a mathematical theory of primal sketch & sketchability c. guo, s. c. zhu, y. n.wu ucla
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![Page 1: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/1.jpg)
A Mathematical Theory of Primal Sketch &
Sketchability
C. Guo, S. C. Zhu, Y. N.WuUCLA
![Page 2: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/2.jpg)
Sketchabilityscale-distance-complexity
UCLA Bruin Walk
![Page 3: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/3.jpg)
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V1 cells: filters or bases?
kyxB ,,
![Page 5: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/5.jpg)
Two mathematical models
1. Sparse coding (Olshausen, Field)
2. Markov random field (Zhu, Wu, Mumford)
)},(exp{1
)( ,, kyxall
k BIZ
Ip
Unif{I: subband histograms = p_k}Restrictive, no inhibition, high complex regime
Coefficients sparseConstructive, inhibition, low complex regime
kkyx pc
kyxkyx BcI~
,,,,
,,
Complete basis: 1 and 2 are equivalent ICA, restructive
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Complexity scaling
)()( IentropyIentropy sub
global sketchability: entropy rate
![Page 7: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/7.jpg)
Markov random field complexity
)},(exp{1
)( ,, kyxall
k BIZ
Ip
0)())ˆ,(());(||(min truetrue pentropyIpentropyIppKL
Sparse coding complexity
)(~
,,,,CpC
kyxkyx BCBcI
))|(())((2/|'|log))(( ICpentropyIpentropyBBCpentropy
tkyxkyxall
k dWdtBBIdI ,,,, ),('
Connection
![Page 8: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/8.jpg)
Strategy of V11. Line-up large filter responses for sketchable 2. Pool weak filter responses for non-sketchable
JBcI ii )},(exp{1
~ ,,,, kyxall
kyx BJZ
J
Local sketchability: for a local patch I
Two interpretations1. Likelihood ratio test2. Coding after lateral inhibition
))ˆ;ˆ(()0|(log
))~
;(()0|(log
iii
i
BcIpentropycIp
IpentropycIp
jijji BBcBIBcBI ,,,
![Page 9: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/9.jpg)
Gestalt field
Model refinements1. Bases extendable ridge functions (Kim’s thesis)2. MRF added MRF interpolating sketchable
})),((exp{1
~),...,( 2~
101
jiji
jin BBAnglernZ
BBB
![Page 10: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/10.jpg)
input imagefast sketchingpursuit result
fast sketching refinement result
synthesized image sketch image fast sketching pursuitand refinement procedure(gif movie, show slide to view it)
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input imagefast sketchingpursuit result
fast sketching refinement result
synthesized image sketch image fast sketching pursuitand refinement procedure
![Page 14: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/14.jpg)
synthesized image sketch image fast sketching pursuitand refinement procedure
input imagefast sketchingpursuit result
fast sketching refinement result
![Page 15: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/15.jpg)
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input imagefast sketchingpursuit result
fast sketching refinement result
synthesized image sketch image fast sketching pursuitand refinement procedure
![Page 18: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/18.jpg)
input imagefast sketchingpursuit result
fast sketching refinement result
synthesized image sketch image fast sketching pursuitand refinement procedure
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synthesized image sketch image fast sketching pursuitand refinement procedure
input imagefast sketchingpursuit result
fast sketching refinement result
![Page 21: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/21.jpg)
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input imagefast sketchingpursuit result
fast sketching refinement result
synthesized image sketch image fast sketching pursuitand refinement procedure
![Page 23: A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA](https://reader036.vdocument.in/reader036/viewer/2022062714/56649d3b5503460f94a15fb9/html5/thumbnails/23.jpg)