In this paper a minimally interactive high-throughput system which employs a color gradient based active contour model for rapid and accurate segmentation of multiple target objects on very large images is presented. While geodesic active contours (GAC) have become very popular tools for image segmentation, they tend to be sensitive to model initialization. A second limitation of GAC models is that the edge detector function typically involves use of gray scale gradients; color images usually being converted to gray scale, prior to gradient computation. For color images, however, the gray scale gradient image results in broken edges and weak boundaries, since the other channels are not exploited in the gradient computation. To cope with these limitations, we present a new GAC model that is driven by an accurate and rapid object initialization scheme; hierarchical normalized cuts (HNCut). HNCut draws its strength from the integration of two powerful segmentation strategies—mean shift clustering and normalized cuts. HNCut involves first defining a color swatch (typically a few pixels) from the object of interest. A multi-scale, mean shift coupled normalized cuts algorithm then rapidly yields an initial accurate detection of all objects in the scene corresponding to the colors in the swatch. This detection result provides the initial contour for a GAC model. The edge-detector function of the GAC model employs a local structure tensor based color gradient, obtained by calculating the local min/max variations contributed from each color channel. We show that the color gradient based edge-detector function results in more prominent boundaries compared to the classical gray scale gradient based function. By integrating the HNCut initialization scheme with color gradient based GAC (CGAC), HNCut-CGAC embodies five unique and novel attributes: 1) Efficiency in segmenting multiple target structures; 2) The ability to segment multiple objects from very large images; 3) Minimal human interaction; 4) Accuracy; and 5) Reproducibility. A quantitative and qualitative comparison of the HNCut-CGAC model against other state of the art active contour schemes (including a Hybrid Active Contour model (Paragios-Deriche) and a region based AC model (Rousson-Deriche)), across 196 digitized prostate histopathology images, suggests that HNCut-CGAC is able to outperform state of the art hybrid and region based AC techniques. Our results show that HNCut-CGAC is computationally efficient and may be easily applied to a variety of different problems and applications.

To this day, von Neumann definition of entropy remains the most popular measure of quantum entanglement. Much of the literature on entanglement entropy, particularly in the context of field theory, has focused on isolating the UV divergences. Zero-mode divergences of the entanglement entropy are less studied in this context, and apart from being easier to isolate, they offer an interesting insight into the physics of the system. To gain a better understanding of the system in this limit, we develop the free particle approximation of Harmonic oscillator, with which we investigate the properties of entropy divergence in continuous bi-partite quantum systems such as the coupled Harmonic oscillators and the Hydrogen atom. We also show zero-mode divergence of the entropy of environment-induced entanglement in a tri-partite oscillator system. We discuss the implications of our result for field theory and IR structure of gravity.

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Ayurveda is a traditional medicine and natural healing system in India. Nadi-Nidan (pulse-based diagnosis) is a prominent method in Ayurveda, and is known to dictate all the salient features of a human body. In this paper, we provide details of our procedure for obtaining the complete spectrum of the nadi pulses as a time series. The system Nadi Tarangini1 contains a diaphragm element equipped with strain gauge, a transmitter cum amplifier, and a digitizer for quantifying analog signal. The system acquires the data with 16-bit accuracy with practically no external electronic or interfering noise. Prior systems for obtaining the nadi pulses have been few and far between, when compared to systems such as ECG. The waveforms obtained with our system have been compared with these other similar equipment developed earlier, and is shown to contain more details. The pulse waveform is also shown to have the desirable variations with respect to age of patients, and the pressure applied at the sensing element. The system is being evaluated by Ayurvedic practitioners as a computer-aided diagnostic tool.

We consider the problems of computing the largest area triangle enclosed within a given n-sided convex polygon and the smallest area triangle which encloses a given convex polygon. We show that these problems are closely related by presenting a single sequential linear time algorithm which essentially solves both problems simultaneously. We also present a cost-optimal parallel algorithm that solves both of these problems in O( log log n) time using n/ log log n processors on a CRCW PRAM. In order to achieve these bounds we develop new techniques for the design of parallel algorithms for computational problems involving the rotating calipers method.

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We present a system for accurately quantifying the presence and extent of stain on account of a vascular biomarker on tissue microarrays. We demonstrate our flexible, robust, accurate, and high-throughput minimally supervised segmentation algorithm, termed hierarchical normalized cuts (HNCuts) for the specific problem of quantifying extent of vascular staining on ovarian cancer tissue microarrays. The high-throughput aspect of HNCut is driven by the use of a hierarchically represented data structure that allows us to merge two powerful image segmentation algorithms-a frequency weighted mean shift and the normalized cuts algorithm. HNCuts rapidly traverses a hierarchical pyramid, generated from the input image at various color resolutions, enabling the rapid analysis of large images (e.g., a 1500 × 1500 sized image under 6 s on a standard 2.8-GHz desktop PC). HNCut is easily generalizable to other problem domains and only requires specification of a few representative pixels (swatch) from the object of interest in order to segment the target class. Across ten runs, the HNCut algorithm was found to have average true positive, false positive, and false negative rates (on a per pixel basis) of 82%, 34%, and 18%, in terms of overlap, when evaluated with respect to a pathologist annotated ground truth of the target region of interest. By comparison, a popular supervised classifier (probabilistic boosting trees) was only able to marginally improve on the true positive and false negative rates (84% and 14%) at the expense of a higher false positive rate (73%), with an additional computation time of 62% compared to HNCut. We also compared our scheme against a k-means clustering approach, which both the HNCut and PBT schemes were able to outperform. Our success in accurately quantifying the extent of vascular stain on ovarian cancer TMAs suggests that HNCut could be a very powerful tool in digital pathology and bioinformatics applications where it could be used to facilitate computer-assisted prognostic predictions of disease outcome.