Amit Chattopadhyay

Topological Data Analysis, Geometric Computing, Optimization on Matrix Manifolds, Visualizations and Graphics

 

• Topological Distance between Multi-Fields Based on Multi-Dimensional Persistence Diagrams.  Yashwanth Ramamurthi, Amit Chattopadhyay. March 2023. (arXiv).
• Topological Distance Measure between Multi-Fields for Classification and Analysis of Shapes and Data.  Yashwanth Ramamurthi, Amit Chattopadhyay. March 2023. (arXiv).
• Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices.  Kalyan Varma Nadimpalli, Amit Chattopadhyay, Bastian Rieck. TAG-PRA (Topology, Geometry, Algebra in Pattern Recognition with Applications). A Workshop at the IEEE Computer Vision and Pattern Recognition (IEEE CVPR) in Vancouver, Canada, June 18th, 2023. (arXiv)
• Topological Shape Matching using Multi-Dimensional Reeb Graphs.  Yashwanth Ramamurthi, Amit Chattopadhyay. The Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP). IIT Gandhinagar. Dec. 8-10, 2022.
• A Topological Similarity Measure between Multi-Resolution Reeb Spaces.  Yashwanth Ramamurthi, Tripti Agarwal, Amit Chattopadhyay. IEEE Transactions on Visualization and Computer Graphics, Pages 4360-4374, Vol. 28, Issue 12. 08 June 2021. (DOI: 10.1109/TVCG.2021.3087273)
• Topological Feature Search in Time-Varying Multifield Data. Tripti Agarwal, Amit Chattopadhyay, Vijay Natarajan. Topological Methods in Visualization: Theory, Software and Applications. Ingrid Hotz, Talha Bin Masood, Filip Sadlo, and Julien Tierny (Eds.) Springer-Verlag, Mathematics and Visualization Series. 2021. 

         ​​(Presented in Workshop on Topological Data Analysis and VisualiationTopoInVis 2019, Nykoping, Sweden, June 17-19, 2019.)

• Certified Computation of planar Morse-Smale Complexes of Smooth Functions. Amit Chattopadhyay, Gert Vegter and Chee K. Yap. Journal of Symbolic Computation: Special Issue on Algorithms and Software for Computational Topology, Elsevier, 78, 3-40, Sept, 2017.
• Multivariate Topology Simplification. Amit Chattopadhyay, Hamish Carr, David Duke, Zhao Geng and Osamu Saeki. Computational Geometry: Theory and Application, Elsevier, 58, 1-24, May 2016.
• A Derivative-Free Riemannian Powell's Method Minimizing Hartley-Entropy-Based ICA Contrast. Amit Chattopadhyay, S. Easter Selvan and Umberto Amato. ​​IEEE Transactions on Neural Networks and Learning Systems, Vol. 27, No. 9, Sept. 2016.
• Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data. Hamish Carr, Zhao Geng, Julien Tierny, Amit Chattopadhyay, Aaron Knoll. ​Computer Graphics Forum, Vol. 34, Issue 3, 2015 (EuroVis 2015).
• Spherical mesh adaptive direct search for separating quasi-uncorrelated sources by range-based independent component analysis. S. Easter Selvan, Pierre B. Borckmans, Amit Chattopadhyay, P.-A. Absil. Neural Computation, MIT Press, Volume 25, Issue 9, Pages 2486-2522, 2013.
• Certified Computation of planar Morse-Smale Complexes of Smooth Functions.   Amit Chattopadhyay, Gert Vegter and Chee K. Yap. 27th ACM Symposium on Computational Geometry. Chapel Hill, NC, USA, Pages 259–268, June 16-20, 2012 (SoCG 2012).
• Range-based non-orthogonal ICA using cross-entropy method. S. Easter Selvan, Amit Chattopadhyay, Umberto Amato, P.-A. Absil. European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium, pages 519-524, 25-27 April 2012 (ESANN 2012).
• Certified Meshing of RBF-based Isosurfaces. Amit Chattopadhyay, Simon Plantinga and Gert Vegter. The Visual Computer, Springer, Vol. 28, Number 5, Pages 445-462, 2011.
• Certain Generalizations of Enestrom-Kakeya Theorem. Amit Chattopadhyay, S. Das, V. K. Jain and H. Konwar. Journal of Indian Mathematical Society, 72,147-156, 2005.

