Scale-space properties of quadratic feature detectors

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 18, Issue 10, 1996, Pages 987-999

  Kube, Paul ^a,b,c   Perona, Pietro ^a,b,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Causality; Edge detection; Energy filters; Feature detection; Nonlinear filtering; Quadratic filters; Scale space

Indexed keywords

DIFFERENTIAL EQUATIONS; DIGITAL FILTERS; EDGE DETECTION; FUNCTIONS; IMAGE ANALYSIS; SIGNAL FILTERING AND PREDICTION;

NONLINEAR FILTERING; QUADRATIC FEATURE DETECTORS; QUADRATIC NONLINEARITY; SCALE SPACE PROPERTIES; SCALING FUNCTIONS;

FEATURE EXTRACTION;

EID: 0030260162     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/34.541408     Document Type: Article

References (30)

1. A. Rosenicld and M. Thurston Edge and Curve Detection for Visual Scene Analysis IEEE Trans. Computers vol. 20 pp. 562-569 May 1971.
2. D. Marr and E. Hildreth Theory of Edge Detection Proc. Royal Soc. London vol. B207 pp. 187-2171980.
3. A.P. Witkin Scale-Space Filtering Int'l Joint Conf. Artificial Intelligence 1983 pp. 1019-1021 Karlsruhe.
4. I.J. Koenderink The Structure of Images biol. Cybern. vol. 50 pp. 363-370 1984.
5. J. Babaud A. Witkin M. Baudin and R. Duda Uniqueness of the Gaussian Kernel for Scale-Space Fillering IEEE Trans. Pattern Analysis and Machine Intelligence vol. 8 pp. 26-33 Jan. 1986.
6. J.J. Clark Singularity Theory and Phantom Edges in Scale Space IEEE Trans. Pattern Analysis and Machine Intelligence vol. 10 no. 5 pp. 720-7271988.
7. A. Yuille and T. Poggio Scaling Theorems for Zero Crossings ICEE Trans. Pallern Analysis and Machine Intelligence vol. 8 pp. 1526 Jan. 1986.
8. R.A. Hummel and A.R. Moniot Reconstructions From Zero Crossings in Scale-Space IEEE Truns. Acuust. Speech Signal Processing Dec. 1989.
9. L. Wu and Z. Xie Scaling Theorems for Zero-Crossings IEEE Trans. Pattern Analysis and Machine intelligence vol. 12 pp. 46-54 Jan. 1991.
10. V. Ann J.Y. Shi and H.T. Tsui Scaling Theorems for Zero Crossings of Bandlimited Signals IEEE Trans. Pattern Analysis und Machine Intelligence vol. 18 no. 3 pp. 309-320 Mar. 1996.
11. P. Perona and J. Malik Scale-Space and Edge Deteclinn Using Anisotropie Diffusion IEEE Irans Pattern Analysis and Machine Intelligence vol. 12 no. 7 pp. 629639 July 1990.
12. Geometry-Driven Diffusion in Computer Vision B.M. ter Haar Romeny ed. Kluwer 1994.
13. G. H. Granlund In Search of a General Picture Processing Operator Computer Graphics and Image Processing vol. 8 pp. 155-1731978.
14. E. Adelson and J. Bergen Spatiotemporal Energy Models for the Perception of Motion J. Optical Soc. Am. vol. 2 no. 2 pp. 284-299 1985.
15. J. Daugman Uncertainty Relation for Resolution in Space Spatial Frequency and Orientation Optimized by Two Dimensional Visual Cortical Filters J. Optical Soc. Am. vol. 2A no. 7 pp. 1160-1169 1985.
16. M.C. Morrone and R.A. Owens Feature Detection From Eocal Energy Pattern Recognition Letters vol. 6 pp. 303-3131987.
17. R. Owens B. Venkatesh and J. Ross Edge Detection is a Projection Pattern Recognition Letters vol. 9 pp. 233-24419S9.
18. VV.T. Freeman and E.H. Adelson The Design and Use of Steerable Filters IEEE Trans. Pattern Analysis and Machine Intelligence vol. 13 pp. 891-9061991.
19. P. Perona and J. Malik Detecting and Localizing Edges Composed of Steps Peaks and Roofs Prut. Third lnt'1 CoJ. Computer Vision Osaka Japan pp. 52-57 1990.
20. P. Perona and J. Malik Boundary Detection Using Quadratic Filters: Performance Criteria and Experimental Assessment Proc. SPIE Con/ on Applications of Artificial Intelligence SPIE vol. 1708 Orlando Apr. 1992.
21. P. Kube Properties of Energy Edge Detectors Proc. IEEE Computer Soc. COMJ. Computer Vision ami Pattern Recognition 1992.
22. P. Perona Deformable Kernels for Early Vision IEEE Trans. Pattern Analysis und Machine Intelligence vol. 17 no. 5 pp. 488-499 May 1995.
23. G.H. Granlund and H. Knuttson Signal Processing for Computer Vision. Kluwer 1995.
24. T. Poston and I. Stewart Catastrophe Theory and its Applications. Eondon: Pitman 1978.
25. V.I. Arnold Singularity Theory. Cambridge Univ. Press 1981.
26. R.N. Bracewell The Fourier Transform and Its Applications. McGraw Hill 1978.
27. M.C. Morrone and D.C. Burr Feature Detection in Human Vision: A Phase Dependent Energy Mode! Proc. Royal Soc. of London vol. B235 pp. 221-2451988.
28. C. Ronse On Idempotence and Related Requirements in Edge Detection IEEE Trans. Pattern Analysis and Machine Intelligence vol. 15 pp. 484-491 1993.
29. A.I. Barvinok Feasibility Testing for Systems of Real Quadratic Equations STOC 1992.
30. P. Kube and P. Perona Scale-Space Properties of Quadratic Edge Detectors Proc. Third European Conf. Computer Vision J.-O. Eklundh ed. LNCS-Series vol. 800-801 pp. 1-115-122. Stockholm: Springer-Verlag May 1994.