CS 641 Term projectLevel-set based segmentation algorithms

Presented by-Karthik Alavala

(under the guidance of Dr. Jundong Liu)

ReferencesCaselles Method• V. Caselles, R. Kimmel, and G. Sapiro. Geodesic active contours. Int. J. of Computer Vision, volume 22, pp.61{79, 1997.

Chan & Vese Method• T. Chan and L. Vese. Active contours without edges. IEEE Trans. Image Process., volume 10, no.02, pp.266{277, 2001.

Lankton Method• S. Lankton and A. Tannenbaum. Localizing region-based active contours. IEEE Trans. Image Process., volume 17, no 11, pp.2029{2039, 2008.

Li Method• C. Li, C.-Y. Kao, J. C. Gore, and Z. Ding. Minimization of region-scalable tting energy for image

segmentation. IEEE Trans. Image Process., volume 17, no.10, pp.1940{1949, 2008.

Shi Method• Y. Shi and W. C. Karl. A real-time algorithm for the approximation of level-set based curve

evolution. IEEE Trans. Image Process., volume 17, no.05, pp.645{656, 2008.

Caselles• Contour based method.

– Motivated by curve evolution approach and not an energy minimization.

• Approach- deforming the initial contour

• Beta is set to zero

I(.) corresponds to the image intensity, (tow) is the parametric curve and G is a gaussian filter of variance 1.

• g(I) is the stopping function. Goal of this function?• Intensity obtained is a smoothed version.

• No regularization term

• Evolution equation:

• Speed of convergence can be varied. Last term is called “area constraint”.

Limitations • Due to large variation of the gradient along the object

boundaries and high noise in the image. The curve did not stop at the correct position and the tumor was detected.

Remedy• Incorporating prior information about the image quality(?)• More stopping conditions.

CHAN- VESE• Region based method. It tends to separate the image into two

homogeneous region.• Snake Model:

• Minimizing the above equation, we are trying to locate at maximum . This acts as an edge detector.

• Edge detector function:

• Model:• Fitting terms: Our motive is to minimize this term

• Energy criterion:

three blurred objects different objects from a noisy image

Limitations• Examples of images for which the averages “inside” and

“outside” the objects are the same.

Remedy:• Make use of prior information from the image.

Chunming LiActive contour model:

This algorithm is a region based active contour model.

Energy Criterion:

Where I(y) is the image intensity at point x and can be controlled by Kernel function.

Fitting functions: They optimally approximate the local image intensities.

• Minimizing Energy function:

• To minimize the above function, its gradient flow is used as the level set evolution equation

• Properties:– This algorithms segments the whole image.– Works with different modalities.– The functions are marginally affected by the noise

• Results:– Emergence of new contours during the curve evolution.– Detection of interior boundaries

• Limitations:– Not clear information about the region scalability.– This is a two phase model and cannot segment regions with multiple junctions.

• Results:

• Remedy:– Changing the local intensity fitting energy for ‘x’ number of disjoint regions.– Extracting as much as prior information about the image.

Lankton method • Synthetic image of a blob with heterogeneous intensity on a background of similar

heterogeneous intensity.

(a) Initial contour. (b) Unsuccessful result of region-based segmentation. (c) Successful result of edge-based segmentation technique.

• Energy criterion:

• B is a ball of radius r centered at point x

• Segmentations are not based on global region models, instead it is done locally.• So, it allows to segment non homogeneous objects.

• Implementation:• Energies are expressed in terms of a signed distance function (phi).

Evolution equation

Here Au and Av are the area of the local interior and local exterior regions

• Comparison of global

vs local.

• Advantages:– Comparison with global energies– Multiple interacting contours– Analyzing the localization radius

• Limitations:– Sensitivity to Initialization ( localized contour may not use enough

information).

Remedy:- Extreme care should be taken while initializing the contour.

Shi• Curve evolution: Powerful technique in many

image and video analysis problems.• Fast algorithm based on the approximation of

level-set based curve evolution. • Piecewise constant function

• Curve evolution equation:

• Curve evolution process:F = F(d) + F(int)

– curve evolve using the data attachment term F(d)

– smoothness term F(int)

Limitations:• It needs to maintain the level-set function as a signed distance

function, which is computationally expensive.

Thank you..