Prof. Mireille Boutin
 

Discrete Inverse Problems

Work on various discrete inverse problems using invariants, moving frames, commutative algebra, PDEs, etc.



Shape from Echoes



  1. •M. Boutin and G. Kemper,  “A Drone Can Hear the Shape of a Room,” SIAM J. Applied Algebra and Geometry, 4:1(2020), 123–140. (arXiv version, PDF)

  2. A data science question answered with a syzygy and some commutative algebra.



Shape from Invariant Statistics



  1. •M. Boutin and G. Kemper, “On Reconstructing n-point Configurations from the Distribution of Distances of Areas,” Advances in Applied Mathematics, Vol. 32, pp. 709-735, 2004.


  1. •M. Boutin and G. Kemper, “On Reconstructing Configurations of Points in P2 from a Joint Distribution of Invariants,” Journal of Applicable Algebra In Engineering, Communication and Computing, Vol. 15, No. 6, pp. 361-391, 2005.


  1. •M. Boutin, K. Lee, M. Comer, “Lossless Shape Representation Using Invariant Statistics: the Case of Point-sets,” Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, October 29–November 1, 2006.


  1. •M. Boutin and M. Comer, “Faithful Shape Representation for 2D Gaussian Mixtures,” IEEE International Conference on Image Processing (ICIP), San Antonio, TX, September 16–19, 2007.


  1. •M. Boutin and G. Kemper, “Which Point Configurations are Reconstructible from the Distribution of their Pairwise Distances?,” International Journal of Computational Geometry and Applications, Vol. 17, No. 1, pp. 31-43, 2007.


  1. •M. Boutin and G. Kemper, “Lossless Representation of Graphs using Distributions,” arXiv manuscript #arXiv:0710.1870, 2007.


  1. •H. Santos-Villalobos, M. Boutin, “A Computationally Efficient Method to Compare the Shape of Planar Gaussian Mixtures From Point Samples,” Journal of Electronic Imaging, Vol. 21, No. 2, 023023, June 22, 2012.



Discrete Objects from Invariant Signatures



  1. •M. Boutin, “Numerically Invariant Signature Curves, ”International Journal of Computer Vision, Vol. 40, No.3, pp. 235-248, 2000.


  1. •M.Boutin,“On Orbit Dimensions Under a Simultaneous Lie Group Action on n Copies of a Manifold,”Journal of Lie Theory, Vol. 12, pp. 191-203, 2002.


  1. •M. Boutin, “Joint Invariant Signatures for Curve Recognition,” Inverse Problems, Image Analysis and Medical Imaging, M.Z. Nashed and O. Schetzer, editors, Contemporary Mathematics, Vol. 313, American Mathematical Society, 2002, pp. 37-52.

  2. •M. Boutin, “Polygon Recognition and Symmetry Detection,” Foundations of Computational Mathematics, Vol. 3, pp. 227-271, 2003.




Structure from motion



  1. •J. Zhang, M. Boutin, and D. G. Aliaga, “Pose-Free Structure from Motion Using Depth From Motion Constraints,” IEEE Transactions on Image Processing, Vol. 20, No. 10, pp. 2937-2953, 2011.


  1. •D. Aliaga, J. Zhang, and M. Boutin, “A Framework for Modeling 3D Scenes using Pose-free Equations,” ACM Transactions on Graphics, Vol. 29, No. 1, (17 pages), 2009.

  2. •J. Zhang, M. Boutin and D. G. Aliaga, “Variable Elimination for 3D from 2D,” IS&T/SPIE Joint Symposium, Visual Communication and Image Processing Conference (VCIP), San Jose, CA, January–February 2007.

  3. •J. Zhang, M. Boutin and D. G. Aliaga, “Robust Bundle Adjustment for Structure from Motion,” IEEE International Conference on Image Processing (ICIP), pp. 2185-2188, Atlanta, GA, Oct. 2006.

  4. •J. Zhang, D.G. Aliaga, M. Boutin and R. Insley, ”Angle-Independent Bundle Adjustment Refinement”, Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), Chapel Hill, NC, June 2006.

  5. •P. L. Bazin and M. Boutin, “Structure from Motion: a New Look from the Point of View of Invariant Theory,” SIAM Journal of Applied Mathematics, Vol. 64, No. 4, pp. 1156-1174, 2004.

  6. •P.-L. Bazin and M. Boutin, “Structure from Motion Using Invariants.” Proceedings of 8o Encuentro de Algebra computational y Aplicaciones (EACA) 2002, pp. 95-98, Penaranda de Duero, Spain. (Invited)




Nutrients from food label



  1. •J. Kim, A. Talikoti, M. Boutin, “A 3-step process to estimate phenylalanine in commercial foods for PKU management,” IEEE Access, Vol. 6, No. 1, December 2018, pp. 30758-30765.

  2. •J. Kim and M. Boutin, “Deriving Nutritional Information Using Mathematics: the Example of Phenylalanine in Sweets with Gelatin,” Journal of the Academy of Nutrition and Dietetics, Vol. 115, No. 9, pp. 1384-1386, 2015.

  3. •J. Kim and M. Boutin, “New Multipliers for Estimating the Phenylalanine Content of Foods from the Protein Content,” Journal of Food Composition and Analysis, Vol. 42, pp. 117-119, 2015.

  4. •J.Kim and M.Boutin, “Estimating the Nutrient Content of Commercial Foods from their Label Using Numerical Optimization,” 1st International Workshop on Multimedia Assisted Dietary Management (MADIMA), Genoa, Italy, September 8, 2015.

  5. •J.Kim and M.Boutin, “An Approximate Inverse Recipe Method with Application to Automatic Food Analysis,” IEEE Symposium Series on Computational Intelligence, Orlando, FL, December 9–12, 2014.



Image Denoising



  1. •H. Siddiqui, M. Boutin and C. Bouman, “Hardware Friendly Descreening,” IEEE International Conference on Image Procession (ICIP), San Diego, CA, October 12–15, 2008.


  1. •H. Siddiqui, M. Boutin and C. A. Bouman, “Hardware Friendly Descreening,” IEEE Transactions on Image Processing, Vol. 19, No. 3, pp. 746-757, 2010.

  2. A PDE discretized in a hardware-friendly manner (+/-, powers of two, few multiplies, no exponentiation, no “if”)