History of Mathematics

" Siddhantasundara of Jnanaraja: An English Translation by Toke Lindegaard Knudsen", The Mathematical Intelligencer, DOI 10.1007/s00283-015-9555-8.[pdf]

"Medieval Eclipse Prediction: A Parallel Bias in Indian and Chinese Astronomy", to appear in a special issue of Ganita Bharati.[pdf]

"A History of Pingala's Combinatorics", Ganita Bharati, v. 35, n. 1-2, June-December, 2013[pdf]

"Absence of Geometric Models in Medieval Chinese Astronomy" Ganita Bharati,v. 33, n. 1-2, June-December, 2011. [pdf]

Computer Vision

''An H2 Riemannian metric on the space of planar curves modulo similitudes", Advances in Applied Mathematics, http://dx.doi.org/10.1016/j.aam.2013.06.003, [pdf]

''A Metric on Shape Space with Explicit Geodesics", Laurent Younes, Peter W. Michor, Jayant Shah, David Mumford, Rendiconti Lincei - Matematica E Applicazioni, vol. 19, Issue 1 (March, 2008), pp. 25-57. [pdf]

''Ho type Riemannian metrics on the space of planar curves", Quarterly of Applied Mathematics,66 (2008), pp. 123-137 [pdf]

''Skeletons via shocks of boundary evolution'', (Jointly with K. Siddiqi and and S. Bouix), in "Medial Representations: Mathematics, Algorithms and Applications", Ed: K. Siddiqi and Stephen Pizer, Springer, 2007. [pdf]

''An H2 type Riemannian metric on the space of planar curves",  Workshop on the Mathematical Foundations of Computational Anatomy, MICCAI2006, Copenhagen, October, 2006. [pdf]

"Model Based Variational Smoothing for Diffusion Tensor Imaging in the Brain", (jointly with M Desai, D. Kennedy, R Mangoubi, C Karl, A Worth, N Markis, H Pien),   Neuroinformatics, vol 4, Issue 3, 2006. [pdf_text] [pdf_figures]

"Shape and appearance modeling with feature distributions for image segmentation", (Jointly with A. Litvin and W.C. Karl),   International Symposium on Biomedical Imaging, Arlington, Virginia, 2006. [pdf]

"Skeletons and segmentation of shapes", Internal Report, 2005. [PDF]

''Skeletons of 3D shapes'', The Fifth International Conference on Scale-Space and PDE Methods in Computer Vision, 2005. [PDF]

''Grayscale skeletons and segmentation of shapes'', Computer Vision and Image Understanding, V.99, Issue 1, pp. 96-109, July 2005. [PDF]

''Functional MRI activity characterization using non-Gaussian detection and curve evolution'', (Jointly with M. Desai, R. Mangoubi, W. Karl, D. Kennedy, H. Pien and A. Worth), IEEE Transactions on Medical Imaging. V. 21. no. 11, Nov. 2002.

''Reaction-diffusion equations and learning'', Proceedings of the Workshop on Variational Methods for Discontinuous Structures, Como, Italy, Progress in Nonlinear Differential Equations and Their Applications, V. 51, 2002, pp. 171-182. [PDF]

''Diffusion tensor model based smoothing'', (Jointly with M. Desai, R. Mangoubi, W. Karl, D. Kennedy, A. Worth and N. Makris) Proceedings of the IEEE International Symposium on Biomedical Imaging, Washington, D.C., July, 2002.

''Reaction-diffusion equations and Learning'', Journal of Visual Communication and Image Representation, v.13, no.1, March, 2002..

''Elastica with hinges'', Journal of Visual Communication and Image Representation, v.13, no.1, March, 2002.[PDF]

''Segmentation of Shapes'', Proceedings of the Workshop on Scale-Space and Morphology, 2001.[PDF]

''Riemannian Drums, Curve Evolution and Segmentation'', Journal of Visual Communication and Image Representation, v. 11, pp. 142-153, 2000.[PDF]

''Nested local symmetry sets'', (jointly with S. Tari), Computer Vision and Image Understanding, v.79, no.2, pp.267-280, 2000.

''Free-discontinuity problems via functionals involving the L1-norm of the gradient and their approximations'', (with R. Alicandro and A. Braides), Journal of Interfaces and Free Boundaries, v. 1, pp. 17-37, 1999.[PDF]

''Segmentation as a Riemannian Drum problem'', International Conference on Image Processing, October, 1998.,a href="papers/RiemDrums98.pdf">[PDF]

''Entropy Minimax and Learning by Diffusion'', IEEE Conference on Computer Vision and Pattern Recogntion, June, 1998.[PDF]

''Local Symmetries of Shapes in Arbitrary Dimension'', (with S. Tari), International Conference on Computer Vision, January, 1998.[PDF]

''Segmentation of MR Images using Curve Evolution and Prior Information'', (with M. Desai and H. Pien), International Journal of Pattern Recognition and Artificial Intelligence.

