Department of Mathematics & Computer Science 

Research Areas

COMPUTER VISION, IMAGE/VIDEO PROCESSING AND MACHINE LEARNING
Computer Vision is to enable the machines to see and interpret the real-world scenes imitating human perception and understanding and then to act upon derived understanding.

Image and Video Processing is the area where captured images and videos are processed to enhance its quality, to segment regions of interest, to extract useful features and to perform detailed analysis in offline and real-time modes to enable higher level tasks in Computer Vision.

Machine Learning area is a sub-field of computer science in which the machines are enabled with the ability to learn from data, an important tool for building intelligent machines that can improve the quality of our lives.
RESEARCH SUMMARY
  • Over two decades, the Department of Mathematics and Computer Science (DMACS), has pioneered work on Image Processing, Computer Vision and Machine Learning domains of research. Healthcare and Defence have been the two major focus areas on which the department had gained considerable expertise. DRDO awarded ₹22.00 lakhs for Aerial Image Mosaicing project, followed by ₹41.4 lakhs for Image Segmentation for Defence and Medical Applications, and recently, DRDO has also awarded ₹48.76 lakhs for Near-real time Super Resolution of IR and Visual Video Sequences.
  • DMACS has acquired skills in the areas of image pre-processing, image denoising, image restoration, image enhancement, image super resolution, image segmentation, image inpainting, image mosaicing, image feature extraction, image descriptors, image classification, and image analysis. Similarly, DMACS has also acquired skills in the area of video pre-processing, video 2D/3D motion estimation, video stabilization, video super resolution, object detection, recognition, and tracking in video sequences.
  • DMACS has applied this capability to screen patients with Diabetic Retinopathy and also Children with Acute Lymphoblastic Leukemia. Currently, a research project to provide an online tool for screening Diabetic Retinopathy patients is being pursued to assist doctors/clinicians. Work is underway to identify best-of-breed algorithms for breast cancer detection.
  • DMACS has to its credit a number of publications in reputed international journals, international and national conferences and book chapters.
MAJOR RESEARCH ACTIVITIES
Research Projects
  • Image Segmentation for Defence and Medical Applications for DRDO
  • Near Real-time Video Super Resolution of Visual and IR Sequences for DRDO for aerial surveillance
Collaborations
  • DRDO ER & IP Delhi and ADE Aerial Image Exploitation Centre
  • Sri Sathya Sai Institute of Higher Medical Sciences (SSSIHMS) at Whitefield and Prasanthigram
  • A number of eye research institutes such as Sankara Nethralaya, Agarwal Eye Hospital, Narayana Nethralaya, and SSSIHMS
  • Zentron labs, Bangalore
Other Activities
  • We have also embarked on a health-informatics project on data pertaining to patients having Rheumatoid Heart Disease using machine learning, data mining and natural language processing
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CRYPTOGRAPHY
Cryptography is a field that focuses on providing safe, and secure communications and exchange of sensitive information between parties. It attempts to develop systems that will make the time to decode the encrypted messages unimaginably large to thwart all possible attacks.
RESEARCH SUMMARY
  • Over the last five years, DMACS has pioneered work on Encryption using Chaotic Dynamical Systems such as Lorentz attractors, Elliptic Curve Cryptography and Number Theoretic Encryption Techniques.
  • DMACS has acquired reasonable skills in the areas of image encryption, multi-linear maps, digital signatures and non-commutative algebraic cryptography. It has also acquired detailed mathematical background for conducting research in use of elliptic curves in cryptography.
  • Currently DMACS is being supported under the ISRO/RESPOND scheme for research work on Elliptic Curve Cryptography.
MAJOR RESEARCH ACTIVITIES
Research Projects
  • ISRO/RESPOND Project on Elliptic Curve Cryptography
Collaborations
  • Advanced Data Research Institute (ADRIN), Dept. of Space, Hyderabad
  • IIIT, Bangalore, Dr. Vijay Patankar
Other Activities
  • The department has also worked on Digital Watermarking to increase the payload capability. It has also researched the possibility of using heterogeneous watermarks such as audio file in an image file.
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HIGH PERFORMANCE COMPUTING (HPC)
HPC is a branch of computer science that concentrates on developing supercomputers and software to run on supercomputers. A main area of this discipline is developing parallel processing algorithms and software programs that can be divided into little pieces so that each piece can be executed simultaneously by separate processors. Finding solutions to the challenges in designing supercomputers and large-scale computer clusters to solve advanced computation problems forms part of the core research area of HPC.

