Download Texture - CS

Texture
Turk, 91
What is texture ?
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There is no accurate definition.
It is often used to represent all the
“details” in the image. (F.e, sometimes
images are divided to shape + texture.
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In our case we refer to the texture
as images or patterns with some
kind of “structure”.
What is texture ? (cont’)
repetition
stochastic
both
fractal
What would we like to do with textures?
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Detect regions / images with
Why is it
textures.
difficult ?
Classify using texture.
Segmentation: divide the image
into regions with uniform texture.
Synthesis – given a sample of the
texture, generate random images
with the same texture.
Compression (Especially fractals)
Periodic Texture
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big assumption: the
image is periodic,
completely specified
by a fundamental
region.
no allowance for
statistical variations
this approach is fine if
image is periodic, but
too limited as a
general texture
model.
Texture primitives
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“we don’t
see the
forest.”
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The basic elements that form the texture.
Sometimes, they are called “texels”.
Primitives do not always exists ( or are
not visible).
In textures which are not periodic, the
texel is the “essential” size of the texture.
There might be textures with structure in
several resolutions (bricks)
Fractals have the similar structure in each
resolution.
Texture Description
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Auto-correlation
Fourier Transform in small windows
Wavlets or Filter banks
Feature vectors
Statistical descriptors
Markov Chains
…
The auto-correlation
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Describes the relations between
neighboring pixels.
Equivalently, we can analyze the power
spectrum of the window: We apply a
Fourier Transform in small windows.
Analyzing the power spectrum:
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Periodicity: The energy of different
frequencies.
Directionality: The energy of slices in different
directions.
Filter banks
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Instead of using the Fourier Basis, apply filters
which best classify different textures.
Use filters of varying orientations.
Use filters of varying scales:
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Laplacian pyramids
Wavlets pyramids
…
Gabor Filters (Local sinuses in varying scales and
directions).
Filters which describe certain properties ( Entropy,
Energy, Coarseness…)
Some successful results in texture segmentation
were achieved using moment-based features
(mean, variance)
What can we do with these features?
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For each pixel (or window) attach a vector of
features.
Use this vector to calculate the “distance”
between different windows.
We can compute statistics of the features in a
region:
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Use the statistics to separate between different
textures.
…
We can determine the “essential” size of the
texture: the size in which the statistics are
“interesting”.
Second order statistics (or cooccurrence matrices)
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The intensity histogram is very limited in describing a
texture (f.e - checkerboard versus white-black regions.
Use higher-level statistics: Pairs distribution.
Example:
•co-occurrence matrix of
I(x,y) and I(x+1,y)
•Normalize the matrix to
get probabilities.
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0
0

0

2
0
0
2
2
1
1
2
3
1
1 
2

3
0
1
2
3
0
1
2
3
2
0

0

0
2
2
0
0
1
0
3
0
0
0
2

1
From this matrix, generate a list of features:
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Energy
Entropy (can also be used as a measure for “textureness”).
Homogeneity (  N (i, j)1 | i  j |)
i, j
Texture as a Stochastic Process
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A random variable is a value with a
given probability distribution.
A discrete stochastic process is a
sequence or array of random
variables, statistically interrelated.
Conditional probability P[A|B,C]
means probability of A given B and C
Markov Chain
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Assume that each variable depends only
on the n preceding values.
In this case, we have a Markov chain of
order n.
We estimate the process using an
histogram of groups of size n (The cooccurrence matrix is a special case with
n=2)
We can use this process to synthesis new
images !
Markov Random Field: The same, but 2D.
Markov Chain Example
Output of 2nd order word-level Markov Chain
[Scientific American, June 1989, Dewdney]
after training on 90,000 word philosophical
“If we were to revive the fable is useless.
Perhaps only the allegory of simulation is
unendurable--more cruel than Artaud’s
Theatre of Cruelty, which was the first to
practice deterrence, abstraction,
disconnection, deterritorialisation, etc.; and
if it were our own past. We are witnessing
the end of the negative form. But nothing
separates one pole from the very swing of
voting ’’rights’’ to electoral...”
Region texels
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Divide the image into uniform regions.
Use this regions as the texels, or
image primitives.
Use the structure of this regions to
make a statistics about the texture.
For example:
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Directionality
diameter versus boundary length
Shape from texture
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Under the assumption of isotropic
patterns, we can use this to recover
shape.
If the texture is periodic, we can use the
size differences between the primitives to
recover shape.
For example, assuming a planar scene,
we can use the direction of maximum rate
of change of the primitives size: “texture
gradient”
Summery
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There are many ways to describe a
texture:
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Different kinds of filters.
Statistical descriptors.
Texture as a random process.
For each pixel/region we attach the vector
of features.
Some works try to recover the primitives.
In some cases, it can be used to learn the
3D shape.
Many applications.
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For example: Texture synthesis.