Balasubramanian S

• Doctor of Philosophy (computer science)
• Sri Sathya Sai Institute of Higher Learning

We obtain rigidity and triviality results for q -solitons, assuming that the structure tensor q satisfies a condition analogous to the twice contracted second Bianchi identity (in particular, divergence free and trace free) and that the soliton vector field is projective and an infinitesimal harmonic transformation. In particular, the efficacy of o...

Feature Distillation (FD) strategies are proven to be effective in mitigating Catastrophic Forgetting (CF) seen in Class Incremental Learning (CIL). However, current FD approaches enforce strict alignment of feature magnitudes and directions across incremental steps, limiting the model's ability to adapt to new knowledge. In this paper we propose S...

Gastrointestinal (GI) bleeding is a serious medical condition that presents significant diagnostic challenges, particularly in settings with limited access to healthcare resources. Wireless Capsule Endoscopy (WCE) has emerged as a powerful diagnostic tool for visualizing the GI tract, but it requires time-consuming manual analysis by experienced ga...

Objects in the visual field are perceived to have an inherent structure that is seen in the way that they are constructed from their components. For example, a face requires its parts to be arranged in a certain spatial configuration. This property, of having such a structure, is termed as compositionality. For deep neural networks to preserve thes...

We provide a direct proof of the result “A closed Yamabe soliton of dimension ≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ge 3$$\end{document} has constant scala...

We derive a divergence formula for an m-quasi Yamabe gradient soliton with finite m, and use it to give a short proof of the result “A compact m-quasi Yamabe gradient soliton \((M^n,g)\), \(n\ge 3\), with finite m, has constant scalar curvature”. We also show that an m-quasi Yamabe gradient soliton with finite m and positive scalar curvature, whose...

It is shown that the scalar curvature of a Yamabe soliton as a Sasakian manifold is constant and the soliton vector field is Killing. The same conclusion is shown to hold for a Yamabe soliton as a K-contact manifold M^{2n+1} if any one of the following conditions hold: (i) its scalar curvature is constant along the soliton vector field V , (ii) V i...

The real-world facial expression recognition (FER) datasets suffer from noisy annotations due to crowd-sourcing, ambiguity in expressions, the subjectivity of annotators, and inter-class similarity. However, the recent deep networks have a strong capacity to memorize the noisy annotations leading to corrupted feature embedding and poor generalizati...

We study a non-trivial radially flat generalized m-quasi Einstein manifold M with finite m and Codazzi Ricci tensor, and obtain an explicit expression of the Ricci tensor over an open dense subset \(M^{*}\) of M on which the gradient of the potential function vanishes nowhere. Further, we prove that \(M^{*}\) is either Ricci-flat or is a non-steady...

The hindering problem in facial expression recognition (FER) is the presence of inaccurate annotations referred to as noisy annotations in the datasets. These noisy annotations are present in the datasets inherently because the labeling is subjective to the annotator, clarity of the image, etc. Recent works use sample selection methods to solve thi...

We study a complete connected generalized m-quasi-Einstein manifold M with finite m, admitting a non-homothetic, non-parallel, complete closed conformal vector field V, and show that either M is isometric to a round sphere, or the Ricci tensor can be expressed explicitly in terms of the conformal data over an open dense subset. In the latter case,...

We study a non-trivial generalized $m$-quasi Einstein manifold $M$ with finite $m$ and associated divergence-free affine Killing vector field, and show that $M$ reduces to an $m$-quasi Einstein manifold. In addition, if $M$ is complete, then it splits as the product of a line and an $(n-1)$-dimensional negatively Einstein manifold. Finally, we show...

The fifth Affective Behavior Analysis in-the-wild (ABAW) competition has multiple challenges such as Valence-Arousal Estimation Challenge, Expression Classification Challenge, Action Unit Detection Challenge, Emotional Reaction Intensity Estimation Challenge. In this paper we have dealt only expression classification challenge using multiple approa...

Automatic facial affect recognition has wide applications in areas like education, gaming, software development, automotives, medical care, etc. but it is non trivial task to achieve appreciable performance on in-the-wild data sets. Though these datasets represent real-world scenarios better than in-lab data sets, they suffer from the problem of in...

Geometric transformations of the training data as well as the test data present challenges to the use of deep neural networks to vision-based learning tasks. To address this issue, we present a deep neural network model that exhibits the desirable property of transformation-robustness. Our model, termed RobustCaps, uses group-equivariant convolutio...

