CAP5415-Computer Vision Lecture 13-Image/Video Segmentation Part II. Dr. Ulas Bagci

Size: px
Start display at page:

Download "CAP5415-Computer Vision Lecture 13-Image/Video Segmentation Part II. Dr. Ulas Bagci"

Transcription

1 CAP-Computer Vision Lecture -Image/Video Segmentation Part II Dr. Ulas Bagci

2 Labeling & Segmentation Labeling is a common way for modeling various computer vision problems (e.g. optical flow, image segmentation, stereo matching, etc)

3 Labeling & Segmentation Labeling is a common way for modeling various computer vision problems (e.g. optical flow, image segmentation, stereo matching, etc) The set of labels can be discrete (as in image segmentation) L = {l,...,l m } with L = m

4 Labeling & Segmentation Labeling is a common way for modeling various computer vision problems (e.g. optical flow, image segmentation, stereo matching, etc) The set of labels can be discrete (as in image segmentation) L = {l,...,l m } with L = m Or continuous (as in optical flow) L R n for n

5 Labeling is a function Labels are assigned to sites (pixel locations)

6 Labeling is a function Labels are assigned to sites (pixel locations) For a given image, we have = N cols.n rows

7 Labeling is a function Labels are assigned to sites (pixel locations) For a given image, we have Identifying a labeling function (with segmentation) is f :! L = N cols.n rows 7

8 Labeling is a function Labels are assigned to sites (pixel locations) For a given image, we have Identifying a labeling function (with segmentation) is f :! L = N cols.n rows We aim at calculating a labeling function that minimizes a given (total) error or energy 8

9 Labeling is a function Labels are assigned to sites (pixel locations) For a given image, we have Identifying a labeling function (with segmentation) is f :! L = N cols.n rows We aim at calculating a labeling function that minimizes a given (total) error or energy E(f) = X p [E data (p, f p )+ X qa(p) E smooth (f p,f q )] *A is an adjacency relation between pixel locations 9

10 Energy Function The role of an energy function in minimizationbased vision is twofold:. as the quantitative measure of the global quality of the solution and. as a guide to the search for a minimal solution. Correct solution is embedded as the minimum. 0

11 Segmentation as an Energy Minimization Problem E data assigns non-negative penalties to a pixel location p when assigning a label to this location.

12 Segmentation as an Energy Minimization Problem E data assigns non-negative penalties to a pixel location p when assigning a label to this location. E smooth assigns non-negative penalties by comparing the assigned labels f p and f q at adjacent positions p and q.

13 Segmentation as an Energy Minimization Problem E data assigns non-negative penalties to a pixel location p when assigning a label to this location. E smooth assigns non-negative penalties by comparing the assigned labels f p and f q at adjacent positions p and q.

14 Segmentation as an Energy Minimization Problem E data assigns non-negative penalties to a pixel location p when assigning a label to this location. E smooth assigns non-negative penalties by comparing the assigned labels f p and f q at adjacent positions p and q. This optimization model is characterized by local interactions along edges between adjacent pixels, and often called MRF (Markov Random Field) model.

15 E(f) = X p Energy Function-Details [E data (p, f p )+ X qa(p) E smooth (f p,f q )]

16 E(f) = X p Energy Function-Details Sample Data Term: [E data (p, f p )+ X qa(p) E smooth (f p,f q )] E data (p, f p )= (p) (p = 0) = logp(p BG) (p = ) = logp(p FG)

17 E(f) = X p Energy Function-Details Sample Data Term: [E data (p, f p )+ X qa(p) E smooth (f p,f q )] E data (p, f p )= (p) (p = 0) = logp(p BG) (p = ) = logp(p FG) Sample Smoothness Term: (p, q) =K pq (p = q) where K pq = exp( (I p I q ) /( )) p, q 7

18 Energy Function-Details E(p) = X p p(p)+ X p X pq(p, q) qa(p) p = argmin pl E(p) 8

19 Energy Function-Details E(p) = X p p(p)+ X p X pq(p, q) qa(p) p = argmin pl E(p) To solve this problem, transform the energy functional into min-cut/max-flow problem and solve it! 9

20 Energy Function Unary Cost (data term) Discontinuity Cost p q 0

21 Recap: Image as a Graph p q Edge Node/vertex pixel

22 Graph Cuts for Optimal Boundary Detection (Boykov ICCV 00) F Binary label: foreground vs. background User labels some pixels B Exploit F F B Statistics of known Fg & Bg F F B Smoothness of label F B B Turn into discrete graph optimization Graph cut (min cut / max flow)

23 Graph-Cut Each pixel is connected to its neighbors in an undirected graph Goal: split nodes into two sets A and B based on pixel values, and try to classify Neighbors in the same way too!

24 Graph-Cut Each pixel is connected to its neighbors in an undirected graph Goal: split nodes into two sets A and B based on pixel values, and try to classify Neighbors in the same way too!

25 Each pixel = node Add two nodes F & B Graph-Cut Labeling: link each pixel to either F or B F Desired result F F F F F B B B B B

26 Cost Function: Data term Put one edge between each pixel and both F & G Weight of edge = minus data term F B

27 Cost Function: Smoothness term Add an edge between each neighbor pair Weight = smoothness term F B 7

28 Min-Cut Energy optimization equivalent to graph min cut Cut: remove edges to disconnect F from B Minimum: minimize sum of cut edge weight F cut B 8

29 Min-Cut Source 9 v v Graph (V, E, C) Vertices V = {v, v... v n } Edges E = {(v, v )...} Costs C = {c (, )...} Sink 9

30 Min-Cut What is a st-cut? Source An st-cut (S,T) divides the nodes between source and sink. 9 v v What is the cost of a st-cut? Sum of cost of all edges going from S to T Sink = 0

31 Min-Cut What is a st-cut? Source An st-cut (S,T) divides the nodes between source and sink. v v 9 Sink + + = 7 What is the cost of a st-cut? Sum of cost of all edges going from S to T What is the st-mincut? st-cut with the minimum cost

32 How to compute min-cut? Source 9 v v Sink Solve the dual maximum flow problem Compute the maximum flow between Source and Sink Constraints Edges: Flow < Capacity Nodes: Flow in & Flow out Min-cut\Max-flow Theorem In every network, the maximum flow equals the cost of the st-mincut

