The Image Foresting Transform: Theory, Algorithms, and Applications

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 26, Issue 1, 2004, Pages 19-29

  Falcão, Alexandre X ^a   Stolfi, Jorge ^a   De Alencar Lotufo, Roberto ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Boundary tracking; Distance transforms; Dljkstra's algorithm; Image analysis; Image segmentation; Morphological reconstruction; Multiscale skeletonization; Regional minima; Shortest path problems; Watershed transform

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; GRAPH THEORY; IMAGE ANALYSIS; INTEGER PROGRAMMING; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; TOMOGRAPHY;

BOUNDARY TRACKING; DIJKSTRA ALGORITHMS; DISTANCE TRANSFORMS; MORPHOLOGICAL RECONSTRUCTION; MULTISCALE SKELETONIZATION; REGIONAL MINIMA; SHORTEST-PATH PROBLEMS; WATERSHED TRANSFORMS;

IMAGE SEGMENTATION;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; BRAIN; CLUSTER ANALYSIS; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; COMPUTER INTERFACE; COMPUTER SIMULATION; EVALUATION; HISTOLOGY; HUMAN; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; INFORMATION RETRIEVAL; MATHEMATICAL COMPUTING; METHODOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; THREE DIMENSIONAL IMAGING; VALIDATION STUDY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; BRAIN; CLUSTER ANALYSIS; COMPUTER GRAPHICS; COMPUTER SIMULATION; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; MAGNETIC RESONANCE IMAGING; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SUBTRACTION TECHNIQUE; USER-COMPUTER INTERFACE;

EID: 0742303474     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.1261076     Document Type: Article

References (52)

