Abstract
We present theoretical and computational results that develop Koenderink’s theory of feature analysis in human vision [1,7]. Employing a scale space framework, the method aims to classify image points into one of a limited number of feature categories on the basis of local derivative measurements up to some order. At the heart of the method is the use of a family of functions, members of which can be used to account for any set of image measurements. We will show how certain families of simple functions naturally induce a categorical structure onto the space of possible measurements. We present two such families suitable for 1D images measured up to 2nd order, and various results relevant to similar analysis of 2D images.
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References
Koenderink, J.J., van Doorn, A. Receptive Field Assembly Specificity. J. Vis. Comm. and Im. Process, Vol.3,No. 1, (1992) 1–12
Koenderink, J.J., van Doorn, A. The Structure of Images. Biol. Cybern., Vol.50, (1984) 363–370
Koenderink, J.J., van Doorn, A. Representation of Local Geometry in the Visual System. Biol. Cybern., Vol.55, (1987) 367–375
Koenderink, J.J., van Doorn, A. Generic Neighborhood Operators. IEEE Trans. on Pattern An. Mach. Intell., Vol.14,No. 6, (1992) 597–605
Koenderink, J.J., van Doorn, A.: Illuminance Critical Points On Generic Smooth Surfaces. J.Opt.Soc.Am. A, Vol.10,No. 5(1923) 844–854
Koenderink, J.J., van Doorn, A. Mensurating the Colour Circle: Ostwald’s “Principle of Internal Symmetry”. ECVP(2000)
Koenderink, J.J. What is a Feature?. J. Intell. Syst., Vol.3,No. 1, (1993) 49–82
ter Haar Romeny, B.M., Florack, L.M.J., Koenderink, J.J., Viergever M.A. Scale Space: Its Natural Operators and Differential Invariants. In: Information Process. in Medical Imag., LCNS, Vol.511, (1991) 239–255
Weickert, J., Ishikawa, S., and Imiya A. On the History of Gaussian Scale Space Axiomatics. In: Gaussian Scale-Space Theory, Kluwer, Dordrecht, (1997) 45–59
ter Haar Romeny, B. Applications of Scale Space Theory. In: Gaussian Scale-Space Theory, Kluwer, Dordrecht, (1997) 3–19
Nielsen, M. Scale Space Generators and Functionals. In: Gaussian Scale-Space Theory, Kluwer, Dordrecht, (1997) 99–114
Lindeberg, T. Scale Space Theory in Computer Vision. Kluwer, Boston, MA, (1994)
Lindeberg, T.: On the Axiomatic Foundations of Linear Scale Space. In: Gaussian Scale-Space Theory, Kluwer, Dordrecht, (1997) 75–97
Richards, W.: Quantifying Sensory Channels-Generalizing Colorimetry To Orientation And Texture, Touch, And Tones. Sensory Processes, Vol.3,No. 3, (1979) 207–229
Young, R.A. The Gaussian Derivative Theory of Spatial Vision: Analysis of Cortical Cell Receptive Field Line-Weighting Profiles. Gen.Motors Res.Tech.Rep. GMR-4920, (1985)
Schrödinger, E.: Theorie der Pigmente von größter Leuchtkraft, Ann. Physik, Vol.62, (1920) 603
Schrödinger, E.: Grundlinien einer Theorie der Farbenmetrik im Tagessehen I, II, Ann. Physik, Vol.63, (1920) 397–427
Majthay, A.: Foundations of Catastrophe Theory, Pitman Adv. Publ. Progr., (1985) 137–146
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Tagliati, E., Griffin, L.D. (2001). Features in Scale Space: Progress on the 2D 2nd Order Jet. In: Kerckhove, M. (eds) Scale-Space and Morphology in Computer Vision. Scale-Space 2001. Lecture Notes in Computer Science 2106, vol 2106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47778-0_5
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DOI: https://doi.org/10.1007/3-540-47778-0_5
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