Survey of Computer Vision and Machine Learning in Gastrointestinal Endoscopy

This paper attempts to provide the reader a place to begin studying the application of computer vision and machine learning to gastrointestinal (GI) endoscopy. They have been classified into 18 categories. It should be be noted by the reader that this is a review from pre-deep learning era. A lot of deep learning based applications have not been covered in this thesis

Benedicks' Theorem for the Weyl Transform

If the set of points where a function is nonzero is of finite measure, and its Weyl transform is a finite rank operator, then the function is identically zero

A non-commutative Sobolev estimate and its application to spectral synthesis

In [M. K. Vemuri, Realizations of the canonical representation], it was shown that the spectral synthesis problem for the Alpha transform is closely related to the problem of classifying realizations of the canonical representation (of the Heisenberg group). In this paper, we show that discrete sets are sets of spectral synthesis for the Alpha transform

Raghavan Narsimhan's proof of L. Schwartz's perturbation theorem

Raghavan Narasimhan outlined a new proof of L. Schwartz's perturbation theorem during a course of lectures at IMSc, Chennai in Spring 2007. The details are given

Hermite expansions and Hardy's theorem

Assuming that both a function and its Fourier transform are dominated by a Gaussian of large variance, it is shown that the Hermite coefficients of the function decay exponentially. A sharp estimate for the rate of exponential decay is obtained in terms of the variance, and in the limiting case (when the variance becomes so small that the Gaussian is its own Fourier transform), Hardy's theorem on Fourier transform pairs is obtained. A quantitative result on the confinement of particle-like states of a quantum harmonic oscillator is obtained. A stronger form of the result is conjectured. Further, it is shown how Hardy's theorem may be derived from a weak version of confinement without using complex analysis.Comment: 11 page

Dictionary Learning and Sparse Coding on Statistical Manifolds

In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new formulation does not explicitly incorporate any sparsity inducing norm in the cost function being optimized but yet yields sparse codes. Our algorithm approximates the data points on the statistical manifold (which are probability distributions) by the weighted Kullback-Leibeler center/mean (KL-center) of the dictionary atoms. The KL-center is defined as the minimizer of the maximum KL-divergence between itself and members of the set whose center is being sought. Further, we prove that the weighted KL-center is a sparse combination of the dictionary atoms. This result also holds for the case when the KL-divergence is replaced by the well known Hellinger distance. From an applications perspective, we present an extension of the aforementioned framework to the manifold of symmetric positive definite matrices (which can be identified with the manifold of zero mean gaussian distributions), $\mathcal{P}_n$. We present experiments involving a variety of dictionary-based reconstruction and classification problems in Computer Vision. Performance of the proposed algorithm is demonstrated by comparing it to several state-of-the-art methods in terms of reconstruction and classification accuracy as well as sparsity of the chosen representation.Comment: arXiv admin note: substantial text overlap with arXiv:1604.0693

Anderson Localization with Second Quantized Fields: Quantum Statistical Aspects

We report a theoretical study of Anderson localization of nonclassical light with emphasis on the quantum statistical aspects of localized light. We demonstrate, from the variance in mean intensity of localized light, as well as site-to-site correlations, that the localized light carries signatures of quantum statistics of input light. For comparison, we also present results for input light with coherent field statistics and thermal field statistics. Our results show that there is an enhancement in fluctuations of localized light due to the medium's disorder. We also find superbunching of the localized light, which may be useful for enhancing the interaction between radiation and matter. Another important consequence of sub-Poissonian statistics of the incoming light is to quench the total fluctuations at the output. Finally, we compare the effects of Gaussian and Rectangular distributions for the disorder, and show that Gaussian disorder accelerates the localization of light

Does normal pupil diameter differences in population underlie the color selection of the #dress?

The fundamental question that arises from the color composition of the #dress is: 'What are the phenomena that underlie the individual differences in colors reported given all other conditions like light and device for display being identical?'. The main color camps are blue/black (b/b) and white/gold (w/g) and a survey of 384 participants showed near equal distribution. We looked at pupil size differences in the sample population of 53 from the two groups plus a group who switched (w/g to b/b). Our results show that w/g and switch population had significantly ( w/g <b/b, p-value = 0.0086) lower pupil size than b/b camp. A standard infinity focus experiment was then conducted on 18 participants from each group to check if there is bimodality in the population and we again found statistically significant difference (w/g < b/b , p-value = 0.0132). Six participants, half from the w/g camp, were administered dilation drops that increased the pupil size by 3-4mm to check if increase in retinal illuminance will trigger a change in color in the w/g group, but the participants did not report a switch. The results suggest a population difference in normal pupil-size in the three groups.Comment: 6 pages, 4 figure

Statistics on the (compact) Stiefel manifold: Theory and Applications

A Stiefel manifold of the compact type is often encountered in many fields of Engineering including, signal and image processing, machine learning, numerical optimization and others. The Stiefel manifold is a Riemannian homogeneous space but not a symmetric space. In previous work, researchers have defined probability distributions on symmetric spaces and performed statistical analysis of data residing in these spaces. In this paper, we present original work involving definition of Gaussian distributions on a homogeneous space and show that the maximum-likelihood estimate of the location parameter of a Gaussian distribution on the homogeneous space yields the Fr\'echet mean (FM) of the samples drawn from this distribution. Further, we present an algorithm to sample from the Gaussian distribution on the Stiefel manifold and recursively compute the FM of these samples. We also prove the weak consistency of this recursive FM estimator. Several synthetic and real data experiments are then presented, demonstrating the superior computational performance of this estimator over the gradient descent based non-recursive counter part as well as the stochastic gradient descent based method prevalent in literature

Targeted Adversarial Examples for Black Box Audio Systems

The application of deep recurrent networks to audio transcription has led to impressive gains in automatic speech recognition (ASR) systems. Many have demonstrated that small adversarial perturbations can fool deep neural networks into incorrectly predicting a specified target with high confidence. Current work on fooling ASR systems have focused on white-box attacks, in which the model architecture and parameters are known. In this paper, we adopt a black-box approach to adversarial generation, combining the approaches of both genetic algorithms and gradient estimation to solve the task. We achieve a 89.25% targeted attack similarity after 3000 generations while maintaining 94.6% audio file similarity.Comment: IEEE Deep Learning and Security Workshop 201