I am working with the National Institute of Standards and Technology on calibration and registration problems which have applications in computer vision, manufacturing, and robotics. For more information, check this article. For code that I often use in my research check my Calibration and Registration website.
I have also worked on calculating a symmetry preserving singular value decomposition (SPSVD), which is a matrix factorization that gives the best symmetric low rank approximation to a set of data. This decomposition has applications in molecular dynamics and face detection. For more information, check my SIMAX paper.
- R. Bostelman, J. Falco, M. Shah, T. Hong,
Dynamic Metrology Performance Measurement of a Six Degrees-of-Freedom
Tracking System Used in Smart Manufacturing, Autonomous Industrial Vehicles: From the Laboratory to the Factory Floor, Book Chapter, (2016).
- R. Bostelman, T. Hong, M. Shah, S. Legowik, Dynamic Metrology and ASTM E57.02 Dynamic Measurement Standard, Coordinate Metrology Society Conference, (2016).
- M. Shah, M. Franaszek, and G. Cheok, Propagation of Error from Registration Parameters to Transformed Data, Journal of Research of the National Institute of Standards and Technology, Volume 121 (2016), pp. 196-221.
- M. Franaszek, M. Shah, G. Cheok, and K. Saidi, The Axes of Random Infinitesimal Rotations and the Propagation of Orientation Uncertainty, Measurement (2015).
- M. Shah, Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product, ASME Journal of Mechanisms and Robotics, Volume 5, Issue 3 (2013).
- M. Shah, R. D. Eastman, T. Hong, An Overview of Robot-Sensor Calibration Methods for Evaluation of Perception Systems, Performance Metrics for Intelligent Systems, (2012).
- M. Shah, Comparing Two Sets of Corresponding Six Degree of Freedom Data, Computer Vision and Image Understanding, Volume 115, Issue 10 (2011), pp. 1355-1362.
- T. Chang, T. Hong, J. Falco, M. Shneier, R. Eastman, M. Shah, Methodology for Evaluating Static Six-Degree-of-Freedom
(6DoF) Perception Systems, Performance Metrics for Intelligent Systems, (2010).
- M. I. Shah, Symmetric Eigenfaces, Technical Report, Loyola University Maryland (2009), TR2009_01.
- M. Shah, T. Chang, T. Hong, R. Eastman, Mathematical Metrology for Evaluating a 6DOF Visual Servoing System, Performance Metrics for Intelligent Systems, (2009).
- M. I. Shah and D. C. Sorensen, Best Non-Spherical Symmetric Low Rank Approximation, SIAM Journal on Matrix Analysis and Applications, 31 (2009), pp. 1019-1039.
- M. I. Shah and D. C. Sorensen, A Symmetry Preserving Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, 28 (2006), pp. 749-769.
- W. Wriggers, Z. Zhang, M. Shah, and D. C. Sorensen, Simulating Nanoscale Functional Motions of Biomolecules, Molecular Simulation, 32 (2006), pp. 803-815.
- D. C. Sorensen and M. Shah, Principal Component Analysis and Model Reduction for Dynamical Systems with Symmetry Constraints, European Control Conference (CDC-ECC), 2005, pp. 2260-2264.