Gradient structure of image in scale space

Journal of Mathematical Imaging and Vision

Volumn 28, Issue 3, 2007, Pages 243-257

  Sakai, Tomoya ^a   Imiya, Atsushi ^a  

^a CHIBA UNIVERSITY   (Japan)

Author keywords

Antidirectional figure flow curve; Deep structure; Euler characteristic; Extended real scale space; Figure field; Temporal segmentation

Indexed keywords

EULER EQUATIONS; GRADIENT METHODS; IMAGE SEGMENTATION; TOPOLOGY; TREES (MATHEMATICS);

ANTIDIRECTIONAL FIGURE-FLOW CURVE; DEEP STRUCTURE; EULER CHARACTERISTICS; EXTENDED REAL SCALE SPACE; FIGURE FIELD; IMAGE SEQUENCES; TEMPORAL SEGMENTATION;

IMAGE ANALYSIS;

EID: 35548961398     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-007-0005-x     Document Type: Article

References (32)

1. Brain Web, http://www.bic.mni.mcgill.ca/brainweb/
2. Computer Vision Laboratory at UMass, http://vis-www.cs.umass.edu/vislib/ Motion/box/images.html
3. Damon, J.: Local Morse theory for solutions to the heat equation and Gaussian blurring. J. Differ. Equations 115(2), 368-401 (1995)
4. Damon, J.: Generic properties of solutions to partial differential equations. Arch. Ration. Mech. Analysis 140, 353-403 (1997)
5. Florack, L.M.J., Kuijper, A.: The topological structure of scale-space images. J. Math. Imaging Vis. 12(1), 65-79 (2000)
6. Griffin, L.D., Colchester, A.C.F.: Superficial and deep structure in linear diffusion scale space: Isophotes, critical points and separatrices. Image Vis. Comput. 13(7), 543-557 (1995)
7. Griffin, L.D., Colchester, A.C.F., Robinson, G.P.: Scale and segmentation of grey-level images using maximum gradient paths. Image Vis. Comput. 10(6), 389-402 (1992)
8. Iijima, T.: Basic theory on the normalization of pattern (in case of typical one-dimensional pattern). Bull. Electro-tech. Lab. 26, 368-388 (1962) (in Japanese)
9. Iijima, T.: Basic theory on the normalization of two-dimensional visual pattern. IEICE Jpn. 1, 15-22 (1963) (in Japanese)
10. Iijima, T.: Basic equation of figure and observational transformations. IEICE Jpn. Trans. C. 54-C, 37-38 (1971)
11. Iijima, T.: Pattern Recognition. Corona Publisher, Tokyo (1973) (in Japanese)
12. Iijima, T.: The Fundamental Theory of Visual Information: The Foundation of the Pattern Recognition Problem. Corona Publisher, Tokyo (1999)
13. Imiya, A., Sugiura, T., Sakai, T., Kato, Y.: Temporal structure tree in digital linear scale space. In: Lecture Notes in Computer Science, vol. 2695, pp. 356-371. Springer, New York (2003)
14. Johansen, P.: On the classification of toppoints in scale space. J. Math. Imaging Vis. 4(1), 57-67 (1994)
15. Johansen, P., Skelboe, S., Grue, K., Andersen, J.D.: Representing signals by their toppoints in scale space. In: Proc. of Int. Conf. on Imag. Anal. and Pat. Recog., Paris, France, pp. 215-217 (1986)
16. Koenderink, J.J.: The structure of images. Biol. Cybern. 50, 363-370 (1984)
17. Koenderink, J.J.: Solid Shape. MIT Press, Cambridge (1990)
18. Kuijper, A.: The deep structure of Gaussian scale space images. PhD thesis, Utrecht University (2002)
19. Kuijper, A., Florack, L.M.J., Viergever, M.A.: Scale space hierarchy. J. Math. Imaging Vis. 18(2), 169-189 (2003)
20. Lifshitz, L.M., Pizer, S.M.: A multiresolution hierarchical approach to image segmentation based on intensity extrema. IEEE Trans. Pattern Analysis Mach. Intell. 12(6), 529-540 (1990)
21. Lindeberg, T.: Scale-Space Theory in Computer Vision. Kluwer Academic, Boston (1994)
22. Loog, M., Duistermaat, J.J., Florack, L.M.J.: On the behavior of spatial critical points under Gaussian blurring. In: Lecture Notes in Computer Science, vol. 2106, pp. 183-192. Springer, New York (2001)
23. Olsen, O.F., Nielsen, M.: Generic events for the gradient squared with application to multi-scale segmentation. In: Lecture Notes in Computer Science, vol. 1252, pp. 101-112. Springer, New York (1997)
24. Otsu, N.: Mathematical studies on feature extraction in pattern recognition. Researches of The Electrotechnical Laboratory 818 (1981) (in Japanese)
25. Sakai, T., Imiya, A.: Figure field analysis of linear scale-space image. In: Lecture Notes in Computer Science, vol. 3459, pp. 374-385. Springer, New York (2005)
26. Sakai, T., Imiya, A.: Scale-space hierarchy of singularities. In: Lecture Notes in Computer Science, vol. 3753, pp. 181-192. Springer, New York (2005)
27. Simmons, A., Arridge, S.R., Tofts, P.S., Barker, G.J.: Application of the Extremum Stack to Neurological MRI. IEEE Trans. Med. Imaging 17(3), 371-382 (1998)
28. Weickert, J., Ishikawa, S., Imiya, A.: On the history of Gaussian scale-space axiomatics. In: Gaussian Scale-Space Theory. Computational Imaging and Vision Series, vol. 8, pp. 45-59. Kluwer Academic, Dordrecht (1997)
29. Weickert, J., Ishikawa, S., Imiya, A.: Linear scale-space has first been proposed in Japan. J. Math. Imaging Vis. 10(3), 237-252 (1999)
30. Witkin, A.P.: Scale space filtering. In: Proc. of 8th Int. Joint Conf. on Artif. Intell., pp. 1019-1022. Karlsruhe, West Germany (1983)
31. Zhao, N.-Y., Iijima, T.: Theory on the method of determination of view-point and field of vision during observation and measurement of figure. IEICE Jpn. Trans. D J68-D, 508-514 (1985) (in Japanese)
32. Zhao, N.-Y., Iijima, T.: A theory of feature extraction by the tree of stable view-points. IEICE Jpn. Trans. D J68-D, 1125-1135 (1985) (in Japanese)