Texture

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Texture
Turk, 91
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What is texture ?

• 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.
• In our case we refer to the texture as images or
  patterns with some kind of structure.

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What is texture ? (cont)
repetition
stochastic
both
fractal
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What would we like to do with textures?

• Detect regions / images with textures.
• 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)

Why is it difficult ?
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Periodic Texture

• 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.

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Texture primitives

• 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.

we dont see the forest.
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Texture Description

• Auto-correlation
• Fourier Transform in small windows
• Wavlets or Filter banks
• Feature vectors
• Statistical descriptors
• Markov Chains

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The auto-correlation

• 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
• Periodicity The energy of different frequencies.
• Directionality The energy of slices in different
  directions.

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Filter banks

• Instead of using the Fourier Basis, apply filters
  which best classify different textures.
• Use filters of varying orientations.
• Use filters of varying scales
• 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)

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What can we do with these features?

• 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
• 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.

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Second order statistics (or co-occurrence
matrices)

• The intensity histogram is very limited in
  describing a texture (f.e - checkerboard versus
  white-black regions.
• Use higher-level statistics Pairs distribution.
• From this matrix, generate a list of features
• Energy
• Entropy (can also be used as a measure for
  textureness).
• Homogeneity ( )

0 1 2 3

• Example
• co-occurrence matrix of I(x,y) and I(x1,y)
• Normalize the matrix to get probabilities.

0 1 2 3
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Texture as a Stochastic Process

• 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 PAB,C means
  probability of A given B and C

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Markov Chain

• 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 co-occurrence matrix is a
  special case with n2)
• We can use this process to synthesis new images !
• Markov Random Field The same, but 2D.

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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 Artauds 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...

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Region texels

• 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
• Directionality
• diameter versus boundary length

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Shape from texture

• 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

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Summery

• There are many ways to describe a texture
• 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.
• For example Texture synthesis.