HPC has the capacity to handle and analyze massive amounts of data at very high speeds. Tasks that can take months using normal computers can be done in days or even minutes. It can be used to model and solve highly complex problems across a range of high-value sectors.
RESEARCH SUMMARY
  • Over the last ten years, DMACS has acquired satisfactory skills in understanding the super-scalar architectures, high performance computing-related bottlenecks, parallel algorithms, and has enhanced skill sets in CUDA programming and research.
  • DMACS has been recognized by NVIDA as their recognized teaching and research centres in CUDA programming. They have signed a Professor-in-Partnership Program with DMACS providing adequate support in terms of GPGPU hardware. DMACS has been receiving latest versions of GPGPU for research and teaching as part of the CTC CUDA Teaching Centre and CRC CUDA Research Centre.
  • A doctoral research work has been completed in the area of “Topology and Routing Aware Mapping on Parallel Processors”. Another doctoral research work is in progress and it focuses on finding solutions to the problem of I/O bottleneck in HPC applications.
  • DMACS has also been active in Hadoop/Spark platform and is in the process of building an 8 node Hadoop cluster. DMACS has established an 8-node cluster to study various architectures and to support scientific computing across all departments.
  • A number of publications by students of DMACS have won prizes and awards in the International Conference on High Performance Computing being held every year in India.
MAJOR RESEARCH ACTIVITIES
Collaborations
  • Prof. Ashok Srinivasan, University of Florida, USA
  • Prof. Sadayappan, Ohio State University, USA
Other Activities
  • A number of papers showcasing the performance enhancement of applications when they are parallelized have been published.
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DIFFERENTIAL EQUATIONS
Differential Equations is a branch of Analysis which uses analytic or numerical methods to address questions on existence, uniqueness and stability of solutions.

Singular Interface Problems are problems with a differential equation defined on a domain with singularity that can be viewed as ‘holes’ or ‘gaps’ in the domain. The conditions imposed usually indicate the interaction of the boundaries of the singularities.

Fractional Calculus or the non-integer order calculus is an extension of traditional calculus. With the flexibility of a non-integer order derivative, fractional calculus has been found to be useful in describing the dynamical behaviour of materials and processes over vast time and frequency scales with very concise and computable models.

Pseudo-differential Operators are generalization of differential equations using tools of Fourier analysis. These operators due to their geometric and algebraic treatment played a major role in the understanding theoretical questions of Partial Differential Equations.
RESEARCH SUMMARY
  • Singular Interface Problems: Over the last two decades, DMACS has established the area of Singular Interface Problems with both analytic and numerical studies of general nth-order non-linear singular interface problems. Two doctoral research works have been completed in these areas. Further research work is being undertaken in the context of boundary value problems. A proposal to DST to further this research work has been submitted for consideration.
  • Fractional Calculus and Applications to Image Processing: Fractional Differentiation, fractional order derivative and its applications in signal and image processing is now assuming importance for the international scientific community. The present work in DMACS aims to contribute to the area of image processing by studying the filters, transforms and other conventional techniques and their fractional or rather generalized counterparts. A doctoral research is in progress in this area.
  • Pseudo-Differential Operators: A doctoral research work is being carried out on the development and extension of tools required for the local and global well-posedness problems of hyperbolic operators using the pseudo-differential calculus. The main aim of this work is a complete resolution of the Ivrii-Petkov conjecture and to extend the theory of pseudo-differential operators of type S.
  • Mathematical Modelling: In Ecological and Epidemic modelling, the department has worked on the provision of additional food as a tool for biological control of predator-prey systems. The preliminary study of neglected tropical diseases is in progress.
MAJOR RESEARCH ACTIVITIES
Research Projects
  • Under SSSIHL with University of Torino: Theory of Pseudo-Differential operators of type S and Global well-posedness of strictly hyperbolic operators
  • Analytical and numerical studies of general nth order non-linear singular interface problems on time scales submitted to DST
Collaborations
  • Dr. Sandro Coriasco, Dr. Marco Cappiallo and Prof. Luigi Rodino, University of Torino, Italy
  • Prof. P D N Srinivas, Head, Dept. of Mathematics, Andhra University
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© Sri Sathya Sai Institute of Higher Learning, Vidyagiri, Prasanthi Nilayam - 515 134, India.