Multiresolution Analysis (Section 7.1) CS474/674 – Prof. Bebis.
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Transcript of Multiresolution Analysis (Section 7.1) CS474/674 – Prof. Bebis.
![Page 1: Multiresolution Analysis (Section 7.1) CS474/674 – Prof. Bebis.](https://reader035.fdocuments.net/reader035/viewer/2022062320/56649d435503460f94a1f493/html5/thumbnails/1.jpg)
Multiresolution Analysis (Section 7.1)
CS474/674 – Prof. Bebis
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Multiresolution Analysis
• Many signals or images contain features at different scales or level of detail (e.g., people vs buildings)
• Analyzing information at the same resolution or at a single scale will not be sufficient!
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Multiresolution Analysis (cont’d)
• Many signals or images contain features at different scales or level of detail (e.g., people vs buildings)
Small size objects shouldbe examined at a high resolution
Large size objects shouldbe examined at a low resolution
Equivalent to using windows of multiple size!
High resolution(high frequencies)
Low resolution(low frequencies)
Intermediate resolution
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Multiresolution Analysis (cont’d)
• We will review two techniques for representing multiresolution information efficiently:– Pyramidal coding
– Subband coding
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high resolution j = J
low resolution j=0
A collection of decreasing resolution images arranged in the shape of a pyramid.
Image Pyramid
(low scale)
(high scale)
If N=256, the pyramid will have 8+1=9 levels
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Pyramidal coding
Two pyramids: approximation and prediction residual
averaging mean pyramidGaussian Gaussian pyramidno filter subsampling pyramid
nearest neighborbilinerbicubic
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Pyramidal coding (cont’d)
Approximation pyramid(based on Gaussian filter)
Prediction residual pyramid(based on bilinear interpolation)
Last level same as that in theapproximation pyramid
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Pyramidal coding (cont’d)
In the absence of quantization errors, the approximation pyramidcan be re-constructed from the prediction residual pyramid.
Keep the prediction residual pyramid only!Much more efficient to represent!
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Subband coding
• Decompose an image (or signal) into a set of
different frequency bands (analysis step).
• Decomposition is performed so that the subbands can be re-assembled to reconstruct the original image without error (synthesis step)
• Analysis/Synthesis are performed using appropriate filters.
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Subband coding – 1D Example
flp(n): approximation of f(n)
fhp(n): detail of f(n)
2-band decomposition
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Subband coding (cont’d)
• For perfect reconstruction, the synthesis filters (g0(n) and g1(n)) must be modulated versions of the analysis filters (h0(n), h1(n)):
or
original modulated
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Subband coding (cont’d)
• Of special interest, are filters satisfying orthonormality conditions:
• An orthonormal filter bank can be designed from a single prototype filter:
(non-orthonormal filters require two prototypes)
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Subband coding (cont’d)Example: orthonornal filters
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Subband coding – 2D Example
4-band decomposition (using separable filters)
approximation
horizontal detail
vertical detail
diagonal detail
LL
LH
HL
HH
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Subband coding (cont’d)
approximation
vertical detail
horizontal detail
diagonal detail