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Scale-space for discrete images
KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.ORCID iD: 0000-0002-9081-2170
1989 (English)In: Scandinavian Conference on Image Analysis: SCIA'89 (Oulo, Finland), 1989, 1098-1107 p.Conference paper (Refereed)
Abstract [en]

This article addresses the formulation of a scale-space theory for one-dimensional discrete images. Two main subjects are treated:

  1. 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?
  2. 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?

We propose that there is only one reasonable way to define a scale-space for discrete images 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 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.

Place, publisher, year, edition, pages
1989. 1098-1107 p.
National Category
Mathematics Computer Science Computer Vision and Robotics (Autonomous Systems) Signal Processing
URN: urn:nbn:se:kth:diva-58612OAI: diva2:473431
6th Scandinavian Conference on Image Analysis, Oulu, Finland, 1989

QC 20150617

Available from: 2012-01-05 Created: 2012-01-05 Last updated: 2015-06-17Bibliographically approved

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