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Image Foresting Transform. for Image Segmentation. Presented by: Michael Fang Weilong Yang. A Few Things to Recall. Image Segmentation Finding homogeneous regions Graph-based Methods Treating images as graphs Image Foresting Transform Unification Efficiency Simplicity.

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image foresting transform

Image Foresting Transform

for Image Segmentation

  • Presented by:
    • Michael Fang
    • Weilong Yang
a few things to recall
A Few Things to Recall
  • Image Segmentation
    • Finding homogeneous regions
  • Graph-based Methods
    • Treating images as graphs
  • Image Foresting Transform
    • Unification
    • Efficiency
    • Simplicity
directed graphs
Directed Graphs

A directed graph is a pair (I, A), where I is a set of nodes and A is a set of ordered pairs of nodes.

paths
Paths
  • A path is a sequence t1, t2, …, tk of distinct nodes in the graph, such that (ti, ti+1)  A for 1  i k – 1.
  • A path is trivial if k = 1;
  • Path    denotes the concatenation of two paths,  and , where  ends at t and  begins at t.
  • Path  =   s, t denotes theconcatenation of the longest prefix  of  and the last arc (s, t).
path costs
Path Costs
  • A path-cost function is a mapping that assigns to each path  a cost (), in some ordered set  of cost values.
  • A function  is said to be monotonic-incremental (MI) when (t) = h(t), (  s, t) = ()  (s, t),where h(t) is a handicap cost value and  satisfies: x’  x  x’  (s, t)  x (s, t) and x  (s, t)  x,for x, x’   and (s, t)  A.
examples of mi cost functions
Examples of MI Cost Functions
  • Additive cost function sum(t) = h(t), sum(  s, t) = sum() + w(s, t),where w(s, t) is a fixed non-negative arc weight.
  • Max-arc cost function max(t) = h(t), max(  s, t) = max{max(),w(s, t)}, where w(s, t) is a fixed arc weight.
predecessor map and spanning forest
Predecessor Map and Spanning Forest
  • A predecessor map is a function P that assigns to each node t I either some other node in I, or a distinctive marker nil  I – in which case t is the root of the map.
  • A spanning forest is a predecessor map which takes every node to nil in a finite number of iterations (i.e., it contains no cycles).
paths of the forest p
Paths of the Forest P
  • For any node t I, there is a path P*(t) which is obtained in backward by following the predecessor nodes along the path.

P*(c) = a, b, c, where P(c) = b, P(b) = a, P(a) = nil

P*(i) = i, where P(i) = nil

optimum path forest
Optimum-path Forest

An optimum-path forest is a spanning forest P, where (P*(t)) is minimum for all nodes t I. Consider cost function sum in the example below.

an image as a directed graph
An Image as a Directed Graph
  • A grayscale image I is a pair (I, I), where I is a finite set of pixels (points in Z2) and I assigns to each pixel t I a value I(t) in some arbitrary value space.
  • An adjacency relation A is a binary relation between pixels of I, which is usually translation-invariant.
  • Once A has been fixed, image I can be interpreted as a directed graph, whose nodes are the image pixels in I and whose arcs are defined by A.
seed pixels
Seed Pixels

In some applications, we would like to use a predefined path-cost function  but constrain the search to paths that start in a given set SI of seed pixels. This constraint can be modeled by defining

ift algorithm for image segmentation
IFT Algorithm for Image Segmentation
  • Path Cost
  • Four-Connected Adjacency
ift algorithm with fifo policy 2
IFT algorithm with FIFO policy(2)

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ift algorithm with fifo policy 4
IFT algorithm with FIFO policy(4)

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IFT algorithm with FIFO policy(4)

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IFT algorithm with FIFO policy(4)

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IFT algorithm with FIFO policy(4)

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IFT algorithm with FIFO policy(4)

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IFT algorithm with FIFO policy(4)

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framework of image segmentation by ift
Framework of Image segmentation by IFT

