A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA

A Mathematical Theory of Primal Sketch &

Sketchability

C. Guo, S. C. Zhu, Y. N.WuUCLA

Sketchabilityscale-distance-complexity

UCLA Bruin Walk

V1 cells: filters or bases?

kyxB ,,

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

Complexity scaling

)()( IentropyIentropy sub

global sketchability: entropy rate

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

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 ,,,

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

input imagefast sketchingpursuit result

fast sketching refinement result

synthesized image sketch image fast sketching pursuitand refinement procedure(gif movie, show slide to view it)



synthesized image sketch image fast sketching pursuitand refinement procedure
















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A Mathematical Theory of Primal Sketch & Sketchability C. Guo, S. C. Zhu, Y. N.Wu UCLA