A new equilibrium torus solution and GRMHD initial conditions

General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.Comment: 8 pages, 4 figures, A&A accepte

On the denseness of minimum attaining operators

Let H1,H2 be complex Hilbert spaces and T be a densely defined closed linear operator (not necessarily bounded). It is proved that for each ϵ>0, there exists a bounded operator S with ∥S∥≤ϵ such that T+S is minimum attaining. Further, if T is bounded below, then S can be chosen to be rank one

Statistical Analysis of Estimated Displacement Measurements using Digital Image Correlation

This paper presents details of the statistical analysis of the estimated displacements on a sample of pearlitic steel. It is mostly used in construction, automobiles, and industries.   The displacement measurement of deformation is computed in the horizontal and vertical direction with pixel accuracy. Digital Image Correlation (DIC) is a non-contact technique to estimate u and v displacement. The deformation of the sample is computed using NCORR software. Detailed statistical analysis has shown that the displacements have a strong correlation between them

Impact of Supervision on Rework in Construction Industry

The role of supervision plays a vital role in the construction projects. Supervision due to unskilled labours is believed to be one of the major causes of rework. Therefore, skilled supervisors along with experience play an important role in reducing the amount of rework due to construction defects. This paper shows the quality of site supervision in India as it is related to the levels of experience and skill of a supervisor. Hence, the paper gives the fair idea about the relationship between the quality of site supervision and rework in construction industry. Based on site data collection considering five building construction sites in India, this paper suggests that the principal cause of rework during construction is due to the unskilled supervision without experience which leads to the defects in construction industry

Facial Expression Recognition Using Euclidean Distance Method

Facial expression recognition is found to be useful for emotion science, clinical psychology and pain assessment. In the proposed method, the face detection algorithm involves lighting compensation for getting uniformity on face and morphological operations for retaining the required face portion. After retaining the face portion in the image, the facial features like eyes, nose, and mouth are extracted using AAM (Active Appearance Model) method. For automatic facial expression recognition, simple Euclidean Distance method is used. In this method, the Euclidean distance between the feature points of the training images and that of the query image is compared. Based on minimum Euclidean distance, output image expression is decided

CORRECTING FALSE SEGMENTATION IN VIDEO USING IMAGE OVER-SEGMENTATION

Moving objects detection is a fundamental step in many vision based applications. Background subtraction is the typical method. When scene exhibits pertinent dynamism method based on mixture of Gaussians is a good balance between accuracy and complexity, but fails due to two kinds of false segmentations i.e moving shadows incorrectly detected as objects and some actual moving objects not detected as moving objects. In computer vision, segmentation refers to process of partitioning a digital image in to multiple segments and goal of segmentation is to simplify and/or change representation of image in to something that is more meaningful and easier to analyse. A colour clustering based on k-means and image over-segmentation are used to segment the input frame into patches and shadow suppression done by HSV colour space, the outputs of mixture of Gaussians are combined with the colour clustered regions to a module for area confidence measurement. In this way, two major segment errors can be corrected. Experimental results show that the proposed approach can significantly enhance segmentation results

Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise

Impulse noise is a most common noise which affects the image quality during acquisition or transmission, reception or storage and retrieval process. Impulse noise comes under two categories: (1) fixed-valued impulse noise, also known as salt-and-pepper noise (SPN) due to its appearance, where the noise value may be either the minimum or maximum value of the dynamic gray-scale range of image and (2) random-valued impulse noise (RVIN), where the noisy pixel value is bounded by the range of the dynamic gray-scale of the image. In literature, many efficient filters are proposed to suppress the impulse noise. But their performance is not good under moderate and high noise conditions. Hence, there is sufficient scope to explore and develop efficient filters for suppressing the impulse noise at high noise densities. In the present research work, efforts are made to propose efficient filters that suppress the impulse noise and preserve the edges and fine details of an image in wide range of noise densities. It is clear from the literature that detection followed by filtering achieves better performance than filtering without detection. Hence, the proposed filters in this thesis are based on detection followed by filtering techniques. The filters which are proposed to suppress the SPN in this thesis are: Adaptive Noise Detection and Suppression (ANDS) Filter Robust Estimator based Impulse-Noise Reduction (REIR) Algorithm Impulse Denoising Using Improved Progressive Switching Median Filter (IDPSM) Impulse-Noise Removal by Impulse Classification (IRIC) A Novel Adaptive Switching Filter-I (ASF-I) for Suppression of High Density SPN A Novel Adaptive Switching Filter-II (ASF-II) for Suppression of High Density SPN Impulse Denoising Using Iterative Adaptive Switching Filter (IASF) In the first method, ANDS, neighborhood difference is employed for pixel classification. Controlled by binary image, the noise is filtered by estimating the value of a pixel with an adaptive switching based median filter applied exclusively to neighborhood pixels that are labeled noise-free. The proposed filter performs better in retaining edges and fine details of an image at low-to-medium densities of fixed-valued impulse noise.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities.The REIR method is based on robust statistic technique, where adaptive window is used for pixel classification. The noisy pixel is replaced with Lorentzian estimator or average of the previously processed pixels. Because of adaptive windowing technique, the filter is able to suppress the noise at a density as high as 90%. In the proposed method, IDPSM, the noisy pixel is replaced with median of uncorrupted pixels in an adaptive filtering window. The iterative nature of the filter makes it more efficient in noise detection and adaptive filtering window technique makes it robust enough to preserve edges and fine details of an image in wide range of noise densities. The forth proposed method is IRIC. The noisy pixel is replaced with median of processed pixels in the filtering window. At high noise densities, the median filtering may not be able to reject outliers always. Under such circumstances, the processed left neighboring pixel is considered as the estimated output. The computational complexity of this method is equivalent to that of a median filter having a 3×3 window. The proposed algorithm requires simple physical realization structures. Therefore, this algorithm may be quite useful for online and real-time applications. Two different adaptive switching filters: ASF-I and ASF-II are developed for suppressing SPN at high noise density. The noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Depending on noise estimation, a small filtering window size is initially selected and then the scheme adaptively changes the window size based on the number of noise-free pixels. Therefore, the proposed method removes the noise much more effectively even at noise density as high as 90% and yields high image quality. In the proposed method IASF, noisy pixel is replaced with alpha-trimmed mean value of uncorrupted pixels in the adaptive filtering window. Due to its iterative structure, the performance of this filter is better than existing order-statistic filters. Further, the adaptive filtering window makes it robust enough to preserve the edges and fine details of an image. Novel Restoration Techniques for Images Corrupted with High Density Impulsive Noise x The filters which are proposed for suppressing random-valued impulse noise (RVIN) are: Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm Adaptive Local Thresholding with MAD (ALT-MAD) Algorithm The proposed method, Adaptive Window based Pixel-Wise MAD (AW-PWMAD) Algorithm is a modified MAD (Median of the Absolute Deviations from the median) scheme alongwith a threshold employed for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in adaptive filtering window. Another proposed method for denoising the random-valued and fixed-valued impulse noise is ALT-MAD. A modified MAD based algorithm alongwith a local adaptive threshold is utilized for pixel-classification. The noisy pixel is replaced with median of uncorrupted pixels in the filtering window of adaptively varied size. Three threshold functions are suggested and employed in this algorithm. Thus, three different versions, namely, ALT-MAD-1, ALT-MAD-2 and ALT-MAD-3 are developed. They are observed to be quite efficient in noise detection and filtering. In the last part of the thesis, some efforts are made to develop filters for color image denoising. The filters which perform better in denoising gray-scale images are developed for suppression of impulsive noise from color images. Since the performance of denoising filters degrades in other color spaces, efforts are made to develop color image denoising filters in RGB color space only in this research work. The developed filters are: Multi-Channel Robust Estimator based Impulse-Noise Reduction (MC-REIR) Algorithm Multi-Channel Impulse-Noise Removal by Impulse Classification (MC-IRIC) Multi-Channel Iterative Adaptive Switching Filter (MC-IASF) Multi-Channel Adaptive Local Thresholding with MAD (MC-ALT-MAD) Algorithm It is observed from the simulation results that the proposed filters perform better than the existing methods. The proposed methods: ASF-1 and IASF exhibit quite superior performance in suppressing SPN in high noise densities compared to other methods. Similarly ALT-MAD-3 exhibits much better performance in suppressing RVIN of low to medium noise densities