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Abstract : |
We address the formulation of a scale-space theory for discrete signals. In one dimension it is possible to characterize the smoothing transformations completely and an exhaustive treatment is given, answering the following two main questions: 1. Which linear transformations remove structure in the sense that the number of local extrema (or zero-crossings) in the output signal does not exceed the number of local extrema (or zero-crossings) in the original signal? 2. How should one create a multi-resolution family of representations with the property that a signal at a coarser level of scale never contains more structure than a signal at a ner level of scale? We propose that there is only one reasonable way to dene a scale-space for 1D discrete signals comprising a continuous scale parameter, namely by (discrete) convolution with the family of kernels T (n; t) = e t I n (t), where I n are the modied, |
