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image segmentations
Cell segmentation
Active contour method
Interactive method (graph cut)
Other examples
Cell Segmentation
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.
2nd Step: Image smooth
To simplify image’s content, noise and detail texture should be removed.
Gaussian filter or Nonlinear diffusion method
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
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.
3rd Step: Find centroids of subregion
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.
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Distance fieldSkeleton of the subregion
Active Contour Model for Image Segmentation
What’s active contour?
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.
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).
Advantages of active contour
Threshold Edge detectionAn image of blood vessel
Nice representation of object boundary: Smooth and closed, good for shape analysis and recognition and other applications.
parametric geometric
Curve:
polygon = parametric AC continuous = geometric AC
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.
||/ ff Gradient vector flow
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.
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:
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.
Its main idea of CV model is to minimize the inter class variances
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CoutsideCinside
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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.
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.
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← Smooth term
← data term
Evolution speed control (CV model)
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To minimize the cost function, Euler-lagrange equation is used:
Evolution speed control (CV model)
Its main idea of CV model is to minimize the inter class variances
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C
• Mean curvature motion is the steepest descent
flow (or gradient flow) that minimizes arc length of the contour:
Parametric Deformable Model • The curves can be represented as level sets of higher dimensional functions
yielding seamless treatment of topological changes.
Research Problem-- weakness of region based model
failure
success
Evolution speed control--GAC model
• A basic version of the speed function that combine curvature and constant deformation is GAC model:
Smooth term data term
NN
ggt
C
g is an edge-stopping function defined as follow: 1
g 21 G 0I
0G I The term denotes the gradient of a Gaussian smoothed image, where is a smooth parameter.
• 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.
GAC model
Features of edge based model
failure
success
3D Case
Interactive segmentation(graph cut and alpha matting)
Reference: Anat Levin, etc. A Closed Form Solution to Natural Image Matting. 2006
Remove complicate background
Over segmentation with meanshift method
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
Construct graph and perform graph cut agorithm
Gaussian Mixture Model and Graph Cut
Gaussian Mixture Model (typically 5-8 components)
Foreground &Background
Background
Foreground
BackgroundG
R
G
RIterated graph cut
More examples
The problem of hard segmentation
Alpha matting
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Alpha matting
iiiii BFI )1(
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Matting is ill posed problem
iiiii BFI )1(
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Scribbles approach
Color Line:
Color lines
213 )1( CCCRC iiii
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Color lines
Color Line: 213 )1( CCCRC iiii
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Matting results
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Combine hard segmentation
More examples
Thanks
