General intensity transformations and differential invariants

We consider the group of invertible image gray-value transformations and propose a generating equation for a complete set of differential gray-value invariants up to any order. Such invariants describe the image's geometrical structure independent of how its gray-values are mapped (contrast or brightness adjustments).

[1]  J. Koenderink,et al.  Cartesian differential invariants in scale-space , 1993, Journal of Mathematical Imaging and Vision.

[2]  Nicholas Ayache,et al.  From voxel to intrinsic surface features , 1992, Image Vis. Comput..

[3]  Max A. Viergever,et al.  General Intensity Transformations and Second Order Invariants , 1992 .

[4]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.

[5]  Max A. Viergever,et al.  Scale and the differential structure of images , 1992, Image Vis. Comput..

[6]  J. Koenderink,et al.  Representation of local geometry in the visual system , 1987, Biological Cybernetics.

[7]  B. M. ter Haar Romeny,et al.  Representation of medical images by visual response functions , 1993, IEEE Engineering in Medicine and Biology Magazine.

[8]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Tony Lindeberg,et al.  Scale-Space for Discrete Signals , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  J. Koenderink,et al.  Invariant Third Order Properties of Isophotes: T-Junction Detection , 1992 .

[11]  Andrew P. Witkin,et al.  Uniqueness of the Gaussian Kernel for Scale-Space Filtering , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  D. F. Lawden.  An introduction to tensor calculus and relativity , 1962 .

[13]  Jan J. Koenderink,et al.  Spatial Derivatives and the Propagation of Noise in Gaussian Scale Space , 1993, J. Vis. Commun. Image Represent..

[14]  James J. Clark.  Authenticating Edges Produced by Zero-Crossing Algorithms , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  J. Koenderink,et al.  Receptive field families , 1990, Biological Cybernetics.

[16]  Andrew P. Witkin,et al.  Scale-Space Filtering , 1983, IJCAI.

[17]  J. Koenderink.  The structure of images , 2004, Biological Cybernetics.