BACKGROUND: Supervised classifiers for digital pathology can improve the ability of physicians to detect and diagnose diseases such as cancer. Generating training data for classifiers is problematic, since only domain experts (e.g. pathologists) can correctly label ground truth data. Additionally, digital pathology datasets suffer from the "minority class problem", an issue where the number of exemplars from the non-target class outnumber target class exemplars which can bias the classifier and reduce accuracy. In this paper, we develop a training strategy combining active learning (AL) with class-balancing. AL identifies unlabeled samples that are "informative" (i.e. likely to increase classifier performance) for annotation, avoiding non-informative samples. This yields high accuracy with a smaller training set size compared with random learning (RL). Previous AL methods have not explicitly accounted for the minority class problem in biomedical images. Pre-specifying a target class ratio mitigates the problem of training bias. Finally, we develop a mathematical model to predict the number of annotations (cost) required to achieve balanced training classes. In addition to predicting training cost, the model reveals the theoretical properties of AL in the context of the minority class problem. RESULTS: Using this class-balanced AL training strategy (CBAL), we build a classifier to distinguish cancer from non-cancer regions on digitized prostate histopathology. Our dataset consists of 12,000 image regions sampled from 100 biopsies (58 prostate cancer patients). We compare CBAL against: (1) unbalanced AL (UBAL), which uses AL but ignores class ratio; (2) class-balanced RL (CBRL), which uses RL with a specific class ratio; and (3) unbalanced RL (UBRL). The CBAL-trained classifier yields 2% greater accuracy and 3% higher area under the receiver operating characteristic curve (AUC) than alternatively-trained classifiers. Our cost model accurately predicts the number of annotations necessary to obtain balanced classes. The accuracy of our prediction is verified by empirically-observed costs. Finally, we find that over-sampling the minority class yields a marginal improvement in classifier accuracy but the improved performance comes at the expense of greater annotation cost. CONCLUSIONS: We have combined AL with class balancing to yield a general training strategy applicable to most supervised classification problems where the dataset is expensive to obtain and which suffers from the minority class problem. An intelligent training strategy is a critical component of supervised classification, but the integration of AL and intelligent choice of class ratios, as well as the application of a general cost model, will help researchers to plan the training process more quickly and effectively.

The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate.

Exploiting the quasi-linear relationship between local phase and disparity, phase-differencing registration algorithms provide a fast, powerful means for disparity estimation. Unfortunately, these phase-differencing techniques suffer a significant impediment: phase nonlinearities. In regions of phase nonlinearity, the signals under consideration possess properties that invalidate the use of phase for disparity estimation. This paper uses the amenable properties of Gaussian white noise images to analytically quantify these properties. The improved understanding gained from this analysis enables us to better understand current methodologies for detecting regions of phase instability. Most importantly, we introduce a new, more effective means for identifying these regions based on the second derivative of phase.

If precise calibration information is unavailable, as is often the case for active binocular vision systems, the determination of epipolar lines becomes untenable. Yet, even without instantaneous knowledge of the geometry, the search for corresponding points can be restricted to areas called epipolar spaces. For each point in one image, we define the corresponding epipolar space in the other image as the union of all associated epipolar lines over all possible system geometries. Epipolar spaces eliminate the need for calibration at the cost of an increased search region. One approach to mitigate this increase is the application of a space variant sampling or foveation strategy. While the application of such strategies to stereo vision tasks is not new, only rarely has a foveation scheme been specifically tailored for a stereo vision task. In this paper we derive a foundation of theorems that provide a means for obtaining optimal sampling schemes for a given set of epipolar spaces. An optimal sampling scheme is defined as a strategy that minimizes the average area per epipolar space.

Depth recovery for active binocular vision systems is simplified if the camera geometry is known and corresponding points can be restricted to epipolar lines. Unfortunately, computation of epipolar lines requires calibration which can be complex and inaccurate. While it is possible to register images without geometric information, such unconstrained algorithms are usually time consuming and prone to error. In this paper we propose a compromise. Even without the instantaneous knowledge of the system geometry, we can restrict the region of correspondence by imposing limits on the possible range of configurations, and as a result, confine our search for matching points to epipolar spaces. For each point in one image, we define the corresponding epipolar space in the other image as the union of all associated epipolar lines over all possible system geometries. Epipolar spaces eliminate the need for calibration at the cost of an increased search region.

Functional (i.e., logic) verification of the current generation of complex, super-scalar microprocessors such as the PowerPC 604 microprocessor presents significant challenges to a project's verification participants. Simple architectural level tests are insufficient to gain confidence in the quality of the design. Detailed planning must be combined with a broad collection of methods and tools to ensure that design defects are detected as early as possible in a project's life-cycle. This paper discusses the methodology applied to the functional verification of the PowerPC 604 microprocessor.