Input Image

Gradient Image

Seeds Labeling

IFT

summary
Summary
  • Basic concept of the Image Foresting Transform
  • IFT for image segmentation
  • Experiment results
references 1
References (1)
  • Martin, D., Fowlkes, C., Tal, D., and Malik, J., A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics, ICCV(2), No. 7-14, January 2001, pp. 416–425.
  • Vincent, L., and Soille, P.[Pierre], Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations, PAMI(13), No. 6, June 1991, pp. 583-598.
  • Makrogiannis, S., Economou, G., Fotopoulos, S., A region dissimilarity relation that combines feature-space and spatial information for color image segmentation, SMC-B(35), No. 1, February 2005, pp. 44-53.
  • Haris, K., Efstratiadis, S.N., Maglaveras, N., Katsaggelos, A.K., Hybrid Image Segmentation Using Watersheds And Fast Region Merging, IP(7), No. 12, December 1998, pp. 1684-1699.
  • Shi, J.[Jianbo], Malik, J.[Jitendra], Normalized Cuts and Image Segmentation, PAMI(22), No. 8, August 2000, pp. 888-905.
  • Zabih, R.[Ramin], Kolmogorov, V.[Valdimir], Spatially coherent clustering using graph cuts, CVPR04(II: 437-444).
  • Boykov, Y.Y.[Yuri Y.], Jolly, M.P.[Marie-Pierre], Interactive Graph Cuts for Optimal Boundary and Region Segmentation of Objects in N-D Images, ICCV01(I: 105-112).
  • Andrew, Y.N., Jordan, M. and Weiss, Y., On Spectral Clustering: Analysis and an Algorithm, NIPS(14), 2002, pp. 849–856.
  • Weiss, Y.[Yair], Segmentation using Eigenvectors: A Unifying View, ICCV99(975-982).
  • Felzenszwalb, P.F.[Pedro F.], Huttenlocher, D.P.[Daniel P.], Image Segmentation Using Local Variation, CVPR98(98-104).
references 2
References (2)
  • Felzenszwalb, P.F.[Pedro F.], Huttenlocher, D.P.[Daniel P.], Efficient Graph-Based Image Segmentation, IJCV(59), No. 2, September 2004, pp. 167-181.
  • Haxhimusa, Y.[Yll] and Kropatsch, W.G.[Walter G.], Segmentation Graph Hierarchies, SSPR&SPR(18-20) August 2004, pp. 343–351.
  • Haxhimusa, Y.[Yll], Ion, A.[Adrian], Kropatsch, W.G.[Walter G.], Illetschko, T.[Thomas], Evaluating Minimum Spanning Tree Based Segmentation Algorithms, CAIP05(579).
  • Falcão, A.X.[Alexandre X.], Stolfi, J.[Jorge], de Alencar Lotufo, R.[Roberto], The Image Foresting Transform: Theory, Algorithms, and Applications, PAMI(26), No. 1, January 2004, pp. 19-29.
  • Falcão, A.X.[Alexandre X.], Bergo, F.[Felipe] and Miranda, P.[Paulo], Image Segmentation by Tree Pruning, Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium, 2004, pp. 65–71.
  • Ding, J., Ma, R., Chen, S. and Wang, B., A Fast Directed Tree Based Neighborhood Clustering for Image Segmentation, NIP(4233), 2006, pp. 369–378.
  • Li, K.[Kang], Wu, X.D.[Xiao-Dong], Chen, D.Z.[Danny Z.], Sonka, M.[Milan], Optimal Surface Segmentation in Volumetric Images: A Graph-Theoretic Approach, PAMI(28), No. 1, January 2006, pp. 119-134.
  • Grady, L.[Leo], Random Walks for Image Segmentation, PAMI(28), No. 11, November 2006, pp. 1768-1783.
  • Pednekar, A.S.[Amol S.], Kakadiaris, I.A.[Ioannis A.], Image Segmentation Based on Fuzzy Connectedness Using Dynamic Weights, IP(15), No. 6, June 2006, pp. 1555-1562.
  • Luo, Q., Khoshgoftaar, T.M., Unsupervised Multiscale Color Image Segmentation Based on MDL Principle, IP(15), No. 9, August 2006, pp. 2755-2761.
references 3
References (3)
  • Arbeláez, P.A.[Pablo A.], Cohen, L.D.[Laurent D.], A Metric Approach to Vector-Valued Image Segmentation, IJCV(69), No. 1, August 2006, pp. 119-126.
  • Cremers, D.[Daniel], Osher, S.J.[Stanley J.], Soatto, S.[Stefano], Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation, IJCV(69), No. 3, September 2006, pp. 335-351.
  • Bresson, X.[Xavier], Vandergheynst, P.[Pierre], Thiran, J.P.[Jean-Philippe], A Variational Model for Object Segmentation Using Boundary Information and Shape Prior Driven by the Mumford-Shah Functional, IJCV(68), No. 2, June, 2006, pp. 145-162.
  • Boykov, Y.Y.[Yuri Y.], Funka-Lea, G.[Gareth], Graph Cuts and Efficient N-D Image Segmentation, IJCV(70), No. 2, November 2006, pp. 109-131.
  • Bresson, X.[Xavier], Vandergheynst, P.[Pierre], Thiran, J.P.[Jean-Philippe], Multiscale Active Contours, IJCV(70), No. 3, December 2006, pp. 197-211