''Extraction of Shape Skeletons from Grayscale Images'',(with S. Tari and H.Pien), Computer Vision and Image Understanding, March, 1997.[PDF]

''Curve Evolution and Segmentation Functionals: Application to Color Images'', IEEE International Conference on Image Processing, Sept. 1996.[PDF]

''Recovery of Shapes of Surfaces with Discontinuities by Fusion of Shading and Range Data within a Variational Framework'', (with H. Pien and J. Gauch), IEEE Trans. on Image Processing, vol.5, no.8, August, 1996.

''A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion, IEEE Conference on Computer Vision and Pattern Recogntion'', June, 1996.[PDF]

''A Computationally Efficient Shape Analysis via Level Sets'', (with S. Tari and H. Pien), IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, June, [PDF]1996.

''Uses of Elliptic Approximations in Computer Vision'', in Variational Methods for Discontinuous Structures}, Ed: R. Serapioni and F. Tomarelli, Progress in Nonlinear Differential Equations and Their Applications, vol.25, Birkhauser, 1996.[PDF]

''Shape Recovery from Noisy Images by Curve Evolution'', International Conference on Signal and Image Processing (SIP'95), November, 1995.[PDF]

''Piecewise Smooth Approximations of Functions'', Calculus of Variations and Partial Differential Equations, Vol.2, pp.315-328, 1994.[PDF]

''A Nonlinear Diffusion Model for Discontinuous Disparity and Half-Occlusions in Stereo'', IEEE Conference on Computer Vision and Pattern Recognition, New York, N.Y., June, 1993.[PDF]

''Segmentation by Nonlinear Diffusion, II'', Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, Champaign, IL, June, 1992.

''Properties of Energy-Minimizing Segmentations'', SIAM Journal on Control and Optimization, January, 1992.

''Segmentation by Nonlinear Diffusion'', Proc. of the IEEE Conference on Computer Vision and Pattern Recognition, Lahaina, Hawaii, June, 1991.

''Parameter Estimation, Multiscale Representation and Algorithms for Energy-Minimizing Segmentations'', Proc. of the 10th International Conference on Pattern Recognition, Atlantic City, NJ, June, 1990.

''Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems'', (with D. Mumford), Comm. on Pure and Applied Math. v. XLII, n.5, pp.577-684 (July, 1989) [PDF]

''Boundary Detection by Minimizing Functionals, I*'', (with D. Mumford),  Image Understanding, 1989}, Ed. S. Ullman and W. Richards, Ablex, 1990.

''Boundary Detection by Minimizing Functionals, I'', (with D. Mumford), Proc. IEEE Conf. on Computer Vision and Pattern Recognition, San Francisco (1985) [PDF]]

''The Representation of Shape'', (With A. Latto and D. Mumford), IEEE Proc. of the Workshop on Computer Vision, pp. 183-198 (1984)

Algebraic Geometry

''Stability of Two-dimensional Local Rings. II'', Contemporary Math. v. 58, Part I (1986)

''Stability of Two-dimensional Local Rings. I'', Invent. math. 64, pp. 297-343 (1981)

''Projective Degenerations of Enriques Surfaces'', Math. Ann. 256, pp. 475-495 (1981)

''Degenerations of K3 Surfaces of Degree 4'', Trans. Amer. Math. Soc. 263, pp. 271-308 (1981)

''A Complete Moduli Space for K3 Surfaces of Degree 2'', Ann. of Math. 112, pp. 485-510 (1980)

''Insignificant Limit Singularities of Surfaces and Their Mixed Hodge Structure'', Ann. of Math. 109, pp. 497-536 (1979)

''Stabililty of Local Rings of Dimension 2'', Proc. Nat'l Acad. Sci. 75, pp. 4085-4086 (1978)

''Surjectivity of the Period Map in the Case of Quartic Surfaces and Sextic Double Planes'', Bull. A.M.S. 82, pp. 716-718 (1976)

''Monodromy of Semistable Quartic Surfaces and Sextic Double Planes'', Ph.D. Thesis, M.I.T. Math. (1974)

Numerical Analysis

''Two-Dimensional Polynomial Splines, Num.Math''. 15, pp. 1-14 (1970)

Structural Mechanics

''Stability of Spaceframes'', (with M. Zarghamee), Amer. Soc. Civil Eng. J. of Mech. 94, pp. 371-384, (1968)

''Ill-conditioned Stiffness Matrices'', Amer. Soc. Civil Eng. J. of Struct. Div. 92, pp. 443-457, (1966)

''Computer Analysis of the F-111 Wing Assembly'', (with J. Antebi, E. Rossow and I. Shah), Amer. Soc. Civil Eng. J. of Struct. Div. 92, pp. 405-424, (1966)

''Nonlinear Dynamic Response of Membranes'', Ph.D. Thesis, M.I.T. Civil Engineering. (1961)

''Response of Concrete Shear Keys to Dynamic Loading'', (with E. Nawy), Amer. Concrete Inst. 32, pp. 1475-1490, (1961)