We study a nearly Kaehler manifold M admitting a closed conformal vector field V, and obtain three results under the following assumptions (i) V is almost analytic, (ii) M has real dimension >6, is complete and strictly nearly Kaehler, and (iii) M is complete strictly nearly Kaehler of global constant type.

Advances in networking and digital technologies have led to the widespread usage of Online Signature Verification (OSV) frameworks in real-time settings to validate a user's identity. Because of the superior performance of Deep Learning frameworks, CNN-based models have been widely used for solving difficult computer vision tasks such as Object Det...

Online Signature Verification (OSV) is a systematically used biometric characteristic to endorse the genuineness of a user to access real time applications like healthcare, m-payment, etc. Because OSV frameworks are used in real-time applications and it is difficult to acquire a sufficient number of signature samples from users, they must meet a cr...

An Online signature is a multivariate time series, a commonly used biometric source for user verification. Deep learning (DL) is increasingly becoming ubiquitous as a paradigm for solving problems that come with a wealth of data. Convolution has been its main workhorse. Recently, DL had marked its entry in online signature verification (OSV), a sta...

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction num...

Transformation-robustness is an important feature for machine learning models that perform image classification. Many methods aim to bestow this property to models by the use of data augmentation strategies, while more formal guarantees are obtained via the use of equivariant models. We recognise that compositional, or part-whole structure is also...

Geometric transformations of the training data as well as the test data present challenges to the use of deep neural networks to vision-based learning tasks. In order to address this issue, we present a deep neural network model that exhibits the desirable property of transformation-robustness. Our model, termed RobustCaps, uses group-equivariant c...

Transformation-robustness is an important feature for machine learning models that perform image classification. Many methods aim to bestow this property to models by the use of data augmentation strategies, while more formal guarantees are obtained via the use of equivariant models. We recognise that compositional, or part-whole structure is also...

The presence of noisy annotations in large-scale facial expression datasets has been a key challenge to Facial expression recognition (FER) performance in the wild. Convolutional neural networks tend to fit clean data in the early stages, however, they memorize noisy labels as training progresses which is detrimental to performance. Our proposed ar...

The real-world facial expression recognition (FER) datasets suffer from noisy annotations due to crowd-sourcing, ambiguity in expressions, the subjectivity of annotators and inter-class similarity. However, the recent deep networks have strong capacity to memorize the noisy annotations leading to corrupted feature embedding and poor generalization....

Automatic affect recognition has applications in many areas such as education, gaming, software development, automotives, medical care, etc. but it is non trivial task to achieve appreciable performance on in-the-wild data sets. In-the-wild data sets though represent real-world scenarios better than synthetic data sets, the former ones suffer from...

Visual Question Answering (VQA) needs a means of evaluating the strengths and weaknesses of models. One aspect of such an evaluation is the evaluation of compositional generalisation, or the ability of a model to answer well on scenes whose scene-setups are different from the training set. Therefore, for this purpose, we need datasets whose train a...

Since the renaissance of deep learning (DL), facial expression recognition (FER) has received a lot of interest, with continual improvement in the performance. Hand-in-hand with performance, new challenges have come up. Modern FER systems deal with face images captured under uncontrolled conditions (also called in-the-wild scenario) including occlu...

The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a population into five compartments. The Positivity and Boundedness of the system is shown. The Existence and Uniqueness condition for the solution of system of equations is presented. The equilibrium points are calculated and stability analysis i...

Convolutional neural networks (CNNs) are workhorses of deep learning. A popular architecture in CNN is Residual Net (ResNet) that emphasizes on learning a residual mapping rather than directly fit input to output. Subsequent to ResNet, Squeeze and Excitation Network (SENet) introduced a squeeze and excitation block (SE block) on every residual mapp...

One of the ways to train deep neural networks effectively is to use residual connections. Residual connections can be classified as being either identity connections or bridge connections with a reshaping convolution. Empirical observations on CIFAR-10 and CIFAR-100 datasets using a baseline ResNet model, with bridge connections removed, have shown...

Presence of noise in the labels of large scale facial expression datasets has been a key challenge towards Facial Expression Recognition (FER) in the wild. During early learning stage, deep networks fit on clean data. Then, eventually, they start overfitting on noisy labels due to their memorization ability, which limits FER performance. This work...

Facial expression recognition (FER) in the wild is crucial for building reliable human-computer interactive systems. However, annotations of large scale datasets in FER has been a key challenge as these datasets suffer from noise due to various factors like crowd sourcing, subjectivity of annotators, poor quality of images, automatic labelling base...

Since the renaissance of deep learning (DL), facial expression recognition (FER) has received a lot of interest, with continual improvement in the performance. Hand-in-hand with performance, new challenges have come up. Modern FER systems deal with face images captured under uncontrolled conditions (also called in-the-wild scenario) including occlu...