33 Max-Flow Algorithms Source v v Flow = 0 9 Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

34 Max-Flow Algorithms Source v v Flow = 0 9 Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

35 Max-Flow Algorithms Source - 9 v v - Flow = 0 + Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

36 Max-Flow Algorithms Source v v Flow = 0 9 Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

37 Max-Flow Algorithms Source v v Flow = 0 9 Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity 7

38 Max-Flow Algorithms Source v v Flow = 0 9 Sink Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity 8

39 Max-Flow Algorithms Source v v Flow = + 0 Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity 9

40 Max-Flow Algorithms Source v v Flow = 0 Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity 0

41 Max-Flow Algorithms Source v v Flow = 0 Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

42 Max-Flow Algorithms Source v v Flow = Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

43 Max-Flow Algorithms Source v v Flow = Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

44 Max-Flow Algorithms Source v v Flow = Sink 0 Augmenting Path Based Algorithms. Find path from source to sink with positive capacity. Push maximum possible flow through this path. Repeat until no path can be found Algorithms assume non-negative capacity

45 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) 8 Find the path in the residual graph sink End

46 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) 8 Find the path in the residual graph sink End

47 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) 8 Find the path in the residual graph sink End flow = 7

48 Another Example-Max Flow - source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) 8- Find the path in the residual graph sink End flow = 8

49 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 9

50 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 0

51 Another Example-Max Flow source 9 Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

52 Another Example-Max Flow source 9- Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

53 Another Example-Max Flow source Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

54 Another Example-Max Flow source Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

55 Another Example-Max Flow source Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

56 Another Example-Max Flow source - Ford & Fulkerson algorithm (9) Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) - Find the path in the residual graph sink End flow =

57 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 7

58 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 8

59 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 9

60 Another Example-Max Flow - source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) - Find the path in the residual graph sink End flow = 0

61 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

62 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

63 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

64 Another Example-Max Flow source Ford & Fulkerson algorithm (9) - 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) - Find the path in the residual graph sink End flow =

65 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

66 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow =

67 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Find the path from source to sink While (path exists) flow += maximum capacity in the path Build the residual graph ( subtract the flow) Find the path in the residual graph sink End flow = 7

68 Another Example-Max Flow source Ford & Fulkerson algorithm (9) 7 Why is the solution globally optimal? sink flow = 8

69 Another Example-Max Flow S source Ford & Fulkerson algorithm (9) 7 Why is the solution globally optimal?. Let S be the set of reachable nodes in the residual graph sink flow = 9

70 Another Example-Max Flow S source 9 8 sink Ford & Fulkerson algorithm (9) Why is the solution globally optimal?. Let S be the set of reachable nodes in the residual graph. The flow from S to V - S equals to the sum of capacities from S to V S 70

71 Another Example-Max Flow / / / 0/ / 0/ 0/ source / 8/8 sink / 0/ flow = 8/9 / 0/ / / / / Individual flows obtained by summing up all paths Ford & Fulkerson algorithm (9) Why is the solution globally optimal?. Let S be the set of reachable nodes in the residual graph. The flow from S to V - S equals to the sum of capacities from S to V S. The flow from any A to V - A is upper bounded by the sum of capacities from A to V A. The solution is globally optimal 7

72 Another Example-Max Flow 7 source sink 9 8 S T cost = 8 source sink 9 8 S T

73 Another Example-Max Flow S source 9 cost = 8 sink T 7

74 Another Example-Max Flow source 9 x x x x x x C(x) = x + 9x + x + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + (-x ) + 8(-x ) + (-x ) 8 sink 7

75 Another Example-Max Flow source 9 x x x x x x C(x) = x + 9x + x + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + (-x ) + (-x ) + (-x ) + x + x (-x ) + x (-x ) + (-x ) 8 sink 7

76 Another Example-Max Flow source 9 x x x x x x 8 sink C(x) = x + 9x + x + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + (-x ) + (-x ) + (-x ) + x + x (-x ) + x (-x ) + (-x ) x + x (-x ) + x (-x ) + (-x ) = + x (-x ) + x (-x ) 7

77 Another Example-Max Flow source 9 x x x x x x sink C(x) = + x + x + x + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + (-x ) + (-x ) + (-x ) + x (-x ) + x + x (-x ) + x (-x ) + (-x ) x + x (-x ) + x (-x ) + (-x ) = + x (-x ) + x (-x ) 77

78 Another Example-Max Flow source x x x x x x C(x) = + x + x + x + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) + (-x ) + x (-x ) + x (-x ) + (-x ) + (-x ) + x (-x ) sink 78

79 Another Example-Max Flow source C(x) = + x + x + x (-x ) + x (-x ) + 7x (-x ) + x (-x ) + x (-x ) + x (-x ) + x (-x ) x x 7 + x (-x ) + (-x ) + x (-x ) + x (-x ) x x cost = 0 x cost = 0 x S sink T S set of reachable nodes from s min cut All coefficients positive Must be global minimum 79

80 History of Max-Flow Algorithms Augmenting Path and Push-Relabel n: #nodes m: #edges U: maximum edge weight Algorithms assume nonnegative edge weights 80

81 Ford-Fulkerson Alg. In each iteration of the Ford-Fulkerson method, we find some augmenting path p and increase the flow f on each edge of p by the residual capacity cf(p). If u and v are not connected by an edge in either direction, we assume implicitly that f[u, v] = 0. The capacities c(u, v) are assumed to be given along with the graph, and c(u, v) = 0 if (u, v) E. 8

82 Example Segmentation in a Video n-links s = 0 st-cut E(x) x * w pq t = Image Flow Global Optimum 8

83 Recap: Data Term Without spatial relationship, data term can be the same for regions that Belong to different objects. Image patches show their similarities although they pertain to different objects 8

84 Segmentation Example 8

85 Segmentation Example 8

86 Segmentation Example 8

87 Optimality? Seeds GrabCut (iterative GC With box prior) 87

88 Vascular Surface Segmentation via GC 0// 88

89 GC Refinement Kohli and Torr 89

90 GC Segmentation in Videos Segmentation of human lame walk in a video sequences Kohli and Torr 90

91 Slide Credits and References FredoDurand of MIT M. Tappen of Amazon R. Szelisky, Univ. of Washington/Seatle J.Malcolm, Graph Cut in Tensor Scale Interactive Graph Cuts for Optimal Boundary & Region Segmentation of Objects in N-D images. Yuri Boykov and Marie-Pierre Jolly. In International Conference on Computer Vision, (ICCV), vol. I, A Comparative Study of Energy Minimization Methods for Markov Random Fields. Rick Szeliski, Ramin Zabih, Daniel Scharstein, Olga Veksler, Vladimir Kolmogorov, Aseem Agarwala, Marshall Tappen, Carsten Rother. ECCV 00 P. Kumar, Oxford University. 9

