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## Scale-Space for Discrete Images## Tony LindebergTechnical report ISRN KTH/NA/P--88/08--SE.Shortened version in Proc. 6th Scandinavian Conference on Image Analysis, (Oulo, Finland), pages 1098--1107, Jun. 1989. ## AbstractThis article addresses the formulation of a scale-space theory for one-dimensionaldiscrete images. Two main subjects are treated:
- Which linear transformations remove structure in the sense that the number of local extrema (or zero-crossings) in the output image does not exceed the number of local extrema (or zero-crossings) in the original image?
- How should one create a multi-resolution family of representations with the property that an image at a coarser level of scale never contains more structure than an image at a finer level of scale?
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 modified Bessel functions of integer order.
Similar arguments applied in the continuous case uniquely lead to the
Gaussian kernel.
Some obvious discretizations of the continuous scale-space theory are discussed in view of the results presented. An important result is that scale-space violations might occur in the family of representations generated by discrete convolution with the sampled Gaussian kernel.
Tony Lindeberg |