Amit Chattopadhyay

Computational Topology and data analysis, topological machine learning, Geometric Computing, Optimization on Matrix Manifolds, Scientific Visualization.

PREPRINTS

• An Improved FPT Algorithm for Computing the Interleaving Distance between Merge Trees via Path-Preserving Maps.
  Althaf P V, Amit Chattopadhyay and Osamu Saeki.
  arXiv:2602.12028.
• A Topological Distance Measure between Multi-Fields for Classification and Analysis of Shapes and Data.
  Yashwanth Ramamurthi, Amit Chattopadhyay.
  arXiv:2303.02902.

JOURNAL PUBLICATIONS

• An Algorithm for Correct Computation of Reeb Spaces for PL Bivariate Fields.
  Amit Chattopadhyay, Yashwanth R, and Osamu Saeki.
  Journal of Applied and Computational Topology, Springer Nature.
  arXiv:2403.06564, (accepted on 28th May, 2026).
• Image complexity-based fMRI-BOLD visual network categorization across visual datasets using topological descriptors and deep-hybrid learning.
  Scientific Reports, 15, Article number: 36845 (2025).
  Debanjali Bhattacharya, Neelam Sinha, Yashwanth Ramamurthi, and Amit Chattopadhyay.
  DOI: 10.1038/s41598-025-20635-0.
• A Topological Distance between Multi-fields based on Multi-Dimensional Persistence Diagrams.
  Yashwanth Ramamurthi, Amit Chattopadhyay.
  IEEE Transactions on Visualization and Computer Graphics.
  Pages 1-18, 2023, DOI: 10.1109/TVCG.2023.3314763, arXiv:2303.03038.
• A Topological Similarity Measure between Multi-Resolution Reeb Spaces.
  Yashwanth Ramamurthi, Tripti Agarwal and Amit Chattopadhyay.
  IEEE Transactions on Visualization and Computer Graphics.
  pages 1-18, 2021, DOI: 10.1109/TVCG.2021.3087273.
• Certified Computation of planar Morse-Smale Complexes.
  A. Chattopadhyay, G. Vegter and C. K. Yap.
  Journal of Symbolic Computation, Elsevier.
  Volume 78, pages 3-40, 2017. DOI: 10.1016/j.jsc.2016.03.006.
• Multivariate Topology Simplification.
  A. Chattopadhyay, H. Carr, D. Duke, Z. Geng and O. Saeki.
  Computational Geometry: Theory and Applications, Elsevier.
  Volume 58, pages 1-24, 2016. DOI: 10.1016/j.comgeo.2016.05.006.
• A derivative-free Riemannian Powell’s method minimizing Hartley-entropy-based ICA contrast.
  A. Chattopadhyay, S. E. Selvan and U. Amato.
  IEEE Transactions on Neural Networks and Learning Systems.
  Volume 27, Issue 9, pages 1983-1990, 2016. DOI: 10.1109/TNNLS.2015.2464157.
• Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data.
  H. Carr, Z. Geng, J. Tierny, A. Chattopadhyay and A. Knoll.
  Computer Graphics Forum, Eurographics.
  Vol. 34, Issue 3, pages 1-10, 2015. DOI:  10.1111/cgf.12636.
• 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.
  Vol. 25, Issue 9, pages 2486-2522, 2013. DOI: 10.1162/NECO_a_00485.
• Certified Meshing of RBF-based Isosurfaces.
  A. Chattopadhyay, S. Plantinga and G. Vegter.
  The Visual Computer, Springer.
  Vol. 28, Number 5, pages 445-462, 2011. DOI: 10.1007/s00371-011-0627-2.
• Certain Generalizations of Enestrom-Kakeya Theorem.
  A. Chattopadhyay, S. Das, V. K. Jain and H. Konwar.
  Journal of Indian Mathematical Society.
  Vol. 72, pages 147-156, 2005. Link, Pdf

BOOK CHAPTERS

• Topological Feature Search in Time-Varying Multifield Data.
  Tripti Agarwal, Amit Chattopadhyay and 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. pp 197-217, 2021, DOI: 10.1007/978-3-030-83500-2_11.
• Certified Geometric Computation: Radial Basis Function based Isosurfaces and Morse-Smale Complexes.
  A. Chattopadhyay, Supervisor: G. Vegter.
  PhD thesis, pp 1-172 University of Groningen, ISBN 978-90-367-4757-8, 2011. Link.
• Pattern Generation using Level Set Based Curve Evolution.
  A. Chattopadhyay and D.P. Mukherjee.
  Advances in Intelligent Information Processing: Tools and Applications. World Scientific, chapter 2, pages 19--36, volume 2, ISBN: 978-981-281-898-0, 2008. DOI: 10.1142/9789812818997_0002.