In this study, we formulate a mathematical model incorporating age specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the model and calculate the basic reproduction number. We then...

Attention based convolutional neural networks(CNNs) for facial expression recognition (FER) apply attention that is uniform across either spatial dimensions or channel dimensions or both spatial and channel dimensions. However, there are many issues viz. (i) in the presence of occlusions and pose variations, different channels respond differently,...

The dynamics of COVID-19 in India are captured using a set of delay differential equations by dividing a constant population into six compartments. The equilibrium points are calculated and stability analysis is performed. Sensitivity analysis is performed on the parameters of the model. Bifurcation analysis is performed and the critical delay is c...

We propose a capsule based regression network (CaReNet), a framework that is based on capsule networks (CapsNet), rather than on the conventional convolutional neural networks (CNNs) to determine estimates of continuous variables. The core principles of CaReNet remain that of routing-by-agreement and translation equivariance proposed in the CapsNet...

Human visual system (HVS) is naturally attracted to the salient regions that appear distinctly in the foreground of a scene. However, for a machine, automatically detecting the region of saliency is a challenging problem. Recently, a generative model namely Saliency GAN (SalGAN) discriminates if a pixel is salient or not by generating the saliency...

Deep Neural Networks (DNNs) are vulnerable to adversarial perturbations of the input data. For DNNs to be deployed in critical applications, they have to be made robust to such perturbations. In this work, we test an existing strategy and propose a new strategy based on autoencoders to defend DNNs against adversarial attacks. The first strategy is...

A formal description of the compositionality of neural networks is associated directly with the formal grammar-structure of the objects it seeks to represent. This formal grammar-structure specifies the kind of components that make up an object, and also the configurations they are allowed to be in. In other words, objects can be described as a par...

Facial expression recognition(FER) in the wild is crucial for building reliable human-computer interactive systems. However, current FER systems fail to perform well under various natural and un-controlled conditions. This report presents attention based framework used in our submission to expression recognition track of the Affective Behaviour Ana...

Deep networks involve a huge amount of computation during the training phase and are prone to over-fitting. To ameliorate these, several conventional techniques such as DropOut, DropConnect, Guided Dropout, Stochastic Depth, and BlockDrop have been proposed. These techniques regularize a neural network by dropping nodes, connections, layers, or blo...

A recent trend to recognize facial expressions in the real-world scenario is to deploy attention based convolutional neural networks (CNNs) locally to signify the importance of facial regions and, combine it with global facial features and/or other complementary context information for performance gain. However, in the presence of occlusions and po...

We propose a capsule based regression network (CaReNet), a framework that is based on capsule networks (CapsNet), rather than on the conventional convolutional neural networks (CNNs) to determine estimates of continuous variables. The core principles of CaReNet remain that of routing-by-agreement and translation equivariance proposed in the CapsNet...

Human visual system (HVS) is naturally attracted to the salient regions that appear distinctly in the foreground of a scene. However, for a machine, automatically detecting the region of saliency is a challenging problem. Recently, a generative model namely Saliency GAN (SalGAN) discriminates if a pixel is salient or not by generating the saliency...

Deep Neural Networks (DNNs) are vulnerable to adversarial perturbations of the input data. For DNNs to be deployed in critical applications, they have to be made robust to such perturbations. In this work, we test an existing strategy and propose a new strategy based on autoencoders to defend DNNs against adversarial attacks. The first strategy is...

Capsule networks are constrained by their, relative, inability to deeper in a parameter-inexpensive manner, and also by the general lack of equivariance guarantees. As a step towards bridging these two gaps, we present a new variation of capsule networks termed Space-of-Variation networks (SOVNET). Each layer in SOVNET learns to projectively repres...

Sketching is more fundamental to human cognition than speech. Deep Neural Networks (DNNs) have achieved the state-of-the-art in speech-related tasks but have not made significant development in generating stroke-based sketches a.k.a sketches in vector format. Though there are Variational Auto Encoders (VAEs) for generating sketches in vector format...

Deep Learning (DL) is emerging victorious in many areas. But very deep networks regularly overfit and involve excess number of computations during training. DropOut, DropConnect, Stochastic Depth, BlockDrop are techniques that regularize the model and also reduce computational burden. These techiques either drop nodes or connections or layers or bl...

Convolutional Neural Networks (CNN) are workhorses of deep learning. A popular architecture in CNN is Residual Net (ResNet) that emphasizes on learning a residual mapping rather than directly fit input to output. Subsequent to ResNet, Squeeze and Excitation network (SENet) introduced a squeeze and excitation block (SE block) on every residual mappi...