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Computer Science:

• CS/DS 871-Basic Computational Topology, Elective, IIIT-Bangalore (Lecturer)
• CS/DS 815-Topological Data Analysis, Elective, IIIT-Bangalore (Lecturer)
• GEN512-Mathematics for Machine Learning, for M.Tech and iMtech, IIIT-Bangalore, (Lecturer)
• CS709-Geometric Modeling, for M.Tech, IIIT-Bangalore, (Lecturer)
• CS815-Computational Topology, Elective for M.Tech, IIIT-Bangalore (Lecturer)
• Numerical Computation and Visualization, for Undergraduate, School of Computing, University of Leeds (Teaching Assistant)
• Mechanics of Structures with Graphics, for Undergraduate, MEMA, UCL, Belgium (Teaching Assistant)

 

​Mathematics:

• SM103-Maths 1, Real Analysis, for iM.Tech, IIIT-Bangalore, (Lecturer)
• SM201-Maths 3, Vector Analysis, Differential Equation, for iM.Tech, IIIT-Bangalore, (Lecturer)
• SM202-Maths 4, Probability and Statistics, for iM.Tech, IIIT-Bangalore, (Lecturer)
• GEN504-Linear Algebra, for M.Tech, IIIT-Bangalore, (Lecturer)
• BS109-Probability and Statistics, for iM.Tech, IIIT-Bangalore, (Lecturer)
• Vector Analysis, for Undergraduate, JBI, University of Groningen (Teaching Assistant)

Research Students

PhD Students at IIITB

• Yashwanth Ramamurthi (since June 2019)

MS by Research Student

• Tripti Agarwal, August 2017-June 2020, MS-Thesis on ''Topological Similarity Measures between Multi-Field Data'',  (Joined as a PhD student at SCI, University of Utah, USA)
• Shweta K Singh, July 2021-May 2022, BS-MS student of IISER Pune, MS-Thesis on "Topological Clustering on Riemannian Manifold".

Project Students

 

Research Projects 

Topological Data Analysis: Tools for Multivariate (funded by SERB-CRG, 2019-2022)

A wide range of data that appear in scientific experiments and simulations are multi-field or multivariate (involving multiple scalar fields simultaneously). For example, the time-varying spatial density data of proton and neutron in the nucleus of a Plutonium atom – where the goal is to detect the time stamp of nuclear scission; molecular biology data of Electrostatic and van der Waal forces – where the goal is to study the protein-protein interaction; combustion data – where the goal is to study the progress of combustion with the fuel in process and so on. Topological and geometrical analysis of such data aims to reveal interesting features useful to the domain scientists. The goal of this project is to develop robust tools for extracting and visualizing topological features based on Reeb space, Reeb skeleton, fiber surfaces, multi-dimensional persistent homology and other techniques from computational topology.

• Dr. Amit Chattopadhyay (PI),

 

High Resolution DNS of 3D-MHD turbulence with varying PRm and Spectral, statistical and topological analysis of Magnetic Structures formed with some implications to Plasma Fusion Devices (funded by DAE, BRNS, 2017-2020)

Turbulence is a chaotic phenomenon observed in fluids which is nonlinear in both space and time. In this project we aim to perform high resolution direct numerical simulations of 3D-MHD turbulent flows, with varying Magnetic Prandtl number using both the initial condition and a forcing that injects magnetic and or kinetic helicities, present in as much small-scales as computationally possible. Using the obtained data from the simulations, three types of analyses are planned namely (a) spectral (b) statistical and (c) topological.

• Dr. Shiva Kumar Malapaka (PI)
• Dr. Jaya Sreevalsan Nayar (Co-PI)
• Dr. Amit Chattopadhyay (Co-PI)
   

Certified Geometric Computation

Certified geometric computation, is a newly emerging branch of computing science where the main goal is not only numerical accuracy, but above all the geometric and topological correctness of the output. More precicsely, in certified geometric computation, the challenge is to develop algorithms for computing topologically correct and geometrically close approximations of implicit or explicit input shapes.

• Dr. Amit Chattopadhyay (PI)

 

3D Volumetric Shape Reconstruction from 2D Image Slices

In computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound imaging, reconstruction of 3D volumetric shape from the 2D cross-sectional images is a challenging problem because of large and unequal spacing between the slice images. In the current project we consider the information of the planar contours extracted from the cross-sectional images to reconstruct the topologically correct (certified) 3D shape.

• Dr. Amit Chattopadhyay (PI)

Open Positions

There are few openings in my group for motivated students who are interested in doing Ph.D. or MS or Master-project (of minimum one-semester) in one of the research topics. Interested candidate can apply by sending (i) CV and (ii) a letter of motivation to my e-mail-id: a.chattopadhyay-at-iiitb.ac.in (please read the project descriptions before applying).