Dr. Ulas Bagci

Dr. Ulas Bagci CAP- Computer Vision Lecture - Image Segmenta;on as an Op;miza;on Problem Dr. Ulas Bagci bagci@ucf.edu Reminders Oct Guest Lecture: SVM by Dr. Gong Oct 8 Guest Lecture: Camera Models by Dr. Shah PA# October

More information

MEDICAL IMAGE COMPUTING (CAP 5937) LECTURE 10: Medical Image Segmentation as an Energy Minimization Problem

MEDICAL IMAGE COMPUTING (CAP 5937) LECTURE 10: Medical Image Segmentation as an Energy Minimization Problem SPRING 06 MEDICAL IMAGE COMPUTING (CAP 97) LECTURE 0: Medical Image Segmentation as an Energy Minimization Problem Dr. Ulas Bagci HEC, Center for Research in Computer Vision (CRCV), University of Central

More information

MEDICAL IMAGE COMPUTING (CAP 5937) LECTURE 10: Medical Image Segmentation as an Energy Minimization Problem

MEDICAL IMAGE COMPUTING (CAP 5937) LECTURE 10: Medical Image Segmentation as an Energy Minimization Problem SPRING 07 MEDICAL IMAGE COMPUTING (CAP 97) LECTURE 0: Medical Image Segmentation as an Energy Minimization Problem Dr. Ulas Bagci HEC, Center for Research in Computer Vision (CRCV), University of Central

More information

Prof. Feng Liu. Spring /17/2017. With slides by F. Durand, Y.Y. Chuang, R. Raskar, and C.

Prof. Feng Liu. Spring /17/2017. With slides by F. Durand, Y.Y. Chuang, R. Raskar, and C. Prof. Feng Liu Spring 2017 http://www.cs.pdx.edu/~fliu/courses/cs510/ 05/17/2017 With slides by F. Durand, Y.Y. Chuang, R. Raskar, and C. Rother Last Time Image segmentation Normalized cut and segmentation

More information

intro, applications MRF, labeling... how it can be computed at all? Applications in segmentation: GraphCut, GrabCut, demos

intro, applications MRF, labeling... how it can be computed at all? Applications in segmentation: GraphCut, GrabCut, demos Image as Markov Random Field and Applications 1 Tomáš Svoboda, svoboda@cmp.felk.cvut.cz Czech Technical University in Prague, Center for Machine Perception http://cmp.felk.cvut.cz Talk Outline Last update:

More information

Markov/Conditional Random Fields, Graph Cut, and applications in Computer Vision

Markov/Conditional Random Fields, Graph Cut, and applications in Computer Vision Markov/Conditional Random Fields, Graph Cut, and applications in Computer Vision Fuxin Li Slides and materials from Le Song, Tucker Hermans, Pawan Kumar, Carsten Rother, Peter Orchard, and others Recap:

More information

CS4670 / 5670: Computer Vision Noah Snavely

CS4670 / 5670: Computer Vision Noah Snavely { { 11/26/2013 CS4670 / 5670: Computer Vision Noah Snavely Graph-Based Image Segmentation Stereo as a minimization problem match cost Want each pixel to find a good match in the other image smoothness

More information

Discrete Optimization Methods in Computer Vision CSE 6389 Slides by: Boykov Modified and Presented by: Mostafa Parchami Basic overview of graph cuts

Discrete Optimization Methods in Computer Vision CSE 6389 Slides by: Boykov Modified and Presented by: Mostafa Parchami Basic overview of graph cuts Discrete Optimization Methods in Computer Vision CSE 6389 Slides by: Boykov Modified and Presented by: Mostafa Parchami Basic overview of graph cuts [Yuri Boykov, Olga Veksler, Ramin Zabih, Fast Approximation

More information

Computer Vision : Exercise 4 Labelling Problems

Computer Vision : Exercise 4 Labelling Problems Computer Vision Exercise 4 Labelling Problems 13/01/2014 Computer Vision : Exercise 4 Labelling Problems Outline 1. Energy Minimization (example segmentation) 2. Iterated Conditional Modes 3. Dynamic Programming

More information

CS6670: Computer Vision

CS6670: Computer Vision CS6670: Computer Vision Noah Snavely Lecture 19: Graph Cuts source S sink T Readings Szeliski, Chapter 11.2 11.5 Stereo results with window search problems in areas of uniform texture Window-based matching

More information

Maximum flows and minimal cuts. Filip Malmberg

Maximum flows and minimal cuts. Filip Malmberg Maximum flows and minimal cuts Filip Malmberg MSF cuts I A Minimum Spanning Forest with respect to a set of seed-points divides a graph into a number of connected components. Thus, it defines a cut on

More information

Energy Minimization for Segmentation in Computer Vision

Energy Minimization for Segmentation in Computer Vision S * = arg S min E(S) Energy Minimization for Segmentation in Computer Vision Meng Tang, Dmitrii Marin, Ismail Ben Ayed, Yuri Boykov Outline Clustering/segmentation methods K-means, GrabCut, Normalized

More information

Graph Cuts vs. Level Sets. part I Basics of Graph Cuts

Graph Cuts vs. Level Sets. part I Basics of Graph Cuts ECCV 2006 tutorial on Graph Cuts vs. Level Sets part I Basics of Graph Cuts Yuri Boykov University of Western Ontario Daniel Cremers University of Bonn Vladimir Kolmogorov University College London Graph

More information

Measuring Uncertainty in Graph Cut Solutions - Efficiently Computing Min-marginal Energies using Dynamic Graph Cuts

Measuring Uncertainty in Graph Cut Solutions - Efficiently Computing Min-marginal Energies using Dynamic Graph Cuts Measuring Uncertainty in Graph Cut Solutions - Efficiently Computing Min-marginal Energies using Dynamic Graph Cuts Pushmeet Kohli Philip H.S. Torr Department of Computing, Oxford Brookes University, Oxford.

