Lecture by Professor Malik


Scribe notes written by Wilson Cheng

Date: October 11, 1999 (Monday)



From last lecture, we learned:


· Textons are atoms of perception.


· Segmentation using normalized cuts.


· Julesz's textons filter representations.


i) Averages


ii) Marginal histograms


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


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


Using the Chi Square test:


    2                               k           [hi(m) – hj(m)]

X   (hi, hj) = ½ å ---------------

                          M=1         hi(m) + hj(m)



Wij = exp (-X (hi, hj) / stex


Review a little bit more about “norm”:

L1 norm |V1| + |V2| + … + |Vn|

                                2          2                2

L2 norm Ö(V1 + V2 + … Vn )


Linf norm = MAX |Vi|


Memo: To get help about normalization in Matlab, type “help norm”


Voronoi Diagram and Delaunay Triangulation


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);


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”


· Measuring texture similarities by using texton histograms.


Cue Integration

   Contour            Texture

Wij = Wij               * Wij


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


Gating the texture Cue



Gating the Contour Cue




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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