are expressed as the product of potential functions. Unfortunately, potential functions are mathematical abstractions, and constructing priors through their selection becomes an ad hoc procedure, resulting in simplistic models such as the Potts. Addressing this problem, we introduce PPMMs which formulate priors in terms of probability density functions, allowing the creation of more sophisticated models. To demonstrate the efficacy of our CaP detection system and assess the advantages of using a PPMM prior instead of the Potts, we alternately incorporate both priors into our algorithm and rigorously evaluate system performance, extracting statistics from over 6000 simulations run across 40 RP specimens. Perhaps the most indicative result is as follows: at a CaP sensitivity of 0.87 the accompanying false positive rates of the system when alternately employing the PPMM and Potts priors are 0.10 and 0.20, respectively.