More information

CS4670: Computer Vision

CS4670: Computer Vision CS4670: Computer Vision Noah Snavely Lecture 34: Segmentation From Sandlot Science Announcements In-class exam this Friday, December 3 Review session in class on Wednesday Final projects: Slides due: Sunday,

More information

Lecture 16 Segmentation and Scene understanding

Lecture 16 Segmentation and Scene understanding Lecture 16 Segmentation and Scene understanding Introduction! Mean-shift! Graph-based segmentation! Top-down segmentation! Silvio Savarese Lecture 15 -! 3-Mar-14 Segmentation Silvio Savarese Lecture 15

More information

CS 5540 Spring 2013 Assignment 3, v1.0 Due: Apr. 24th 11:59PM

CS 5540 Spring 2013 Assignment 3, v1.0 Due: Apr. 24th 11:59PM 1 Introduction In this programming project, we are going to do a simple image segmentation task. Given a grayscale image with a bright object against a dark background and we are going to do a binary decision

More information

Efficient Parallel Optimization for Potts Energy with Hierarchical Fusion

Efficient Parallel Optimization for Potts Energy with Hierarchical Fusion Efficient Parallel Optimization for Potts Energy with Hierarchical Fusion Olga Veksler University of Western Ontario London, Canada olga@csd.uwo.ca Abstract Potts frequently occurs in computer vision applications.

More information

CSE 417 Network Flows (pt 3) Modeling with Min Cuts

CSE 417 Network Flows (pt 3) Modeling with Min Cuts CSE 417 Network Flows (pt 3) Modeling with Min Cuts Reminders > HW6 is due on Friday start early bug fixed on line 33 of OptimalLineup.java: > change true to false Review of last two lectures > Defined

More information

MRFs and Segmentation with Graph Cuts

MRFs and Segmentation with Graph Cuts 02/24/10 MRFs and Segmentation with Graph Cuts Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem Today s class Finish up EM MRFs w ij i Segmentation with Graph Cuts j EM Algorithm: Recap

More information

Image Segmentation Using Iterated Graph Cuts Based on Multi-scale Smoothing

Image Segmentation Using Iterated Graph Cuts Based on Multi-scale Smoothing Image Segmentation Using Iterated Graph Cuts Based on Multi-scale Smoothing Tomoyuki Nagahashi 1, Hironobu Fujiyoshi 1, and Takeo Kanade 2 1 Dept. of Computer Science, Chubu University. Matsumoto 1200,

More information

Graphs, graph algorithms (for image segmentation),... in progress

Graphs, graph algorithms (for image segmentation),... in progress Graphs, graph algorithms (for image segmentation),... in progress Václav Hlaváč Czech Technical University in Prague Czech Institute of Informatics, Robotics and Cybernetics 66 36 Prague 6, Jugoslávských

More information

Chapter 8 of Bishop's Book: Graphical Models

Chapter 8 of Bishop's Book: Graphical Models Chapter 8 of Bishop's Book: Graphical Models Review of Probability Probability density over possible values of x Used to find probability of x falling in some range For continuous variables, the probability

More information

Reduce, Reuse & Recycle: Efficiently Solving Multi-Label MRFs

Reduce, Reuse & Recycle: Efficiently Solving Multi-Label MRFs Reduce, Reuse & Recycle: Efficiently Solving Multi-Label MRFs Karteek Alahari 1 Pushmeet Kohli 2 Philip H. S. Torr 1 1 Oxford Brookes University 2 Microsoft Research, Cambridge Abstract In this paper,

More information

MULTI-REGION SEGMENTATION

MULTI-REGION SEGMENTATION MULTI-REGION SEGMENTATION USING GRAPH-CUTS Johannes Ulén Abstract This project deals with multi-region segmenation using graph-cuts and is mainly based on a paper by Delong and Boykov [1]. The difference

More information

Graphs and Network Flows IE411. Lecture 13. Dr. Ted Ralphs

Graphs and Network Flows IE411. Lecture 13. Dr. Ted Ralphs Graphs and Network Flows IE411 Lecture 13 Dr. Ted Ralphs IE411 Lecture 13 1 References for Today s Lecture IE411 Lecture 13 2 References for Today s Lecture Required reading Sections 21.1 21.2 References

More information

Announcements. Image Segmentation. From images to objects. Extracting objects. Status reports next Thursday ~5min presentations in class

Announcements. Image Segmentation. From images to objects. Extracting objects. Status reports next Thursday ~5min presentations in class Image Segmentation Announcements Status reports next Thursday ~5min presentations in class Project voting From Sandlot Science Today s Readings Forsyth & Ponce, Chapter 1 (plus lots of optional references

More information

Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters

Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters Comparison of Graph Cuts with Belief Propagation for Stereo, using Identical MRF Parameters Marshall F. Tappen William T. Freeman Computer Science and Artificial Intelligence Laboratory Massachusetts Institute

More information

LOOSECUT: INTERACTIVE IMAGE SEGMENTATION WITH LOOSELY BOUNDED BOXES

LOOSECUT: INTERACTIVE IMAGE SEGMENTATION WITH LOOSELY BOUNDED BOXES Loose Input Box LOOSECUT: INTERACTIVE IMAGE SEGMENTATION WITH LOOSELY BOUNDED BOXES Hongkai Yu 1, Youjie Zhou 1, Hui Qian 2, Min Xian 3, and Song Wang 1 1 University of South Carolina, SC 2 Zhejiang University,

More information

Network Design and Optimization course

Network Design and Optimization course Effective maximum flow algorithms Modeling with flows Network Design and Optimization course Lecture 5 Alberto Ceselli alberto.ceselli@unimi.it Dipartimento di Tecnologie dell Informazione Università degli

More information

Models for grids. Computer vision: models, learning and inference. Multi label Denoising. Binary Denoising. Denoising Goal.

Models for grids. Computer vision: models, learning and inference. Multi label Denoising. Binary Denoising. Denoising Goal. Models for grids Computer vision: models, learning and inference Chapter 9 Graphical Models Consider models where one unknown world state at each pixel in the image takes the form of a grid. Loops in the

More information

Stereo Correspondence with Occlusions using Graph Cuts

Stereo Correspondence with Occlusions using Graph Cuts Stereo Correspondence with Occlusions using Graph Cuts EE368 Final Project Matt Stevens mslf@stanford.edu Zuozhen Liu zliu2@stanford.edu I. INTRODUCTION AND MOTIVATION Given two stereo images of a scene,

More information

Fast Approximate Energy Minimization via Graph Cuts

Fast Approximate Energy Minimization via Graph Cuts IEEE Transactions on PAMI, vol. 23, no. 11, pp. 1222-1239 p.1 Fast Approximate Energy Minimization via Graph Cuts Yuri Boykov, Olga Veksler and Ramin Zabih Abstract Many tasks in computer vision involve

