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Texture. Turk, 91. 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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### Texture

Turk, 91

• 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”.

repetition

stochastic

both

fractal

• 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 ?

• 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.

• 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 don’t see the forest.”

• Auto-correlation

• Fourier Transform in small windows

• Wavlets or Filter banks

• Feature vectors

• Statistical descriptors

• Markov Chains

• 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.

• 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)

• 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”.

• 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(x+1,y)

• Normalize the matrix to get probabilities.

0

1

2

3

• 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

• 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 n=2)

• We can use this process to synthesis new images !

• Markov Random Field: The same, but 2D.

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...”

• 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

• 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”

• 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.