Leo Grady

    I am a Senior Member of Technical Staff with Siemens Corporate Research in Princeton, New Jersey. I received my PhD in 2003 from Boston University in the Computer Vision and Computational Neuroscience Laboratory under the supervision of Dr. Eric Schwartz.


Contact Information


Research Interests

    My research has primarily focused on image segmentation, data clustering, learning and filtering using techniques from graph theory, combinatorial topology and partial differential equations. Other interests include pattern/object recognition, applied mathematics, non-uniform data processing, image registration, cellular automata, robotics and emergent phenomena.
   


Software

The Graph Analysis Toolbox for MATLAB was written as a by-product of my PhD thesis. My intention was to allow for flexible representation and analysis of data associated with a graph, specifically slanted toward computer vision applications. You can read some reviews at the Mathworks page.

I have written a short MATLAB function that runs the random walker image segmentation algorithm as an add-on to the above Graph Analysis Toolbox. The files contain a function to run the random walker algorithm and a script demonstrating its usage. The code may be found here. To see an (html) demo of the random walker algorithm, click here.

Upcoming

1) Dec. 3rd, 2008, MGH/MIT, Boston, MA - Invited talk at the Martinos Center for Biomedical Imaging


Recent Activities

1) Oct. 12th, 2008, Marseilles, France - ECCV 2008 tutorial entitled "Combinatorial Calculus in Computer Vision: Formulating and Solving Continuous PDEs on Graphs" (with Sébastien Bougleux). Slides are also available.
2) February 21-22, 2008, University of Maryland, College Park, MD - Invited talk at the February Fourier Talks
3) February 25-29, 2008, UCLA, Los Angeles, CA - Invited talk at IPAM 2008: Graph Cuts and Related Discrete or Continuous Optimization Problems. Slides are also available (requires TeX4PPT to view equations).
4) October 2nd, 2007, Johns Hopkins University, Baltimore MD - Invited talk at the Center for Imaging Science
5) June 18th, 2007, Minneapolis, MN- CVPR 2007 short course entitled "Fundamentals Linking Discrete and Continuous Approaches to Computer Vision - A Topological View". Course page.
6) June 11th, 2007, Alicante (Spain) - Invited talk at 6th IAPR-TC-15 Workshop on Graph-based Representations in Pattern Recognition

Publications

In Press
1) Leo Grady and Christopher Alvino, "Reformulating and Optimizing the Mumford-Shah Functional on a Graph - A Faster, Lower Energy Solution", Accepted to ECCV 2008. PDF

2) Leo Grady, "A Lattice-Preserving Multigrid Method for Solving the Inhomogeneous Poisson Equations used in Image Analysis", Accepted to ECCV 2008. PDF


Published
23) Leo Grady and Marie-Pierre Jolly, "Weights and Topology: A Study of the Effects of Graph Construction on 3D Image Segmentation", Proc. of MICCAI 2008, vol. 1, 2008, pp. 153-161, Sept., New York City, New York. PDF, BIB, Poster (PPT)

22) Leo Grady and Ali Kemal Sinop, "Fast Approximate Random Walker Segmentation Using Eigenvector Precomputation", Proc. of CVPR 2008, Anchorage, Alaska, June 24-26, 2008. PDF, BIB, Poster (PPT)

21) Dheeraj Singaraju, Leo Grady and René Vidal, "Interactive Image Segmentation of Quadratic Energies on Directed Graphs", Proc. of CVPR 2008, Anchorage, Alaska, June 24-26, 2008 PDF, BIB

20) Marie-Pierre Jolly and Leo Grady, "3D General Segmentation in CT", Proc. of ISBI 2008, Paris, France, May 14-17 2008. pp. 796-799. PDF, BIB

19) Ali Kemal Sinop and Leo Grady, "A Seeded Image Segmentation Framework Unifying Graph Cuts and Random Walker Which Yields A New Algorithm", in Proc. of ICCV 2007, Rio de Janeiro, Brazil, Oct. 14-20, 2007 (Oral presentation) PDF, BIB, ICCV Talk (requires TeX4PPT to view equations)

18) Ali Kemal Sinop and Leo Grady, "Uninitialized, Globally Optimal, Graph-Based Rectilinear Shape Segmentation - The Opposing Metrics Method", In Proc. of ICCV 2007, Rio de Janeiro, Brazil, Oct. 14-20, 2007 (Poster presentation) PDF, BIB, ICCV Poster (requires TeX4PPT to view equations)

17) Osman Bodur, Leo Grady, Arthur Stillman, Randolph Setser, Gareth Funka-Lea, Thomas O'Donnell, "Semi-Automatic Aortic Aneurysm Analysis", in A. Manduca and X.P. Hu (Eds), Proc. SPIE Medical Imaging 2007: Physiology, function, and structure from medical images, 6511 PDF

16) Leo Grady, "Random Walks for Image Segmentation", IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 28, No. 11, pp. 1768-1783, Nov., 2006. PDF, BIB, MATLAB Code, Demo (html)

15) Leo Grady, Gareth Funka-Lea, "An Energy Minimization Approach to the Data Driven Editing of Presegmented Images/Volumes", Proceedings of MICCAI 2006, vol. 2, 2006, pp. 888-895, Oct., Copenhagen, Denmark. PDF, BIB, Poster (PDF)

14) Ali Kemal Sinop, Leo Grady, "Accurate Banded Graph Cut Segmentation of Thin Structures Using Laplacian Pyramids", Proceedings of MICCAI 2006, vol. 2, 2006, pp. 896-903, Oct., Copenhagen, Denmark. PDF, BIB, Poster (PDF)