CONFERENCE PUBLICATIONS

• A Topological Distance between Multi-fields based on Multi-Dimensional Persistence Diagrams.
  Yashwanth Ramamurthi and A. Chattopadhyay.
  (IEEE-TVCG paper accepted for presentation in)
  Eurographics Conference on Visualization, EuroVis 2024.
  Odense, Denmark, May 27-31, 2024. DOI: 10.1109/TVCG.2023.3314763, arXiv:2303.03038.
• Euler Curve Based Topological Loss for Reconstructing 3D Images from Single 2D Image Slices.
  Kalyan Varma Nadimpalli, Amit Chattopadhyay, Bastian Rieck.
  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, TAG-PRA (Topology, Geometry, Algebra in Pattern Recognition with Applications),
  pp. 571–579, 2023. In Vancouver, Canada, June 18th, 2023. Link, arxiv: 2303.05286.
• Topological Shape Matching using Multi-Dimensional Reeb Graphs.
  Yashwanth Ramamurthi and Amit Chattopadhyay.
  The Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP), IIT Gandhinagar, Dec. 8-10, 2022. DOI: 10.1145/3571600.3571606.
• Topological Feature Search in Time-Varying Multifield Data.
  Tripti Agarwal, Amit Chattopadhyay and Vijay Natarajan.
  TopoInVis 2019, Nyk, Sweden, June 17-19, 2019. DOI: 10.1007/978-3-030-83500-2_11.
• Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data (Extended Abstract).
  H. Carr, Z. Geng, J. Tierny, A. Chattopadhyay and A. Knoll.
  Computer Graphics & Visual Computing, CGVC 2015.
  University College London, Malet Street, London, UK, September 16-17, 2015. Link.
• Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data
  H. Carr, Z. Geng, J. Tierny, A. Chattopadhyay and A. Knoll.
  Eurographics Conference on Visualization, EuroVis 2015.
  Cagliari, Sardinia, Italy, May 25-29, 2015. DOI:  10.1111/cgf.12636.
• Simplifying Multivariate Topology (Extended Abstract).
  A. Chattopadhyay, H. Carr, D. Duke and Z. Geng.
  Computer Graphics & Visual Computing, CGVC 2014,
  September 10-11, Leeds, UK, pages 51-52, 2014. DOI: 10.2312/cgvc.20141208.
• Visual Analysis of Hurricane Data Using Joint Contour Net.
  Z. Geng, D. Duke, H. Carr, and A. Chattopadhyay.
  Computer Graphics & Visual Computing, CGVC 2014.
  10-11 September, Leeds, UK, pages 33-40, 2014. DOI: 10.2312/cgvc.20141205.
• Extracting Jacobi Structures in Reeb Spaces.
  A. Chattopadhyay, H. Carr, D. Duke and Z. Geng.
  Eurographics Conference on Visualization, Eurovis 2014.
  9-13 June, Swansea, UK, Short Paper, pages 1-4, 2014. DOI: 10.2312/eurovisshort.20141156.
• Certified Computation of Planar Morse-Smale Complexes of Smooth Functions.
  A. Chattopadhyay, G. Vegter and C. K. Yap.
  ACM Symposium on Computational Geometry, SoCG 2012.
  Chapel Hill, NC, USA, pages 259–268, June 16-20, 2012. DOI: 10.1145/2261250.2261288.
• Range-based non-orthogonal ICA using cross-entropy method.
  S. Easter Selvan, A. Chattopadhyay, U. Amato and P.-A. Absil.
  European Symposium on Artificial Neural Networks, ESANN 2012.
  Computational Intelligence and Machine Learning, Bruges (Belgium), pages 519-524, 25 - 27 April, 2012. Link.
• Certified Computation of Morse-Smale Complexes on Implicit Surfaces.
  A. Chattopadhyay and G. Vegter
  European Workshop on Computational Geometry, EuroCG 2011.
  Morschach, Switzerland, pages 221-224, March 28-30, 2011. Link.
• Certified Computation of planar Morse-Smale Complexes.
  A. Chattopadhyay, S.J. Holtman and G. Vegter.
  European Workshop on Computational Geometry, EuroCG 2010.
  Dortmund, Germany, pages 105-108, March 22-24, 2010. Link.
• Certified Meshing of RBF-based Isosurfaces (Poster).
  Amit Chattopadhyay, Simon Plantinga and Gert Vegter.
  Workshop: Subdivide and Tile (Triangulating spaces for understanding the world),
  Lorentz Center, the Netherlands, Nov. 16-20, 2009. 
  Link.
• Certified Meshing of RBF-based Isosurfaces.
  A. Chattopadhyay, S. Plantinga, and G. Vegter.
  European Workshop on Computational Geometry, EuroCG 2009.
  Brussels, Belgium, pages 101-104, March 16-18, 2009. Link.

Released Software

• TopoDistMF-v1: Software for computing topological distances between multi-field data.

Computer Science:

• CSE 102: Data Structures and Algorithms IIIT-Bangalore (Lecturer)
• 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 

• Yashwanth Ramamurthi (Aug 2019 --Defended thesis: on 23rd May 2024) Thesis Title: ``Tools for Multi-Field Topological Data Analysis''
• Karthikeya Subramanian (Aug 2023--)
• Althaf P V (Aug 2023--)
• Snigdhashree Mallick (Supervisor: Dr. Shiva Kumar Malapaka, Co-supervisor: Dr. Amit Chattopadhyay)

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".
• Rishendra Chauhan, July 2023-May 2024, BS-MS student of IISER Berhampur

MTech thesis student

• Kalyan Varma Nadimpalli (IMT2018034, graduated in 2023), Thesis Title: ``Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices''Euler Characteris-
  tic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D SlicesEuler Characteris-
  tic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices

Research Associates

• Yashwanth Ramamurthi (June 2019-July 2019)
• Karthikeya Subramanian (May 2023--July 2023)

Funded Research Projects 

1. Persistent Homology based Matching of Large Point Clouds for Applications in Robotics (funded by MINRO, INR 60L)

• Dr. Amit Chattopadhyay (PI),
• Dr. Sachit Rao (Co-PI)

2. Topological Data Analysis: Tools for Multivariate (funded by SERB-CRG, 2019-2022, INR 28L)

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),

3. 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, INR 35L)

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)
   

Open Positions

There are openings in my group for motivated students who are interested in doing a Ph.D.  in one of the related research topics. Interested candidates can apply by sending (i) a 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).