1. Image Segmentation
some examples
Zhiqiang wang

2. Interactive method (graph cut)
Cell segmentation
Active contour method
image segmentations
Interactive method (graph cut)
Other examples

3. Cell Segmentation

4. 1st Step: Image resize
Since original image’s resolution is 3978*3054, its size is very big and may let extracting algorithm be time consuming.

5. 2nd Step: Image smooth
To simplify image’s content, noise and detail texture should be removed.
Gaussian filter or Nonlinear diffusion method

6. 3rd Step: interactive segmentation
Using interacting method to select which cell we want to extract.
Level set : initial contour
Water shed : seed point
Graph cut: label foreground and background

7. 3rd Step: Find centroids of subregion
After segmentation, we can get 59 subregions. For each region, we find centroids for each subregion as a seed point.

8. 3rd Step: Find centroids of subregion

9. How to find center point
In some cases, centroid is outside of the subregion. As a seed point, it would impede further segmentation.
Possible solution:
erode the subregion until it become a point.
computing the distance between inside pixels and the contour of subregion, take the point which have max distance value as the seed point.
Skeleton of the subregion
Distance field

10. Active Contour Model for Image Segmentation

11. What’s active contour? AC = Curve fitted iteratively to an image
evolve based on its shape and the image value until it stabile (ideally on an object’s boundary).
This method can also be understood as a special case of a more general technique of matching a deformable model to an image by energy minimization.

12. Advantages of active contour
An image of blood vessel
Threshold
Edge detection
Nice representation of object boundary: Smooth and closed, good for shape analysis and recognition and other applications.

13. parametric geometric Curve: polygon = parametric AC
continuous = geometric AC
geometric
parametric

14. Parametric Model: Gradient vector flow (GVF)
GVF field is a non-irrotational external force field that points toward the boundaries when in their proximity and varies smoothly over homogeneous image regions all the way to image borders.
Gradient vector flow

15. Example: Gradient vector flow
GVF field is a non-irrotational external force field that points toward the boundaries when in their proximity and varies smoothly over homogeneous image regions all the way to image borders.

16. General Curve evolution
Let a curve moving in time t be denoted by X[x(s,t), y(s,t)）, where s is curve parameterization. Let N be the moving curve’s inward normal, and c curvature. And let the curve develop along its normal direction according to the partial differential equation:

17. Basic deformation equation
Constant Speed Motion (Area decreasing flow)
Mean curvature motion (Length shortening flow)
During the evolution process for image segmentation, curvature deformation and/or constant deformation are used and the speed of curve evolution is locally dependent on the image data.

18. CV model
Its main idea of CV model is to minimize the inter class variances

19. Evolution speed control (CV model)
A basic version of the speed function that combine curvature and constant deformation is CV model(Active contour model without edge) Its main idea is to consider the information inside the regions.
← Smooth term
← data term
Let be the original image to be segmented and C denote the evolving curve. and are positive weights to control C’s smoothness. is the mean value of inside the C and is the mean outside C.
To minimize the cost function, Euler-lagrange equation is used:

20. Evolution speed control (CV model)
Its main idea of CV model is to minimize the inter class variances
Mean curvature motion is the steepest descent
flow (or gradient flow) that minimizes arc length of the contour:

21. Parametric Deformable Model
The curves can be represented as level sets of higher dimensional functions yielding seamless treatment of topological changes.

22. Research Problem-- weakness of region based model
success
failure

23. Evolution speed control--GAC model
During the evolution process for image segmentation, curvature deformation and/or constant deformation are used and the speed of curve evolution is locally dependent on the image data.
A basic version of the speed function that combine curvature and constant deformation is GAC model:
Smooth term
data term
g is an edge-stopping function defined as follow:
The term denotes the gradient of a Gaussian smoothed image, where
is a smooth parameter.

24. GAC model

25. Features of edge based model
success
failure

26. 3D Case

27. Interactive segmentation (graph cut and alpha matting)
Reference: Anat Levin, etc. A Closed Form Solution to Natural Image Matting. 2006

28. Remove complicate background

29. Over segmentation with meanshift method

30. Construct graph and perform graph cut agorithm
Source (Label 0)
Sink (Label 1)
Cost to assign to 0
Cost to assign to 1
Cost to split nodes

31. Construct graph and perform graph cut agorithm

32. Gaussian Mixture Model and Graph Cut
Iterated graph cut
Foreground & Background
Foreground
Background G
Background G
Gaussian Mixture Model (typically 5-8 components)

33. More examples

34. The problem of hard segmentation

35. Alpha matting +

36. Alpha matting = x + x
Matting is ill posed problem

37. Scribbles approach

39. Color lines
Color Line: B R G

40. Color lines
Color Line: B R G

41. Matting results +

42. Combine hard segmentation

43. More examples

44. Thanks