Mona Mahmoudi
Ph.D. Candidate

Electrical and Computer Engineering
University of Minnesota

Email:   mona [at] umn [dot] edu

Biography

I am a PhD student at Electrical Engineering department at University of Minnesota. I am working with Prof. Guillermo Sapiro.

I received my B.Sc degree in Electrical Engineering from Sharif University of Technology in 2004, and my M.Sc degree in Electrical Engineering from University of Minnesota under the supervision of Prof. Guillermo Sapiro in 2006.

Research

Sparse Representations for Three-dimensional Range Data Restoration: Sparse representations of signals, in particular with learned dictionaries, are widely used for state-of-the-art audio, image, and video restoration. In this work, the problem of denoising and occlusion restoration of 3D range data based on dictionary learning and sparse representations is explored. We consider the 3D surface obtained from a desktop range scanner as an image, where the value of each pixel represents the depth of a point on the 3D surface. Having this image, we apply techniques from dictionary learning and sparse representation to enhance the acquired 3D surface. These techniques use the spare decomposition of the overlapping patches in the image, over an adapted over-complete dictionary, for enhancing the data. We present experimental results of denoising 3D surfaces following this approach. We also propose an algorithm for filling the missing information regions on 3D scans and demonstrate its effectiveness. Our experimental results are on range data obtained from a low-cost structured-light range scanner.

A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-robust Non-rigid Shape Matching: In this work, the problem of non-rigid shape recognition is viewed from the perspective of metric geometry, and the applicability of diffusion distances within the Gromov-Hausdorff framework is explored. The diffusion distance provides an intrinsic distance measure which is robust, in particular to topological changes. The presentation of the proposed framework is complemented with numerous examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes.

Three-dimensional Object Recognition and Partial Matching of 3D Shapes: Three-dimensional (3D) data is becoming ubiquitous. With the increasing number of 3D data, 3D object retrieval is essential for tasks such as navigation, target recognition, and identification. In our work, we have introduced new features for shape comparison based on intrinsic distances (diffusion distance, geodesic distance, their ratio, and a centrality measure) and curvature (curvature classifier and a curvature weighted distance).

Estimation of Geodesic Distances after Random Projection: In this work, we focused on the use of random projections as a dimensionality reduction tool for sampled manifolds in high dimensional Euclidean spaces. We showed that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved by Gaussian projections and we characterized the distribution of geodesic lengths in the reduced dimensional point cloud.  To validate our theoretical findings, we applied them to a real-world data set of human faces.

Image Denoising via Non-local Means: In this work, we presented some improvements on the original Non-local means method for image denoising introduced by Baudes et al. in 2004. Our improvements makes the algorithm much faster and sometimes more accurate in the sense that it reduces the blurring effect after averaging. We also obtained good results for color images and videos.

Publications

M. Mahmoudi and G. Sapiro, “Sparse representations for three-dimensional range data restoration”, ICASSP, submitted. [PDF]

A. M. Bronstein, M. M. Bronstein, R. Kimmel, M. Mahmoudi, and G. Sapiro, “A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching”, International Journal of Computer Vision (IJCV), 2009, to appear. [PDF]

M. Mahmoudi, P. Vandergheynst, and M. Sorci, “On the estimation of geodesic paths on sampled manifolds under random projections,” IEEE International Conference on Image Processing (ICIP), October 2008. [PDF]

M. Mahmoudi and G. Sapiro, “Fast Image and Video Denoising via Non-local Means of Similar Neighborhoods,”  IEEE Signal Processing Letters, vol. 12, no. 12, pp. 839-842, Dec. 2005. [PDF]