More information

A Principled Deep Random Field Model for Image Segmentation

A Principled Deep Random Field Model for Image Segmentation A Principled Deep Random Field Model for Image Segmentation Pushmeet Kohli Microsoft Research Cambridge, UK Anton Osokin Moscow State University Moscow, Russia Stefanie Jegelka UC Berkeley Berkeley, CA,

More information

Markov Random Fields and Segmentation with Graph Cuts

Markov Random Fields and Segmentation with Graph Cuts Markov Random Fields and Segmentation with Graph Cuts Computer Vision Jia-Bin Huang, Virginia Tech Many slides from D. Hoiem Administrative stuffs Final project Proposal due Oct 27 (Thursday) HW 4 is out

More information

Jessica Su (some parts copied from CLRS / last quarter s notes)

Jessica Su (some parts copied from CLRS / last quarter s notes) 1 Max flow Consider a directed graph G with positive edge weights c that define the capacity of each edge. We can identify two special nodes in G: the source node s and the sink node t. We want to find

More information

Mathematics in Image Processing

Mathematics in Image Processing Mathematics in Image Processing Michal Šorel Department of Image Processing Institute of Information Theory and Automation (ÚTIA) Academy of Sciences of the Czech Republic http://zoi.utia.cas.cz/ Mathematics

More information

Quadratic Pseudo-Boolean Optimization(QPBO): Theory and Applications At-a-Glance

Quadratic Pseudo-Boolean Optimization(QPBO): Theory and Applications At-a-Glance Quadratic Pseudo-Boolean Optimization(QPBO): Theory and Applications At-a-Glance Presented By: Ahmad Al-Kabbany Under the Supervision of: Prof.Eric Dubois 12 June 2012 Outline Introduction The limitations

More information

GRAPH BASED SEGMENTATION WITH MINIMAL USER INTERACTION. Huaizhong Zhang, Ehab Essa, and Xianghua Xie

GRAPH BASED SEGMENTATION WITH MINIMAL USER INTERACTION. Huaizhong Zhang, Ehab Essa, and Xianghua Xie GRAPH BASED SEGMENTATION WITH MINIMAL USER INTERACTION Huaizhong Zhang, Ehab Essa, and Xianghua Xie Computer Science Department, Swansea University, Swansea SA2 8PP, United Kingdom *http://csvision.swan.ac.uk/

More information

Learning CRFs using Graph Cuts

Learning CRFs using Graph Cuts Appears in European Conference on Computer Vision (ECCV) 2008 Learning CRFs using Graph Cuts Martin Szummer 1, Pushmeet Kohli 1, and Derek Hoiem 2 1 Microsoft Research, Cambridge CB3 0FB, United Kingdom

More information

Uncertainty Driven Multi-Scale Optimization

Uncertainty Driven Multi-Scale Optimization Uncertainty Driven Multi-Scale Optimization Pushmeet Kohli 1 Victor Lempitsky 2 Carsten Rother 1 1 Microsoft Research Cambridge 2 University of Oxford Abstract. This paper proposes a new multi-scale energy

More information

Image Segmentation. Marc Pollefeys. ETH Zurich. Slide credits: V. Ferrari, K. Grauman, B. Leibe, S. Lazebnik, S. Seitz,Y Boykov, W. Freeman, P.

Image Segmentation. Marc Pollefeys. ETH Zurich. Slide credits: V. Ferrari, K. Grauman, B. Leibe, S. Lazebnik, S. Seitz,Y Boykov, W. Freeman, P. Image Segmentation Perceptual and Sensory Augmented Computing Computer Vision WS 0/09 Marc Pollefeys ETH Zurich Slide credits: V. Ferrari, K. Grauman, B. Leibe, S. Lazebnik, S. Seitz,Y Boykov, W. Freeman,

More information

Graph Cuts. Srikumar Ramalingam School of Computing University of Utah

Graph Cuts. Srikumar Ramalingam School of Computing University of Utah Graph Cuts Srikumar Ramalingam School o Computing University o Utah Outline Introduction Pseudo-Boolean Functions Submodularity Max-low / Min-cut Algorithm Alpha-Expansion Segmentation Problem [Boykov

More information

Maximum Flow. Flow Networks. Flow Networks Ford-Fulkerson Method Edmonds-Karp Algorithm Push-Relabel Algorithms. Example Flow Network

Maximum Flow. Flow Networks. Flow Networks Ford-Fulkerson Method Edmonds-Karp Algorithm Push-Relabel Algorithms. Example Flow Network Flow Networks Ford-Fulkerson Method Edmonds-Karp Algorithm Push-Relabel Algorithms Maximum Flow Flow Networks A flow network is a directed graph where: Each edge (u,v) has a capacity c(u,v) 0. If (u,v)

More information

Image Segmentation Using Iterated Graph Cuts BasedonMulti-scaleSmoothing

Image Segmentation Using Iterated Graph Cuts BasedonMulti-scaleSmoothing Image Segmentation Using Iterated Graph Cuts BasedonMulti-scaleSmoothing Tomoyuki Nagahashi 1, Hironobu Fujiyoshi 1, and Takeo Kanade 2 1 Dept. of Computer Science, Chubu University. Matsumoto 1200, Kasugai,

More information

Capacity Scaling for Graph Cuts in Vision

Capacity Scaling for Graph Cuts in Vision Capacity Scaling for Graph Cuts in Vision Olivier Juan and Yuri Boykov Computer Science Department University of Western Ontario, London, ON, Canada juan@csd.uwo.ca, yuri@csd.uwo.ca Abstract Capacity scaling

More information

Segmentation with non-linear constraints on appearance, complexity, and geometry

Segmentation with non-linear constraints on appearance, complexity, and geometry IPAM February 2013 Western Univesity Segmentation with non-linear constraints on appearance, complexity, and geometry Yuri Boykov Andrew Delong Lena Gorelick Hossam Isack Anton Osokin Frank Schmidt Olga

More information

Graph Cut based Continuous Stereo Matching using Locally Shared Labels

Graph Cut based Continuous Stereo Matching using Locally Shared Labels Graph Cut based Continuous Stereo Matching using Locally Shared Labels Tatsunori Taniai University of Tokyo, Japan taniai@iis.u-tokyo.ac.jp Yasuyuki Matsushita Microsoft Research Asia, China yasumat@microsoft.com