13) Leo Grady, "Computing Exact Discrete Minimal Surfaces: Extending and Solving the Shortest Path Problem in 3D with Application to Segmentation", Proceedings of CVPR 2006, vol. 1, 2006, pp. 69-78, June, New York, New York. PDF, BIB, Code (MATLAB)

12) Leo Grady, "Fast, Quality, Segmentation of Large Volumes - Isoperimetric Distance Trees", Proceedings of ECCV 2006, vol. 3, 2006, pp. 449-462, May, Graz, Austria, Springer. PDF, BIB, Poster (PDF)

11) Daniel Cremers, Leo Grady, "Statistical Priors for Efficient Combinatorial Optimization via Graph Cuts", Proceedings of ECCV 2006, vol. 3, 2006, pp. 263-274, May, Graz, Austria, Springer. PDF, BIB

10) Leo Grady, Yiyong Sun and James Williams, "Three Interactive Graph-Based Segmentation Methods Applied to Cardiovascular Imaging", In "Mathematical Models in Computer Vision: The Handbook", 453-469, ed. Nikos Paragios, Yunmei Chen, Oliver Faugeras, Springer 2006 PDF, BIB

9) Leo Grady and Eric L. Schwartz, "Isoperimetric Partitioning: A new algorithm for graph partitioning", SIAM Journal on Scientific Computing, vol. 27, no. 6, pp. 1844-1866, June 2006. PDF, BIB

8) Leo Grady and Eric L. Schwartz, "Isoperimetric Graph Partitioning for Image Segmentation", IEEE Trans. on Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp. 469-475, March 2006. PDF, BIB, Full paper (rejected by PAMI to a short contribution), MATLAB code to generate figures

7) Leo Grady, Thomas Schiwietz, Shmuel Aharon, Rudiger Westermann, "Random Walks for Interactive Organ Segmentation in Two and Three Dimensions: Implementation and Validation", Proceedings of MICCAI 2005, vol. 2, 2005, pp. 773-780, October, Palm Springs, CA, Springer. PDF, BIB, Poster (PDF)

6) Herve Lombaert, Yiyong Sun, Leo Grady, Chenyang Xu "A Multilevel Banded Graph Cuts Method for Fast Image Segmentation", Proceedings of ICCV 2005, vol. 1, 2005, pp. 259-265, October, Bejing, China, IEEE. PDF (link), BIB

5) Leo Grady, Tolga Tasdizen "A Geometric Multigrid Approach to Solving the 2D Inhomogeneous Laplace Equation with Internal Dirichlet Boundary Conditions", Proceedings of ICIP 2005, vol. 2, 2005, pp. 642-645, September, Genoa. PDF, BIB, Poster (PDF)

4) Leo Grady, Thomas Schiwietz, Shmuel Aharon , Rudiger Westermann, "Random Walks for Interactive Alpha-Matting", Proceedings of VIIP 2005, September, Benidorm, Spain pp. 423-429, ACTA Press. PDF, BIB, Talk (PDF)

3) Leo Grady, "Multilabel Random Walker Image Segmentation Using Prior Models", in Proceedings of CVPR05, Vol. 1, p. 763-770, San Diego, CA June 2005. PDF, BIB, Poster (PDF), Demo (html)

2) Leo Grady and Eric L. Schwartz. "Faster graph-theoretic image processing via small-world and quadtree topologies." In Proceedings of CVPR04, pp. 360-365, Washington, DC, June-July 2004. IEEE. PDF, BIB, Talk (PDF), Code to generate all figures

1) Leo Grady and Gareth Funka-Lea, "Multi-Label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials", in Proceedings of the 8th ECCV04, Workshop on Computer Vision Approaches to Medical Image Analysis and Mathematical Methods in Biomedical Image Analysis, p. 230-245, May 15th, 2004, Prague, Czech Republic, Springer-Verlag. PDF, BIB, Poster (PDF), MATLAB Code, Demo (html)


Technical reports
1) Leo Grady and Eric L. Schwartz, "The Graph Analysis Toolbox: A User's Manual", which serves as the user's manual for the Graph Analysis Toolbox. Technical Report CAS/CNS-TR-03-021, Department of Cognitive and Neural Systems, Boston University, Boston, MA, Aug. 2003. PDF, BIB

2) Leo Grady and Eric L. Schwartz, "Isoperimetric graph partitioning for data clustering and image segmentation", Technical Report, CAS/CNS-TR-03-015, Department of Cognitive and Neural Systems, Boston University, Boston, MA, July 2003. PDF, BIB

3) Leo Grady and Eric L. Schwartz, "Anisotropic interpolation on graphs: The combinatorial Dirichlet problem", Technical Report, CAS/CNS-TR-03-014, Department of Cognitive and Neural Systems, Boston University, Boston, MA, July 2003. PDF, BIB


PhD Thesis
My PhD thesis is entitled "Space-Variant Machine Vision - A Graph Theoretic Approach",
PDF, BIB Defense (PDF), Code to generate figures (MATLAB)


Miscellaneous
An old class project of potential interest is "The relationship of a species' visual ecology to the design of their visual system"


Links

Here are a set of links to sites that I have found very useful.  I tried to limit myself to links that visitors probably weren't aware of (e.g., not Google,  Mathworld or Slashdot).  All the links below point to sites with content.

Research related links
Natural Image Database This database contains many high resolution (grayscale) natural images.  They use a home-grown image format that I wrote a MATLAB function to read, which may be found here

Online Dictionary of Algorithms and Data Structures  This self-explanatory page is rather extensive, with many diagrams, demonstrations, references and even some code.
 


Last updated 7/24/08 by Leo Grady