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Image Segmentation some examples Zhiqiang wang [email protected] Cell segmentation Active contour method image segmentations 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. 20 40 40 20 60 80 0 100 120 -20 140 -40 160 180 -60 Skeleton of the subregion 200 20 40 60 80 100 120 140 Distance field 160 180 200 Active Contour Model for Image Segmentation 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. 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. Curve: polygon = parametric AC parametric continuous = geometric AC geometric 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. f / | flow f | Gradientvector 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. CV model Its main idea of CV model is to minimize the inter class variances inf c1 , c 2 , C 1 E c1 , c 2 , C ds inside ( C ) C I 0 c1 dxdy 2 outside ( C ) I 0 c 2 dxdy 2 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. inf E u 1 , u 2 , C ds C c1 , c 2 , C 1 inside ( C ) ← Smooth term I 0 u1 2 dxdy outside ( C ) I 0 u 2 2 dxdy ← data term Let I 0 be the original image to be segmented and C denote the evolving curve. and are positive weights to control C’s smoothness.u1 is the mean value of I 0 inside the C and u 2 is the mean outside C. To minimize the cost function, Euler-lagrange equation is used: C t N I 0 u1 I 0 u 2 2 2 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: C t N I 0 c1 I 0 c 2 2 2 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 success failure 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: C t g g N N Smooth term data term g is an edge-stopping function defined as follow: 1 g 1 G I 0 2 The term G I denotes the gradient of a Gaussian smoothed image, where is a smooth parameter. 0 GAC model Features of edge based model success failure 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) Cost to assign to 0 Cost to split nodes Cost to assign to 1 Sink (Label 1) Construct graph and perform graph cut agorithm Gaussian Mixture Model and Graph Cut R Foreground & Background Background Iterated graph cut R Foreground G Gaussian Mixture Model (typically 5-8 components) Background G More examples The problem of hard segmentation Alpha matting + Alpha matting I i i Fi (1 i ) B i = x Matting is ill posed problem + x Scribbles approach 0 1 I i i Fi (1 i ) B i Color lines Color Line: C i R 3 C i i C 1 (1 i ) C 2 B R G Color lines Color Line: C i R 3 C i i C 1 (1 i ) C 2 B R G Matting results + Combine hard segmentation More examples Thanks