More information

CS448f: Image Processing For Photography and Vision. Graph Cuts

CS448f: Image Processing For Photography and Vision. Graph Cuts CS448f: Image Processing For Photography and Vision Graph Cuts Seam Carving Video Make images smaller by removing seams Seam = connected path of pixels from top to bottom or left edge to right edge Don

More information

CSE 417 Network Flows (pt 4) Min Cost Flows

CSE 417 Network Flows (pt 4) Min Cost Flows CSE 417 Network Flows (pt 4) Min Cost Flows Reminders > HW6 is due Monday Review of last three lectures > Defined the maximum flow problem find the feasible flow of maximum value flow is feasible if it

More information

Supervised texture detection in images

Supervised texture detection in images Supervised texture detection in images Branislav Mičušík and Allan Hanbury Pattern Recognition and Image Processing Group, Institute of Computer Aided Automation, Vienna University of Technology Favoritenstraße

More information

and 6.855J March 6, Maximum Flows 2

and 6.855J March 6, Maximum Flows 2 5.08 and.855j March, 00 Maximum Flows Network Reliability Communication Network What is the maximum number of arc disjoint paths from s to t? How can we determine this number? Theorem. Let G = (N,A) be

More information

Segmentation. Bottom up Segmentation Semantic Segmentation

Segmentation. Bottom up Segmentation Semantic Segmentation Segmentation Bottom up Segmentation Semantic Segmentation Semantic Labeling of Street Scenes Ground Truth Labels 11 classes, almost all occur simultaneously, large changes in viewpoint, scale sky, road,

More information

CSC 8301 Design & Analysis of Algorithms: Linear Programming

CSC 8301 Design & Analysis of Algorithms: Linear Programming CSC 8301 Design & Analysis of Algorithms: Linear Programming Professor Henry Carter Fall 2016 Iterative Improvement Start with a feasible solution Improve some part of the solution Repeat until the solution

More information

Segmentation. Separate image into coherent regions

Segmentation. Separate image into coherent regions Segmentation II Segmentation Separate image into coherent regions Berkeley segmentation database: http://www.eecs.berkeley.edu/research/projects/cs/vision/grouping/segbench/ Slide by L. Lazebnik Interactive

More information

s-t Graph Cuts for Binary Energy Minimization

s-t Graph Cuts for Binary Energy Minimization s-t Graph Cuts for Binary Energy Minimization E data term ( L) = D ( ) + ( ) P Lp λ Ι Lp Lq p prior term Now that we have an energy function, the big question is how do we minimize it? pq N n Exhaustive

More information

Data-driven Depth Inference from a Single Still Image

Data-driven Depth Inference from a Single Still Image Data-driven Depth Inference from a Single Still Image Kyunghee Kim Computer Science Department Stanford University kyunghee.kim@stanford.edu Abstract Given an indoor image, how to recover its depth information

More information

Graph Based Image Segmentation

Graph Based Image Segmentation AUTOMATYKA 2011 Tom 15 Zeszyt 3 Anna Fabijañska* Graph Based Image Segmentation 1. Introduction Image segmentation is one of the fundamental problems in machine vision. In general it aims at extracting

More information

Undirected Graphical Models. Raul Queiroz Feitosa

Undirected Graphical Models. Raul Queiroz Feitosa Undirected Graphical Models Raul Queiroz Feitosa Pros and Cons Advantages of UGMs over DGMs UGMs are more natural for some domains (e.g. context-dependent entities) Discriminative UGMs (CRF) are better

More information

A Multilevel Banded Graph Cuts Method for Fast Image Segmentation

A Multilevel Banded Graph Cuts Method for Fast Image Segmentation Proceedings of the Tenth IEEE International Conference on Computer Vision, ICCV 2005 Volume 1, pp. 259 A Multilevel Banded Graph Cuts Method for Fast Image Segmentation Herve Lombaert Yiyong Sun Leo Grady

More information

Multi-Label Moves for Multi-Label Energies

Multi-Label Moves for Multi-Label Energies Multi-Label Moves for Multi-Label Energies Olga Veksler University of Western Ontario some work is joint with Olivier Juan, Xiaoqing Liu, Yu Liu Outline Review multi-label optimization with graph cuts

More information

Supplementary Material: Adaptive and Move Making Auxiliary Cuts for Binary Pairwise Energies

Supplementary Material: Adaptive and Move Making Auxiliary Cuts for Binary Pairwise Energies Supplementary Material: Adaptive and Move Making Auxiliary Cuts for Binary Pairwise Energies Lena Gorelick Yuri Boykov Olga Veksler Computer Science Department University of Western Ontario Abstract Below

More information

Saliency Cut in Stereo Images

Saliency Cut in Stereo Images 2013 IEEE International Conference on Computer Vision Workshops Saliency Cut in Stereo Images Jianteng Peng, Jianbing Shen, Yunde Jia Beijing Laboratory of Intelligent Information Technology, School of

More information

Lecture 11: Maximum flow and minimum cut

Lecture 11: Maximum flow and minimum cut Optimisation Part IB - Easter 2018 Lecture 11: Maximum flow and minimum cut Lecturer: Quentin Berthet 4.4. The maximum flow problem. We consider in this lecture a particular kind of flow problem, with

More information

Approximate decoding: ICM, block methods, alpha-beta swap & alpha-expansion

Approximate decoding: ICM, block methods, alpha-beta swap & alpha-expansion Approximate decoding: ICM, block methods, alpha-beta swap & alpha-expansion Julieta Martinez University of British Columbia August 25, 2015 https://www.youtube.com/watch?v=kp3ik5f3-2c&t=18m36s Outline

More information

Markov Random Fields with Efficient Approximations

Markov Random Fields with Efficient Approximations Markov Random Fields with Efficient Approximations Yuri Boykov Olga Veksler Ramin Zabih Computer Science Department Cornell University Ithaca, NY 14853 Abstract Markov Random Fields (MRF s) can be used

More information

IMPROVED FINE STRUCTURE MODELING VIA GUIDED STOCHASTIC CLIQUE FORMATION IN FULLY CONNECTED CONDITIONAL RANDOM FIELDS

IMPROVED FINE STRUCTURE MODELING VIA GUIDED STOCHASTIC CLIQUE FORMATION IN FULLY CONNECTED CONDITIONAL RANDOM FIELDS IMPROVED FINE STRUCTURE MODELING VIA GUIDED STOCHASTIC CLIQUE FORMATION IN FULLY CONNECTED CONDITIONAL RANDOM FIELDS M. J. Shafiee, A. G. Chung, A. Wong, and P. Fieguth Vision & Image Processing Lab, Systems