One of the ways to train deep neural networks effectively is to use residual connections. Residual connections can be classified as being either identity connections or bridge-connections with a reshaping convolution. Empirical observations on CIFAR-10 and CIFAR-100 datasets using a baseline Resnet model, with bridge-connections removed, have shown...

The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the existence of a test or criterion for deciding the feasibility of attempting to learn. We investigate the existence...

We obtain an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient. Next we provide a condition for a Ricci soliton on a Kaehler manifold to be a Kaehler–Ricci soliton. Finally we give an example supporting the first result.

Popular code optimization techniques involve static examination of the code to find the scope for optimization. In this work we propose a first of its kind machine learning based kernel specific model that is architecture independent to automate the selection of block dimensions for GPU kernels. A neural network model is trained using problem sizes...

Image inpainting is a process of retrieving missing portions of an image without introducing undesirable artifacts. Methods based on partial differential equations, variational formulations and diffusion are local in nature. They work well in propagating the geometry of images into target region. However, they fail to predict the values for large m...

General spectral Clustering(SC) algorithms employ top eigenvectors of normalized Laplacian for spectral rounding. However, recent research has pointed out that in case of noisy and sparse data, all top eigenvectors may not be informative or relevant for the purpose of clustering. Use of these eigenvectors for spectral rounding may lead to bad clust...

Image reconstruction is a process of obtaining the original image from corrupted data. Applications of image reconstruction include Comput er Tomography, radar imaging, weather forecasting etc. Recently steering kernel regressio n method has been applied for image reconstruction [1]. There are two major drawbacks i n this technique. Firstly, it...

The PageRank algorithm for determining the "importance" of Web pages forms the core component of Google's search technology. As the Web graph is very large, containing over a billion nodes, PageRank is generally computed offline, during the preprocessing of the Web crawl, before any queries have been issued. Viewed math-ematically, PageRank is noth...

In this paper we propose a novel method for automatic detection red lesions in digital fundus images. Candidate red lesions are extracted by a novel method called automatic seed generation (ASG). For classification, an implicitly hybrid classifier called spatio temporal feature map classifier (STFM) has been employed. Inclusion of a new feature cal...

In this paper we propose a novel method for automatic detection of microaneurysms (MA) and hemorrhages (HG)grouped as red lesions. Candidate extraction is achieved by automatic seed generation (ASG) which is devoid of morphological top hat transform (MTH). For classification we tested on linear discriminant classifier (LMSE), kNN, GMM, SVM and prop...

One of the major areas of medical research is the design and implementation of intelligent decision support systems for medical professionals. In this context, digital medical image analysis plays an important role in building computational tools to assist physicians in quantification and visualization of pathology and anatomical structures. Such t...

Segmentation of Blood vessels is of key importance in the diagnosis of retinal images and early detection of diabetic retinopathy. In this paper, we propose a novel approach for segmentation of blood vessels in digital fundus retinal images using a fractional derivative-based edge operator. We have tested our algorithm on the standard DRIVE databas...

The automatic screening of patients for early detection and prevention of diabetic retinopathy (DR) has been the prime focus in recent times due to the large ratio of patients to medical ophthalmologists. Exudate detection is one of the main steps of DR. A reliable method for detection of exudates is presented in this paper. Optic disc (OD) is loca...

Accurate segmentation of optic disc (OD) in retinal images is of critical importance in diagnosis of diabetic retinopathy (DR). The accuracy of OD boundary detection using active contours is based on homogeneity of OD region. In this work we improve upon active contour model segmentation of OD from morphologically preprocessed fundus image in the L...

This paper proposes a novel system for the automatic detection of important anatomical structures such as the Optic Disc (OD), Blood Vessels and Macula in digital fundus retinal images. The novelty is in extraction of blood vessels and localization of macula. OD localization is done using Principle Component Analysis (PCA) followed by an active con...

Localization and segmentation of Optic Disk (OD) is an important prerequisite for automatic detection of Diabetic Retinopathy (DR) from digital retinal fundus images. Considerable research has been done to isolate OD with varying degrees of success but on a limited number of images. In this paper we propose a novel algorithm based on Independent Co...

A novel approach for image mosaicing in the JPEG compressed domain is presented in this paper. This technique employs the Hausdorff Distance Metric (HDM) to compute the regions of overlap between two JPEG images. The DCT blocks of the two overlapping images having significant activity are identified using a variance measure and the HDM metric is em...