  • Tu, Z.W.[Zhuo-Wen], Zhu, S.C.[Song-Chun], Parsing Images into Regions, Curves, and Curve Groups, IJCV(69), No. 2, August 2006, pp. 223-249.
  • Seghers, D., Loeckx, D.[Dirk], Maes, F.[Frederik], Vandermeulen, D., Suetens, P.[Paul], Minimal Shape and Intensity Cost Path Segmentation, MedImg(26), No. 8, August 2007, pp. 1115-1129.
  • Papandreou, G., Maragos, P., Multigrid Geometric Active Contour Models, IP(16), No. 1, January 2007, pp. 229-240.
  • Tao, W., Jin, H., Zhang, Y., Color Image Segmentation Based on Mean Shift and Normalized Cuts, SMC-B(37), No. 5, October 2007, pp. 1382-1389.
  • Wu, J., Chung, A.C.S., A Segmentation Model Using Compound Markov Random Fields Based on a Boundary Model, IP(16), No. 1, January 2007, pp. 241-252.
references 4
References (4)
  • Pavan, M.[Massimiliano], Pelillo, M.[Marcello], Dominant Sets and Pairwise Clustering, PAMI(29), No. 1, January 2007, pp. 167-172.
  • Tai, Y.W.[Yu-Wing], Jia, J.[Jiaya], Tang, C.K.[Chi-Keung], Soft Color Segmentation and Its Applications, PAMI(29), No. 9, September 2007, pp. 1520-1537.
  • Pyun, K., Lim, J., Won, C.S., Gray, R.M., Image Segmentation Using Hidden Markov Gauss Mixture Models, IP(16), No. 7, July 2007, pp. 1902-1911.
  • Arias, P., Pini, A., Sanguinetti, G., Sprechmann, P., Cancela, P., Fernandez, A., Gomez, A., Randall, G., Ultrasound Image Segmentation With Shape Priors: Application to Automatic Cattle Rib-Eye Area Estimation, IP(16), No. 6, June 2007, pp. 1637-1645.
  • Nikou, C.[Christophoros], Galatsanos, N.P.[Nikolaos P.], Likas, A.C.[Aristidis C.], A Class-Adaptive Spatially Variant Mixture Model for Image Segmentation, IP(16), No. 4, April 2007, pp. 1121-1130.
  • Benboudjema, D.[Dalila], Pieczynski, W.[Wojciech], Unsupervised Statistical Segmentation of Nonstationary Images Using Triplet Markov Fields, PAMI(29), No. 8, August 2007, pp. 1367-1378.
  • Michailovich, O.V.[Oleg V.], Rathi, Y.[Yogesh], Tannenbaum, A.[Allen], Image Segmentation Using Active Contours Driven by the Bhattacharyya Gradient Flow, IP(16), No. 11, November 2007, pp. 2787-2801.
  • Zoller, T.[Thomas], Buhmann, J.M.[Joachim M.], Robust Image Segmentation Using Resampling and Shape Constraints, PAMI(29), No. 7, July 2007, pp. 1147-1164.
  • Qiu, H.J.[Huai-Jun], Hancock, E.R.[Edwin R.], Clustering and Embedding Using Commute Times, PAMI(29), No. 11, November 2007, pp. 1873-1890.
  • Rivera, M., Ocegueda, O., Marroquin, J.L., Entropy-Controlled Quadratic Markov Measure Field Models for Efficient Image Segmentation, IP(16), No. 12, December 2007, pp. 3047-3057.
references 5
References (5)
  • Chen, S.F.[Shi-Feng], Cao, L.L.[Liang-Liang], Liu, J.Z.[Jian-Zhuang], Tang, X.[Xiaoou], Iterative MAP and ML Estimations for Image Segmentation, CVPR07(1-6).
  • Allili, M.S.[Mohand Said], Ziou, D.[Djemel], Object of Interest segmentation and Tracking by Using Feature Selection and Active Contours, CVPR07(1-8).
  • Liu, T.[Tie], Sun, J.[Jian], Zheng, N.N.[Nan-Ning], Tang, X.[Xiaoou], Shum, H.Y.[Heung-Yeung], Learning to Detect A Salient Object, CVPR07(1-8).
  • Cremers, D.[Daniel], Rousson, M.[Mikael], Deriche, R.[Rachid], A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape, IJCV(72), No. 2, April 2007, pp. 195-215.
  • Tai, X.C.[Xue-Cheng], Christiansen, O.[Oddvar], Lin, P.[Ping], SkjÆlaaen, I.[Inge], Image Segmentation Using Some Piecewise Constant Level Set Methods with MBO Type of Projection, IJCV(73), No. 1, June 2007, pp. 61-76.
  • Riklin-Raviv, T.[Tammy], Kiryati, N.[Nahum], Sochen, N.A.[Nir A.], Prior-based Segmentation and Shape Registration in the Presence of Perspective Distortion, IJCV(72), No. 3, May 2007, pp. 309-328.
  • Sofou, A., Maragos, P.[Petros], Generalized Flooding and Multicue PDE-Based Image Segmentation, IP(17), No. 3, March 2008, pp. 364-376.
  • Ding, J., Ma, R., Chen, S., A Scale-Based Connected Coherence Tree Algorithm for Image Segmentation, IP(17), No. 2, February 2008, pp. 204-216.
  • Du, X., Bui, T.D., A New Model for Image Segmentation, SPLetters(15), 2008, pp. 182-185.
  • Orbanz, P.[Peter], Buhmann, J.M.[Joachim M.], Nonparametric Bayesian Image Segmentation, IJCV(77), No. 1-3, May 2008, pp. 25-45.

Thank You!Questions?