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TEXTURE
• An attribute
representing the
spatial arrangement
of the gray levels of
the pixels in a
region.
November 3, 1998
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TEXTURE
REGULAR
STATISTICAL ISOTROPIC
STATISTICAL ANISOTROPIC
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STATISTICAL METHODS FOR
TEXTURE ANALYSIS
FIRST ORDER STATISTICS
How often does a given grey value
occur at a pixel in an image….
Single Pixel
HISTOGRAM
# OF
OCCURRENCES
H(g)
0
255
GREY VALUES
H
SECOND ORDER STATISTICS
How often do grey values co-occur
at two pixels separated by a fixed
distance and direction …..
(Di,Dj)
November 3, 1998
(Di,Dj)
(g1,g2)
# OF
CO-OCCURRENCES
0
255
255
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STATISTICAL METHODS FOR
TEXTURE ANALYSIS
H
SECOND ORDER STATISTICS
(Di,Dj)
(g1,g2)
# OF
CO-OCCURRENCES
How often do grey values co-occur
at two pixels separated by a fixed
distance and direction …..
0
(Di,Dj)
255
255
256
256
November 3, 1998
256 x 256 2D matrix array
where entries are
co-occurrence values
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Nth-order STATISTICS
(Di,Dj) 3
(Di,Dj)
2
(Di,Dj) 1
N-dimensional matrix
..
(Di,Dj)
n
It has been found that humans can discriminate textures with different
2nd-order statistics but are bad at discriminating 3rd order statistics
(Julesz 1981).
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2nd ORDER STATISTICS
SECOND ORDER STATISTICS
How often do grey values co-occur
at two pixels separated by a fixed
distance and direction …..
(Di,Dj)
256
256
256 x 256 2D matrix array
where entries are
co-occurrence values
Since only pixel elements over short distances are correlated (Di,Dj) is typically
small [e.g., (1,0), (0,1), (1,1) ]
Since for 256 grey values the 2D matrix is typically sparse, co-occurences are
typically taken over 8 grey value ranges and less (e.g., for 256 grey values they are
grouped into 8 grey value bins or less)
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2nd ORDER STATISTICS
SECOND ORDER STATISTICS
# grey values
How often do grey values co-occur
at two pixels separated by a fixed
distance and direction …..
2D matrix array
where entries are
co-occurrence values
# grey
values
(Di,Dj)
‘Symmetrize’ the co-occurrence matrix by adding itself to its transpose.
C
(g1,g2)
(Di,Dj)
=
H
(Di,Dj)
(g1,g2)
+
H
T
(Di,Dj)
(g1,g2)
Besides making this less sensitive to how the image plane is coordinatized
this real positive symmetric matrix has nice rotational invariants such as
eigenvalues.
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TEXTURE MEASURES DERIVED FROM
THE CO-OCCURRENCE MATRIX
ENTROPY
S S Cij logCij
S S (i - j) Cij
2
INERTIA
ENERGY
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SS
2
Cij
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SOME EXAMPLE TEXTURES TO
CLASSIFY FOR A FINAL PROJECT
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PHOTOMETRIC STEREO
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PHOTOMETRIC STEREO
• No correspondence problem as is present in
binolcular stereo
• Measures surface orientation rather than
depth.
• Is active rather than passive.
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