More information

Markov Random Fields and Segmentation with Graph Cuts

Markov Random Fields and Segmentation with Graph Cuts Markov Random Fields and Segmentation with Graph Cuts Computer Vision Jia-Bin Huang, Virginia Tech Many slides from D. Hoiem Administrative stuffs Final project Proposal due Oct 30 (Monday) HW 4 is out

More information

ESSP: An Efficient Approach to Minimizing Dense and Nonsubmodular Energy Functions

ESSP: An Efficient Approach to Minimizing Dense and Nonsubmodular Energy Functions 1 ESSP: An Efficient Approach to Minimizing Dense and Nonsubmodular Functions Wei Feng, Member, IEEE, Jiaya Jia, Senior Member, IEEE, and Zhi-Qiang Liu, arxiv:145.4583v1 [cs.cv] 19 May 214 Abstract Many

More information

Image Segmentation with a Bounding Box Prior Victor Lempitsky, Pushmeet Kohli, Carsten Rother, Toby Sharp Microsoft Research Cambridge

Image Segmentation with a Bounding Box Prior Victor Lempitsky, Pushmeet Kohli, Carsten Rother, Toby Sharp Microsoft Research Cambridge Image Segmentation with a Bounding Box Prior Victor Lempitsky, Pushmeet Kohli, Carsten Rother, Toby Sharp Microsoft Research Cambridge Dylan Rhodes and Jasper Lin 1 Presentation Overview Segmentation problem

More information

Multi-view object segmentation in space and time. Abdelaziz Djelouah, Jean Sebastien Franco, Edmond Boyer

Multi-view object segmentation in space and time. Abdelaziz Djelouah, Jean Sebastien Franco, Edmond Boyer Multi-view object segmentation in space and time Abdelaziz Djelouah, Jean Sebastien Franco, Edmond Boyer Outline Addressed problem Method Results and Conclusion Outline Addressed problem Method Results

More information

A robust stereo prior for human segmentation

A robust stereo prior for human segmentation A robust stereo prior for human segmentation Glenn Sheasby, Julien Valentin, Nigel Crook, Philip Torr Oxford Brookes University Abstract. The emergence of affordable depth cameras has enabled significant

More information

Image Segmentation continued Graph Based Methods. Some slides: courtesy of O. Capms, Penn State, J.Ponce and D. Fortsyth, Computer Vision Book

Image Segmentation continued Graph Based Methods. Some slides: courtesy of O. Capms, Penn State, J.Ponce and D. Fortsyth, Computer Vision Book Image Segmentation continued Graph Based Methods Some slides: courtesy of O. Capms, Penn State, J.Ponce and D. Fortsyth, Computer Vision Book Previously Binary segmentation Segmentation by thresholding

More information

GRMA: Generalized Range Move Algorithms for the Efficient Optimization of MRFs

GRMA: Generalized Range Move Algorithms for the Efficient Optimization of MRFs International Journal of Computer Vision manuscript No. (will be inserted by the editor) GRMA: Generalized Range Move Algorithms for the Efficient Optimization of MRFs Kangwei Liu Junge Zhang Peipei Yang

More information

In IEEE conference on Computer Vision and Pattern Recognition (CVPR), New York, June 2006, vol. I, p Active Graph Cuts

In IEEE conference on Computer Vision and Pattern Recognition (CVPR), New York, June 2006, vol. I, p Active Graph Cuts In IEEE conference on Computer Vision and Pattern Recognition (CVPR), New York, June 2006, vol. I, p.1023 Active Graph Cuts Olivier Juan CERTIS, Ecole Nationale des Ponts et Chaussees Champs-sur-Marne,

More information

Iterative MAP and ML Estimations for Image Segmentation

Iterative MAP and ML Estimations for Image Segmentation Iterative MAP and ML Estimations for Image Segmentation Shifeng Chen 1, Liangliang Cao 2, Jianzhuang Liu 1, and Xiaoou Tang 1,3 1 Dept. of IE, The Chinese University of Hong Kong {sfchen5, jzliu}@ie.cuhk.edu.hk

More information

Network flows and Menger s theorem

Network flows and Menger s theorem Network flows and Menger s theorem Recall... Theorem (max flow, min cut strong duality). Let G be a network. The maximum value of a flow equals the minimum capacity of a cut. We prove this strong duality

More information

USING ONE GRAPH-CUT TO FUSE MULTIPLE CANDIDATE MAPS IN DEPTH ESTIMATION

USING ONE GRAPH-CUT TO FUSE MULTIPLE CANDIDATE MAPS IN DEPTH ESTIMATION USING ONE GRAPH-CUT TO FUSE MULTIPLE CANDIDATE MAPS IN DEPTH ESTIMATION F. Pitié Sigmedia Group, Trinity College Dublin, fpitie@mee.tcd.ie Abstract Graph-cut techniques for depth and disparity estimations

More information

Algorithms for Markov Random Fields in Computer Vision

Algorithms for Markov Random Fields in Computer Vision Algorithms for Markov Random Fields in Computer Vision Dan Huttenlocher November, 2003 (Joint work with Pedro Felzenszwalb) Random Field Broadly applicable stochastic model Collection of n sites S Hidden

More information

arxiv: v2 [cs.dm] 28 Dec 2010

arxiv: v2 [cs.dm] 28 Dec 2010 Multiple-source multiple-sink maximum flow in planar graphs Yahav Nussbaum arxiv:1012.4767v2 [cs.dm] 28 Dec 2010 Abstract In this paper we show an O(n 3/2 log 2 n) time algorithm for finding a maximum

More information

A Comparative Study of Energy Minimization Methods for Markov Random Fields

A Comparative Study of Energy Minimization Methods for Markov Random Fields A Comparative Study of Energy Minimization Methods for Markov Random Fields Richard Szeliski 1, Ramin Zabih 2, Daniel Scharstein 3, Olga Veksler 4, Vladimir Kolmogorov 5, Aseem Agarwala 6, Marshall Tappen

More information

Image Segmentation. April 24, Stanford University. Philipp Krähenbühl (Stanford University) Segmentation April 24, / 63

Image Segmentation. April 24, Stanford University. Philipp Krähenbühl (Stanford University) Segmentation April 24, / 63 Image Segmentation Philipp Krähenbühl Stanford University April 24, 2013 Philipp Krähenbühl (Stanford University) Segmentation April 24, 2013 1 / 63 Image Segmentation Goal: identify groups of pixels that

