**Lecture
by Professor Malik**

** **

**Scribe
notes written by Wilson Cheng**

**Date:
October 11, 1999 (Monday)**

**==============================================================================================**

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**From
last lecture, we learned:**

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**·**** Textons are atoms of
perception.**

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**·**** Segmentation using normalized
cuts.**

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**·**** Julesz's textons filter
representations.**

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**i)
Averages**

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**ii)
Marginal histograms**

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**iii)
Joint histograms --> ('new' textons)**

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**We
understand how to find W ij but how do we find the texture
boundaries? We must find textons
boundaries and compare them.**

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**Using
the Chi Square test: **

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** _{2}**

**X (h***i*, h*j*) = **½ ****å**** ---------------**

**
****M=1 h***i*(m) + h*j*(m)

**
**

** _{2}**

**Wij
= exp (-X (h****i,
h****j) / ****stex**

** **

**Review a little bit more about “norm”:**

**L***1*** norm |V***1*| + |V*2*| + … + |V*n*|

_{ 2 2 2}

**L***2* norm **Ö(V***1* + V*2* + … V*n* )

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**L***inf* norm = MAX |V*i*|

*
i*

** **

** **

**Using
an example of post offices as an illustration:**

**P’s
are post offices.**

**Goto
nearest post office, then find the space closest to the next post office**

**(“Dual”
notion of neighbors also known as “dual” representation);**

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**Then
compute set of neighbors == Delaunay neighbors**

** **

**Find
average distance by taking the median.**

** **

** **

** **

**Whether
a line is a boundary of another object or it’s interior segments can be tested using
the Chi-Square test.**

**If
texture is inside, Chi-Square ****»**** 0.**

** **

**The
above phenomenon where boundaries are seen as interior segments is called
“crowding”**

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**·**** Measuring texture
similarities by using texton histograms.**

** **

** Contour
****Texture**

**W****ij = W****ij * W****ij **

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**Gate
contour texture cues are based on boundary versus interior test.**

** **

** **

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__ __

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__Conclusion__**: **

**If
possible, we should use global analysis for it’s more accurate than local
examination. Also combining information
from different scientific sources gets you more accurate results.**

** **

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END OF SCRIBE NOTES =================**