A note on shrinking and expanding operations in pyramids |
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| Affiliation: | 1. University of Alabama at Birmingham, School of Medicine, Birmingham, Alabama;2. University of Alabama at Birmingham, Civitan International Research Center, Birmingham, Alabama;3. Health Informatics Institute, Department of Pediatrics, Morsani College of Medicine, University of South Florida, Tampa, Florida;4. Greenwood Genetic Center, Greenwood, South Carolina;5. Boston Children''s Hospital (Harvard), Boston, Massachusetts;6. Baylor College of Medicine, Houston, Texas;7. University of California San Diego, San Diego, California;1. Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education & International Center for Dielectric Research, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China;2. Faculty of Materials and Energy, Southwest University, Chongqing 400715, China;1. Universidad Autónoma de Chile, Chile;2. Universidad de Sevilla, Spain |
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| Abstract: | Simple pyramid algorithms are described that, in O(k) steps, shrink or expand the 1's in a binary image by 2k − 1 (k = 1,2, …) and resample the results at intervals of 2k. For a one-dimensional image, the results can be computed without resampling provided the kth step is allowed to involve O(k) computation; but in two dimensions, O(2k) computation would be required, so that the pyramid has no advantages over a mesh. For grayscale images (with local Min and local Max playing the roles of shrinking and expanding), the resampled computation is still straightforward, but the unresampled computation cannot be done economically even in the one-dimensional case. |
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