Abstract
Wavelet decompositions are more recent addition to the arsenal of multiscale signal processing techniques. Unlike the Gaussian and Laplacian pyramids, they provide a complete image representation and perform decomposition according to both scale and orientation. They are implemented using cascaded filter banks in which the lowpass and highpass filters satisfy certain specific constraints. While classical signal processing concepts provide an operational understanding of such systems, there exist remarkable connections with work in applied mathematics and psychophysics, which provide a deeper understanding of wavelet decompositions and their role in vision. From a mathematical standpoint, wavelet decompositions are equivalent to signal expansions in a wavelet basis. The regularity and vanishing moment properties of the lowpass filter impact the shape of the basis functions and hence their ability to efficiently represent typical images. From a psychophysical perspective, early stages of human visual information processing apparently involve decomposition of retinal images into a set of bandpass components corresponding to different scales and orientations. This suggests that multiscale/multiorientation decompositions are indeed natural and efficient for visual information processing.
| Original language | English (US) |
|---|---|
| Title of host publication | The Essential Guide to Image Processing |
| Publisher | Elsevier Inc. |
| Pages | 123-142 |
| Number of pages | 20 |
| ISBN (Print) | 9780123744579 |
| DOIs | |
| State | Published - Dec 1 2009 |
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ASJC Scopus subject areas
- Computer Science(all)
Cite this
Multiscale Image Decompositions and Wavelets. / Moulin, Pierre.
The Essential Guide to Image Processing. Elsevier Inc., 2009. p. 123-142.Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Multiscale Image Decompositions and Wavelets
AU - Moulin, Pierre
PY - 2009/12/1
Y1 - 2009/12/1
N2 - Wavelet decompositions are more recent addition to the arsenal of multiscale signal processing techniques. Unlike the Gaussian and Laplacian pyramids, they provide a complete image representation and perform decomposition according to both scale and orientation. They are implemented using cascaded filter banks in which the lowpass and highpass filters satisfy certain specific constraints. While classical signal processing concepts provide an operational understanding of such systems, there exist remarkable connections with work in applied mathematics and psychophysics, which provide a deeper understanding of wavelet decompositions and their role in vision. From a mathematical standpoint, wavelet decompositions are equivalent to signal expansions in a wavelet basis. The regularity and vanishing moment properties of the lowpass filter impact the shape of the basis functions and hence their ability to efficiently represent typical images. From a psychophysical perspective, early stages of human visual information processing apparently involve decomposition of retinal images into a set of bandpass components corresponding to different scales and orientations. This suggests that multiscale/multiorientation decompositions are indeed natural and efficient for visual information processing.
AB - Wavelet decompositions are more recent addition to the arsenal of multiscale signal processing techniques. Unlike the Gaussian and Laplacian pyramids, they provide a complete image representation and perform decomposition according to both scale and orientation. They are implemented using cascaded filter banks in which the lowpass and highpass filters satisfy certain specific constraints. While classical signal processing concepts provide an operational understanding of such systems, there exist remarkable connections with work in applied mathematics and psychophysics, which provide a deeper understanding of wavelet decompositions and their role in vision. From a mathematical standpoint, wavelet decompositions are equivalent to signal expansions in a wavelet basis. The regularity and vanishing moment properties of the lowpass filter impact the shape of the basis functions and hence their ability to efficiently represent typical images. From a psychophysical perspective, early stages of human visual information processing apparently involve decomposition of retinal images into a set of bandpass components corresponding to different scales and orientations. This suggests that multiscale/multiorientation decompositions are indeed natural and efficient for visual information processing.
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UR - http://www.scopus.com/inward/citedby.url?scp=84858640027&partnerID=8YFLogxK
U2 - 10.1016/B978-0-12-374457-9.00006-8
DO - 10.1016/B978-0-12-374457-9.00006-8
M3 - Chapter
AN - SCOPUS:84858640027
SN - 9780123744579
SP - 123
EP - 142
BT - The Essential Guide to Image Processing
PB - Elsevier Inc.
ER -