Image Segmentation

* Image Segmentation using level sets and the piecewise constant Mumford-Shah Model
* Active Contours without Edges for Vector-Valued Images
* Active Contours without Edges

Image Segmentation using level sets and the piecewise constant Mumford-Shah Model

We propose a multiphase level set algorithm for solving the minimal partition Problem for image segmentation. Our starting point is the piecewise constant Mumford-Shah model for segmentation. The proposed method can also be viewed as as an extension and generalization of as active contour model without edges based on a 2-phase segmentation (Chan and Vese, 1999). Our Multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases; it can represent boundaries with complex topologies, including triple junctions.(from CAM 00-14 abstract, April 2000). Report by Chan and Vese .

( Double Click to see Movies )
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Active Contours without Edges for Vector-Valued Images

We propose an active contour algorithm for object detection in vector valued images (such as RGB or Multi-spectral). The model is as extension of the scalar Chan-Vese(1999) algorithm to the vector-valued case. The model minimizes a Mumford-Shah functional over the length of the contour, plus the sum of the fitting error over the each component of the vector-valued image. Like the C-V model, our vector-valued model can detect both edges with or without gradient. We show examples where our model detects vector-valued objects, which are undetectable in any scalar representation. For instance, objects with different missing parts in different channels are completely detected (such as occlusion). Also, in color images, objects which are invisible in each channel or in intensity, can be detected by our algorithm. Finally, the model is robust with respect to noise, requiring no a priori denoising step.(from CAM 99-35 abstract, Oct 1999). Report by Chan, Sandberg and Vese .

Active Contours without Edges

We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by gradient. We minimize an energy which can be seen as a particular case of so-called minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the images, as in the classical active contour models, but is instead related to a particular segmentation of the image. (from CAM 98-53 abstract, Dec. 98). Report by Chan and Vese .

Image with Three Objects ( Double Click to see Movies )
Blured image and Noisy Plain
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For Cluster Map
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Galaxie and Spiral
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Reports on Segmentations
Reports on Computational Techniques
Reports on Level Set Methods

Tony Chan , Luminita Vese , Berta Sandberg