Madhur Srivastava

Madhur Srivastava

The paper presents a binarization scheme that converts non-binary data into a set of binary strings. At present, there are many binarization algorithms, but they are optimal for only specific probability distributions of the data source. Overcoming the problem, it is shown in this paper that the presented binarization scheme conserves the entropy of the original data having any probability distribution of $m$-ary source. The major advantages of this scheme are that it conserves entropy without the knowledge of the source and the probability distribution of the source symbols. The scheme has linear complexity in terms of the length of the input data. The binarization scheme can be implemented in Context-based Adaptive Binary Arithmetic Coding (CABAC) for video and image compression. It can also be utilized by various universal data compression algorithms that have high complexity in compressing non-binary data, and by binary data compression algorithms to optimally compress non-binary data.

Madhur Srivastava, Subhayan R. Moulick, Prasanta K. Panigrahi

We propose a novel method for image representation in quantum computers, which uses the two-dimensional (2-D) quantum states to locate each pixel in an image through row-location and column-location vectors for identifying each pixel location. The quantum state of an image is the linear superposition of the tensor product of the m-qubits row-location vector and the n-qubits column-location vector of each pixel. It enables the natural quantum representation of rectangular images that other methods lack. The amplitude/intensity of each pixel is incorporated into the coefficient values of the pixel's quantum state, without using any qubits. Due to the fact that linear superposition, tensor product and qubits form the fundamental basis of quantum computing, the proposed method presents the machine level representation of images on quantum computers. Unlike other methods, this method is a pure quantum representation without any classical components.

Madhur Srivastava, Satish K. Singh, Prasanta K. Panigrahi

The paper presents a non-uniform quantization method for the Detail components in the JPEG2000 standard. Incorporating the fact that the coefficients lying towards the ends of the histogram plot of each Detail component represent the structural information of an image, the quantization step sizes become smaller at they approach the ends of the histogram plot. The variable quantization step sizes are determined by the actual statistics of the wavelet coefficients. Mean and standard deviation are the two statistical parameters used iteratively to obtain the variable step sizes. Moreover, the mean of the coefficients lying within the step size is chosen as the quantized value, contrary to the deadzone uniform quantizer which selects the midpoint of the quantization step size as the quantized value. The experimental results of the deadzone uniform quantizer and the proposed non-uniform quantizer are objectively compared by using Mean-Squared Error (MSE) and Mean Structural Similarity Index Measure (MSSIM), to evaluate the quantization error and reconstructed image quality, respectively. Subjective analysis of the reconstructed images is also carried out. Through the objective and subjective assessments, it is shown that the non-uniform quantizer performs better than the deadzone uniform quantizer in the perceptual quality of the reconstructed image, especially at low bitrates. More importantly, unlike the deadzone uniform quantizer, the non-uniform quantizer accomplishes better visual quality with a few quantized values.

Madhur Srivastava, Satish K. Singh, Prasanta K. Panigrahi

We explicate a semi-automated statistical algorithm for object identification and segregation in both gray scale and color images. The algorithm makes optimal use of the observation that definite objects in an image are typically represented by pixel values having narrow Gaussian distributions about characteristic mean values. Furthermore, for visually distinct objects, the corresponding Gaussian distributions have negligible overlap with each other and hence the Mahalanobis distance between these distributions are large. These statistical facts enable one to sub-divide images into multiple thresholds of variable sizes, each segregating similar objects. The procedure incorporates the sensitivity of human eye to the gray pixel values into the variable threshold size, while mapping the Gaussian distributions into localized δ-functions, for object separation. The effectiveness of this recursive statistical algorithm is demonstrated using a wide variety of images.

Madhur Srivastava, Prasanta K. Panigrahi

The paper introduces the idea of non-uniform quantization in the detail components of wavelet transformed image. It argues that most of the coefficients of horizontal, vertical and diagonal components lie near to zeros and the coefficients representing large differences are few at the extreme ends of histogram. Therefore, this paper advocates need for variable step size quantization scheme which preserves the edge information at the edge of histogram and removes redundancy with the minimal number of quantized values. To support the idea, preliminary results are provided using a non-uniform quantization algorithm. We believe that successful implementation of non-uniform quantization in detail components in JPEG-2000 still image standard will improve image quality and compression efficiency with lesser number of quantized values.

Madhur Srivastava, Yashwant Yashu, Satish K. Singh et al.

In this paper, we carry out a comparative study of the efficacy of wavelets belonging to Daubechies and Coiflet family in achieving image segmentation through a fast statistical algorithm.The fact that wavelets belonging to Daubechies family optimally capture the polynomial trends and those of Coiflet family satisfy mini-max condition, makes this comparison interesting. In the context of the present algorithm, it is found that the performance of Coiflet wavelets is better, as compared to Daubechies wavelet.