022510 Graphbased Segmentation Computer Vision CS 543 ECE

02/25/10 Graph-based Segmentation Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem

Last class • Gestalt cues and principles of organization • Mean-shift segmentation – Good general-purpose segmentation method – Generally useful clustering, tracking technique • Watershed segmentation – Good for hierarchical segmentation – Use in combination with boundary prediction

Today’s class • Treating the image as a graph – Normalized cuts segmentation – MRFs Graph cuts segmentation • Recap • Go over HW 2 instructions

Images as graphs i wij j c • Fully-connected graph – node for every pixel – link between every pair of pixels, p, q – similarity wij for each link Source: Seitz

Similarity matrix Increasing sigma

Segmentation by Graph Cuts w A B C • Break Graph into Segments – Delete links that cross between segments – Easiest to break links that have low cost (low similarity) • similar pixels should be in the same segments • dissimilar pixels should be in different segments Source: Seitz

Cuts in a graph A B • Link Cut – set of links whose removal makes a graph disconnected – cost of a cut: One idea: Find minimum cut • gives you a segmentation • fast algorithms exist for doing this Source: Seitz

But min cut is not always the best cut. . .

Cuts in a graph A B Normalized Cut • a cut penalizes large segments • fix by normalizing for size of segments • volume(A) = sum of costs of all edges that touch A Source: Seitz

Recursive normalized cuts 1. Given an image or image sequence, set up a weighted graph: G=(V, E) – – Vertex for each pixel Edge weight for nearby pairs of pixels 2. Solve for eigenvectors with the smallest eigenvalues: (D − W)y = λDy – – Use the eigenvector with the second smallest eigenvalue to bipartition the graph Note: this is an approximation 4. Recursively repartition the segmented parts if necessary Details: http: //www. cs. berkeley. edu/~malik/papers/SM-ncut. pdf

Normalized cuts results

Normalized cuts: Pro and con • Pros – – • Generic framework, can be used with many different features and affinity formulations Provides regular segments Cons – – – Need to chose number of segments High storage requirement and time complexity Bias towards partitioning into equal segments • Usage – Use for oversegmentation when you want regular segments

Graph cuts segmentation

Markov Random Fields Node yi: pixel label Edge: constrained pairs Cost to assign a label to each pixel Cost to assign a pair of labels to connected pixels

Markov Random Fields • Example: “label smoothing” grid Unary potential 0: -log. P(yi = 0 ; data) 1: -log. P(yi = 1 ; data) Pairwise Potential 0 1 0 0 K 1 K 0

Solving MRFs with graph cuts Source (Label 0) Cost to assign to 0 Cost to split nodes Cost to assign to 1 Sink (Label 1)

Solving MRFs with graph cuts Source (Label 0) Cost to assign to 0 Cost to split nodes Cost to assign to 1 Sink (Label 1)

Grab cuts and graph cuts Magic Wand (198? ) Intelligent Scissors Mortensen and Barrett (1995) Grab. Cut User Input Result Regions Boundary Regions & Boundary Source: Rother

Colour Model R Foregroun d& Backgroun d Backgroun G d Iterated graph cut R Foreground Backgroun d G Gaussian Mixture Model (typically 5 -8 components) Source: Rother

Graph cuts Boykov and Jolly (2001) Image Foreground (source) Min Cut Background (sink) Cut: separating source and sink; Energy: collection of edges Min Cut: Global minimal enegry in polynomial time Source: Rother

Graph cuts segmentation 1. Define graph – usually 4 -connected or 8 -connected 2. Define unary potentials – Color histogram or mixture of Gaussians for background and foreground 3. Define pairwise potentials 4. Apply graph cuts 5. Return to 2, using current labels to compute foreground, background models

Moderately straightforward examples … Grab. Cut completes automatically Grab. Cut – Interactive Foreground Extraction 10

Difficult Examples Camouflage & Low Contrast Fine structure Harder Case Initial Rectangle Initial Result Grab. Cut – Interactive Foreground Extraction 11

Using graph cuts for recognition Texton. Boost (Shotton et al. 2009 IJCV)

Using graph cuts for recognition Unary Potentials Alpha Expansion Graph Cuts Texton. Boost (Shotton et al. 2009 IJCV)

Limits of graph cuts • Associative: edge potentials penalize different labels Must satisfy • If not associative, can sometimes clip potentials • Approximate for multilabel – Alpha-expansion or alpha-beta swaps

Graph cuts: Pros and Cons • Pros – Very fast inference – Can incorporate recognition or high-level priors – Applies to a wide range of problems (stereo, image labeling, recognition) • Cons – Not always applicable (associative only) – Need unary terms (not used for generic segmentation) • Use whenever applicable

Further reading and resources • Normalized cuts and image segmentation (Shi and Malik) http: //www. cs. berkeley. edu/~malik/papers/SM-ncut. pdf • N-cut implementation http: //www. seas. upenn. edu/~timothee/software/ncut. html • Graph cuts – http: //www. cs. cornell. edu/~rdz/graphcuts. html – Classic paper: What Energy Functions can be Minimized via Graph Cuts? (Kolmogorov and Zabih, ECCV '02/PAMI '04)

Recap of Grouping and Fitting

Line detection and Hough transform • Canny edge detector = smooth derivative thin threshold link • Generalized Hough transform = points vote for shape parameters • Straight line detector = canny + gradient orientations orientation binning linking check for straightness

Robust fitting and registration Key algorithm • RANSAC

Clustering Key algorithm • Kmeans

EM and Mixture of Gaussians Tutorials: http: //www. cs. duke. edu/courses/spring 04/cps 196. 1/. . . /EM/tomasi. EM. pdf http: //www-clmc. usc. edu/~adsouza/notes/mix_gauss. pdf

Segmentation • Mean-shift segmentation – Flexible clustering method, good segmentation • Watershed segmentation – Hierarchical segmentation from soft boundaries • Normalized cuts – Produces regular regions – Slow but good for oversegmentation • MRFs with Graph Cut – Incorporates foreground/background/object model and prefers to cut at image boundaries – Good for interactive segmentation or recognition

Next section: Recognition • How to recognize – Specific object instances – Faces – Scenes – Object categories – Materials