1. E.F. Moore, "The Shortest Path through a Maze," Proc. Int'l Symp. Theory of Switching, pp. 285-292, Apr. 1959.
2. R. Bellman, "On a Routing Problem," Quarterly of Applied Math., vol. 16, pp. 87-90, 1958.
3. E.W. Dijkstra, "A Note on Two Problems in Connexion with Graphs," Numerische Mathematik, vol. 1, pp. 269-271, 1959.
4. R.B. Dial, "Shortest-Path Forest with Topological Ordering," Comm. ACM, vol. 12, no. 11, pp. 632-633, Nov. 1969.
5. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network Flows: Theory, Algorithms and Applications. Prentice-Hall, 1993.
6. R.A. Lotufo and A.X. Falcão, "The Ordered Queue and the Optimality of the Watershed Approaches," Math. Morphology and Its Applications to Image and Signal Processing, vol. 18, pp. 341-350, June 2000.
7. R.A. Lotufo, A.X. Falcão, and F. Zampirolli, "IFT-Watershed from Gray-Scale Marker," Proc. 15th Brazilian Symp. Computer Graphics and Image Processing, pp. 146-152, Oct. 2002.
8. J.K. Udupa and S. Samarasekera, "Fuzzy Connectedness and Object Definition: Theory, Algorithms, and Applications in Image Segmentation," Graphical Models and Image Processing, vol. 58, pp. 246-261, 1996.
9. P.K. Saha and J.K. Udupa, "Relative Fuzzy Connectedness Among Multiple Objects: Theory, Algorithms, and Applications in Image Segmentation," Computer Vision and Image Understanding, vol. 82, pp. 42-56, 2001.
10. L.G. Nyúl, A.X. Falcão, and J.K. Udupa, "Fuzzy-Connected 3D Image Segmentation at Interactive Speeds," Graphical Models, vol. 64, no. 5, pp. 259-281, 2003.
11. B.S. Cunha, "Projeto de Operadores de Processamento e Análise de Imagens Baseados na Transformada Imagem-Floresta," Master's thesis, Universidade Estadual de Campinas, Instituto de Computação, Ago 2001.
12. A.X. Falcão, B.S. daCunha, and R.A. Lotufo, "Design of Connected Operators Using the Image Foresting Transform," Proc. SPIE Medical Imaging, vol. 4322, pp. 468-479, Feb. 2001.
13. R.A. Lotufo, A.X. Falcão, and P.A. Zampirolli, "Fast Euclidean Distance Transform Using a Graph-Search Algorithm," Proc. XIII Brazilian Symp. Computer Graphics and Image Processing, pp. 269-275, Oct. 2000.
14. A.X. Falcão, L.F. Costa, and B.S. da Cunha, "Multiscale Skeletons by Image Foresting Transform and Its Applications to Neuromorphometry," Pattern Recognition, vol. 35, no. 7, pp. 1571-1582, Apr. 2002.
15. R.S. Torres, A.X. Falcão, and L.F. Costa, "Shape Description by Image Foresting Transform," Proc. 14th Int'l Conf. Digital Signal Processing, pp. 1089-1092, July 2002.
16. R.S. Torres, A.X. Falcão, and L.F. Costa, "A Graph-Based Approach for Multiscale Shape Analysis," Technical Report IC-03-03, Inst. of Computing, Univ. Campinas, Jan. 2003.
17. A.X. Falcão, J.K. Udupa, S. Samarasekera, S. Sharma, B.E. Hirsch, and R.A. Lotufo, "User-Steered Image Segmentation Paradigms: Live-Wire and Live-Lane," Graphical Models and Image Processing, vol. 60, no. 4, pp. 233-260, July 1998.
18. A.X. Falcão, J.K. Udupa, and F.K. Miyazawa, "An Ultra-Fast User-Steered Image Segmentation Paradigm: Live-Wire-on-the-Fly," IEEE Trans. Medical Imaging, vol. 19, no. 1, pp. 55-62, Jan. 2000.
19. A.X. Falcão and J.K. Udupa, "A 3D Generalization of User-Steered Live Wire Segmentation," Medical Imaging Analysis, vol. 4, no. 4, pp. 389-402, Dec. 2000.
20. L. Vincent and P. Soille, "Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 6, pp. 583-598, June 1991.
21. S. Beucher and F. Meyer, "The Morphological Approach to Segmentation: The Watershed Transformation," Mathematical Morphology in Image Processing, chapter 12, pp. 433-481, Marcel Dekker, 1993.
22. L. Vincent, "Morphological Area Opening and Closings for Greyscale Images," Proc. Shape in Picture '92-NATO Workshop, Sept. 1992.
23. L. Vincent, "Morphological Grayscale Reconstruction in Image Analysis," IEEE Trans. Image Processing, vol. 2, no. 2, pp. 176-201, Apr. 1993.
24. F. Meyer, "The Levelings," Proc. Fourth Int'l Symp. Math. Morphology, pp. 190-207, 1998.
25. R.A. Lotufo, A.X. Falcão, and F. Zampirolli, "IFT-Watershed from Gray-Scale Marker," Technical Report IC-02-12, Inst. of Computing, Univ. of Campinas, Dec. 2002.
26. A.X. Falcão and F.P.G. Bergo, "The Iterative Image Foresting Transform and Its Application to User-Steered 3D Segmentation," Proc. SPIE Medical Imaging, vol. 5032, pp. 1464-1475, Feb. 2003.
27. N. Deo and C. Pang, "Shortest-Path Algorithms: Taxonomy and Annotation," Networks, vol. 14, pp. 275-323, 1984.
28. T. Cormen, C. Leiserson, and R. Rivest, Introduction to Algorithms. MIT, 1990.
29. M. Mohri, "Semiring Frameworks and Algorithms for Shortest-Distance Problems," J. Automata, Languages, and Combinatorics, vol. 7, no. 3, pp. 321-350, 2002.
30. A. Frieze, "Minimum Paths in Directed Graphs," Operational Research Quarterly, vol. 28, no. 2, i, pp. 339-346, 1977.
31. U. Montanari, "On the Optimal Detection of Curves in Noisy Pictures," Comm. ACM, vol. 14, no. 5, pp. 335-345, 1971.
32. A. Martelli, "Edge Detection Using Heuristic Search Methods," Computer Graphics and Image Processing, vol. 1, pp. 169-182, 1972.
33. A. Martelli, "An Application of Heuristic Search Methods to Edge and Contour Detection," Comm. ACM, vol. 19, no. 2, pp. 73-83, 1976.
34. F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. Springer 1985.
35. E.N. Mortensen and W.A. Barrett, "Interactive Segmentation with Intelligent Scissors," Graphical Models and Image Processing, vol. 60, pp. 349-384, 1998.
36. B.J.H. Verwer, P.W. Verbeek, and S.T. Dekker, "An Efficient Uniform Cost Algorithm Applied to Distance Transforms," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 4, pp. 425-429, Apr. 1989.
37. M.Y. Sharaiha and N. Christofides, "A Graph-Theoretic Approach to Distance Transformations," Pattern Recognition Letters, vol. 15, pp. 1035-1041, Oct. 1994.
38. F. Meyer, "Topographic Distance and Watershed Lines," Signal Processing, vol. 38, pp. 113-125, 1994.
39. I. Ragnemalm, "Neighborhoods for Distance Transformations Using Ordered Propagation," CVGIP: Image Understanding, vol. 56, no. 3, pp. 399-409, 1992.
40. O. Cuisenaire and B. Macq, "Fast Euclidean Distance Transformation by Propagation Using Multiple Neighborhoods," Computer Vision and Image Understanding, vol. 76, no. 1, pp. 163-172, Nov. 1999.
41. J.B.T.M. Roerdink and A. Meijster, "The Watershed Transform: Definitions, Algorithms and Parallelization Strategies," Fundamenta Informaticae, vol. 41, pp. 187-228, 2000.
42. J.A. Sethian, "Curvature and the Evolution of Fronts," Comm. Math. Physics, vol. 101, pp. 487-499, 1985.
43. J.A. Sethian, "A Fast Marching Level Set Method for Monotonically Advancing Fronts," Proc. Nat'l Academy of Science, vol. 93, no. 4, pp. 1591-1595, 1996.
44. L. Bischof and R. Adams, "Seeded Region Growing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 6, pp. 641-647, June 1994.
45. R. Bellman, Dynamic Programming. Princeton Univ., 1957.
46. M. Sonka, R. Boyle, and V. Hlavac, Image Processing, Analysis, and Machine Vision. ITP, 1999.
47. P.E. Danielsson, "Euclidean Distance Mapping," Computer Graphics and Image Processing, vol. 14, pp. 227-248, 1980.
48. C.R. Maurer Jr., R. Qi, and V. Raghavan, "A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 2, pp. 265-270, Feb. 2003.
49. G. Borgefors, "Distance Transformations in Digital Images," Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
50. A. Palcão, J. Stolfi, and R. Lotufo, "The IFT Project," http:// www.ic.unicamp.br/̃afalcao/ift.html, 2003.
51. G. Castellano, R.A. Lotufo, A.X. Falcão, and F. Cendes, "Characterization of the Human Cortex in MR Images through the Image Foresting Transform," Proc. IEEE Int'l Conf. Image Processing (ICIP), Sept. 2003.
52. F.P.G. Bergo and A.X. Falcão, "Interactive 3D Segmentation of Brain MR-Images with the Image Foresting Transform," Technical Report IC-03-16, Inst. of Computing, Univ. of Campinas, July 2003.