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Alternatively, the operator T s;s can be said to be homogeneous across space-time. Convolution structure Together, the assumptions of linearity and shift-invariance imply that the internal representations Lð$; $; s; sÞ are given by convolution transformations Lðx; t; s; sÞ ¼ ðT ð$; $; s; sÞ Ã f Þðx; tÞ Z Z ¼ T ðx; h; s; sÞ f ðx À x; t À hÞdx dh; (72) x˛RN h˛R where T ð$; $; s; sÞ denotes some family of convolution kernels. These convolution kernels and their spatio-temporal derivatives can also be referred to as spatio-temporal receptive fields.

19 Spatiochromatic receptive fields corresponding to the application of Gaussian derivative operators up to order two to red/green and yellow/blue coloropponent channels, respectively. Ó 2013 Tony Lindeberg. ) Generalized Axiomatic Scale-Space Theory 39 where yellow is approximated by the average of the R and G channels and f can be defined as a channel of pure intensity information. 19 shows equivalent spatiochromatic receptive fields corresponding to the application of Gaussian derivative operators according to Eq.

2010), Linde & Lindeberg (2012), Zhang et al. (2012), it is shown how such color-opponent spatiochromatic receptive fields, in combination with regular spatial receptive fields, can constitute a very effective basis for object recognition. 5. Uniqueness of the Gaussian Kernel on a Spatial Domain The Gaussian scale-space concept satisfies the requirements of (1) linearity, (2) shift invariance, (3) semigroup property, (4) existence of an infinitesimal generator, (5) non-creation of local extrema, (6) non-enhancement of local extrema, (7) rotational symmetry, (8) positivity, (9) normalization, and (10) scale invariance.

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Applications for data hiding by Bender

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