More information

Introduction à la vision artificielle X

Introduction à la vision artificielle X Introduction à la vision artificielle X Jean Ponce Email: ponce@di.ens.fr Web: http://www.di.ens.fr/~ponce Planches après les cours sur : http://www.di.ens.fr/~ponce/introvis/lect10.pptx http://www.di.ens.fr/~ponce/introvis/lect10.pdf

More information

Iterated Graph Cuts for Image Segmentation

Iterated Graph Cuts for Image Segmentation Iterated Graph Cuts for Image Segmentation Bo Peng 1, Lei Zhang 1, and Jian Yang 2 1 Department of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China. 2 School of Computer Science

More information

Comparison of energy minimization algorithms for highly connected graphs

Comparison of energy minimization algorithms for highly connected graphs Comparison of energy minimization algorithms for highly connected graphs Vladimir Kolmogorov 1 and Carsten Rother 2 1 University College London; vnk@adastral.ucl.ac.uk 2 Microsoft Research Ltd., Cambridge,

More information

Dynamic Planar-Cuts: Efficient Computation of Min-Marginals for Outer-Planar Models

Dynamic Planar-Cuts: Efficient Computation of Min-Marginals for Outer-Planar Models Dynamic Planar-Cuts: Efficient Computation of Min-Marginals for Outer-Planar Models Dhruv Batra 1 1 Carnegie Mellon University www.ece.cmu.edu/ dbatra Tsuhan Chen 2,1 2 Cornell University tsuhan@ece.cornell.edu

More information

GENERAL. CSE 559A: Computer Vision STEREO ROUNDUP STEREO ROUNDUP

GENERAL. CSE 559A: Computer Vision STEREO ROUNDUP STEREO ROUNDUP CSE 559A: Computer Vision GENERAL roblem Set 3 Due Thursday. roject roposals Deadline Extended to 11:59 M Tuesday Oct 31st. Submitted through blackboard. 2-3 aragraphs. Can be DF / Text File / ut directly

More information

Stereo Matching and Graph Cuts

Stereo Matching and Graph Cuts 21 Stereo Matching and Graph Cuts Ayman Zureiki 1,2, Michel Devy 1,2 and Raja Chatila 1,2 1 CNRS; LAAS; 7 avenue du Colonel Roche, F-31077 Toulouse, 2 Université de Toulouse; UPS, INSA, INP, ISAE; LAAS-CNRS

More information

Performance of Stereo Methods in Cluttered Scenes

Performance of Stereo Methods in Cluttered Scenes Performance of Stereo Methods in Cluttered Scenes Fahim Mannan and Michael S. Langer School of Computer Science McGill University Montreal, Quebec H3A 2A7, Canada { fmannan, langer}@cim.mcgill.ca Abstract

More information

Fast Interactive Image Segmentation by Discriminative Clustering

Fast Interactive Image Segmentation by Discriminative Clustering Fast Interactive Image Segmentation by Discriminative Clustering Dingding Liu Department of Electrical Engineering University of Washington Seattle, WA, USA, 98105 liudd@u.washington.edu Kari Pulli Nokia

More information

Outline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem

Outline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem Outline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem Uncapacitated Networks: Basic primal and dual solutions Flow conservation constraints

More information

Shape Prior Segmentation of Multiple Objects with Graph Cuts

Shape Prior Segmentation of Multiple Objects with Graph Cuts Shape Prior Segmentation of Multiple Objects with Graph Cuts Nhat Vu and B.S. Manjunath Department of Electrical and Computer Engineering University of California, Santa Barbara, CA 93106-9560 {nhat,manj}@ece.ucsb.edu

More information

Graph cut based image segmentation with connectivity priors

Graph cut based image segmentation with connectivity priors Graph cut based image segmentation with connectivity priors Sara Vicente Vladimir Kolmogorov University College London {s.vicente,vnk}@adastral.ucl.ac.uk Carsten Rother Microsoft Research Cambridge carrot@microsoft.com

More information

Simultaneous Multi-class Pixel Labeling over Coherent Image Sets

Simultaneous Multi-class Pixel Labeling over Coherent Image Sets Simultaneous Multi-class Pixel Labeling over Coherent Image Sets Paul Rivera Research School of Computer Science Australian National University Canberra, ACT 0200 Stephen Gould Research School of Computer

More information

Stereo Matching.

Stereo Matching. Stereo Matching Stereo Vision [1] Reduction of Searching by Epipolar Constraint [1] Photometric Constraint [1] Same world point has same intensity in both images. True for Lambertian surfaces A Lambertian

More information

Computing Visual Correspondence with Occlusions via Graph Cuts

Computing Visual Correspondence with Occlusions via Graph Cuts Computing Visual Correspondence with Occlusions via Graph Cuts Vladimir Kolmogorov vnk@cs.cornell.edu Ramin Zabih rdz@cs.cornell.edu Computer Science Department Cornell University Ithaca, NY 14853 Abstract

More information

Homework 3 Solutions

Homework 3 Solutions CS3510 Design & Analysis of Algorithms Section A Homework 3 Solutions Released: 7pm, Wednesday Nov 8, 2017 This homework has a total of 4 problems on 4 pages. Solutions should be submitted to GradeScope

More information

Inference in Higher Order MRF-MAP Problems with Small and Large Cliques

Inference in Higher Order MRF-MAP Problems with Small and Large Cliques Inference in Higher Order MRF-MAP Problems with Small and Large Cliques Ishant Shanu 1 Chetan Arora 1 S.N. Maheshwari 2 1 IIIT Delhi 2 IIT Delhi Abstract Higher Order MRF-MAP formulation has been a popular

More information

ADAPTIVE GRAPH CUTS WITH TISSUE PRIORS FOR BRAIN MRI SEGMENTATION

ADAPTIVE GRAPH CUTS WITH TISSUE PRIORS FOR BRAIN MRI SEGMENTATION ADAPTIVE GRAPH CUTS WITH TISSUE PRIORS FOR BRAIN MRI SEGMENTATION Abstract: MIP Project Report Spring 2013 Gaurav Mittal 201232644 This is a detailed report about the course project, which was to implement

More information

Neighbourhood-consensus message passing and its potentials in image processing applications

Neighbourhood-consensus message passing and its potentials in image processing applications Neighbourhood-consensus message passing and its potentials in image processing applications Tijana Ružić a, Aleksandra Pižurica a and Wilfried Philips a a Ghent University, TELIN-IPI-IBBT, Sint-Pietersnieuwstraat

More information