Scale-space for 1-D discrete signals
Apply the results from the continuous scale-space theory by discretizing the occurring equations. For example, the convolution integral (1.3) can be approximated by a sum using standard numerical methods. Or, the diffusion equation (1.5) can be discretized in space with the ordinary five-point operator forming a set of coupled ordinary differential equations, which can be further discretized in scale. If the numerical methods are chosen with care, reasonable approximations to the continuous numerical values can certainly be expected. But it is not guaranteed that the original scale-space conditions, however formulated in a discrete situation, will be preserved.
Formulate a genuinely discrete theory by postulating suitable axioms.
KeywordsGaussian Kernel Local Extremum Filter Coefficient Coarse Level Discrete Analogue
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