Here are the abstracts for the 3 topics that will be reviewed in this tutorial.
I will present the `geodesic active contours' approach for object segmentation. It is a geometric scheme derived from a variational principle for the detection of objects boundaries. The technique is based on contours or surfaces that evolve in time according to intrinsic geometric measures of the image. The evolving contours naturally split and merge, allowing the simultaneous detection of multiple objects and both interior and exterior boundaries. The approach is based on the relation between active contours and the computation of geodesics. These geodesics are curves embedded in a Riemannian space whose metric is defined by the image content. Our object segmentation approach links between classical ``snakes'' which are based on energy minimization and geometric active contours based on the theory of geometric curve evolution. The scheme was implemented using efficient and stable algorithms for curve and surface evolution. We will also present a recent result that revisits classical theory of edge detectors (like the Marr-Hildreth, and Canny) and leads to better geometric active contours. Experimental results of applying the scheme to images including objects with holes, 2D, 3D, and even 4D medical data imagery, and segmentation and tracking in color movies, demonstrate the power of this framework.
For further reading see:
V Caselles, R Kimmel, and G Sapiro. Geodesic active contours. International Journal of Computer Vision, 22(1):61-79, 1997.
V Caselles, R Kimmel, G Sapiro, and C Sbert. Minimal surfaces: A geometric three dimensional segmentation approach. Numerische Mathematik, 77(4):423-451, 1997.
V Caselles, R Kimmel, G Sapiro, and C Sbert. Minimal surfaces based object segmentation. IEEE Trans. on PAMI, 19(4):394-398, 1997.
R. Goldenberg, R. Kimmel, E. Rivlin, and M. Rudzsky. Fast Geodesic Active Contours. Accepted to IEEE Tran. on Image Processing, 2001.
R. Kimmel, A.M. Bruckstein, Regularized Laplacian Zero Crossings as Optimal Edge Integrators, In Proc. of Image and Vision Computing, IVCNZ01, New Zealand, Nov. 2001.to appear.
available at http://www.cs.technion.ac.il/~ron/pub.html
We review a computationally optimal numerical answer to the question of how to compute the shortest path between two points on a surface, also known as the `minimal geodesic problem'. We have extended a numerical technique for solving Eikonal equations on flat domains to triangulated curved domains. It provides a scheme for computing geodesic distances and thereby solving the minimal geodesic problem. Next, we show who to use the method to compute Voronoi diagrams and offset curves on surfaces. We present applications of the technique to areas like 3D shape reconstruction in computer vision, path planning in robotic navigation, and texture mapping in computer graphics. Finally, it will be shown how to use the method to flatten surfaces into bending invariant canonical forms and thereby obtain isometric invariant `signatures' for surfaces.
For further reading see:
L. Cohen and R. Kimmel. Global minimum for active contours models: A minimal path approach. International Journal of Computer Vision, 24(1):57-78, 1997.
R. Kimmel and J. A. Sethian. Computing Geodesic Paths on Manifolds in the Proceedings of National Academy of Sciences, 95(15):8431-8435, July, 1998.
R. Kimmel and J. A. Sethian. Optimal algorithm for shape from shading and path planning. Accepted to Journal of Mathematical Imaging and Vision, 2001.
G. Zigelman, R. Kimmel, and N. Kiryati, Texture mapping using surface flattening via multi-dimensional scaling, Accepted to IEEE Trans. on Visualization and Computer Graphics, 2001. (PDF).
A. Elad, and R. Kimmel, CVPR'2001 to appear.
all available at http://www.cs.technion.ac.il/~ron/pub.html
Recently we (Sochen-Kimmel-Malladi) introduced a geometric framework for image processing in which images are treated as surfaces and denoising is performed by minimizing the image area in a special way. In this talk I will briefly review the scale space theory in computer vision and image processing and show the connection to our geometric framework. I will introduce a `bending invariant' flow for images painted on surfaces.
Next, we learn how a simplified color image formation model motivates the `Beltrami flow' for color images and color movies. The color formation model leads to extensions that go beyond the metric framework. One such example is an inverse diffusion across edges for color coherence enhancement, which is an extension of Gabor's idea from 1965.
For further reading see:
R. Kimmel. Intrinsic scale space for images on surfaces: The geodesic curvature flow. Graphical Models and Image Processing, 59(5):365-372, 1997.
N Sochen, R Kimmel and R Malladi. A Geometrical Framework for Low Level Vision IEEE Trans. on Image Processing, Special Issue on PDE based Image Processing , 7(3):310-318, 1998.
R. Kimmel. Demosaicing: Image reconstruction from color CCD samples. IEEE Trans. on Image Processing, 8(9):1221-8, Sept. 1999
R. Kimmel, R. Malladi, and N. Sochen. Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images. International Journal of Computer Vision, 39(2):111-129, Sept. 2000.
N. Sochen, R. Kimmel, and A.M. Bruckstein. Diffusions and confusions in signal and image processing, Accepted to Journal of Mathematical Imaging and Vision, 2001
available at http://www.cs.technion.ac.il/~ron/pub.html
The cost of this tutorial is A$ 400.