Texture

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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”.

What is texture ? (cont’)

repetition

stochastic

both

fractal

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 ?

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.

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 don’t see the forest.”

Texture Description

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

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.

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)

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”.

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 ( )

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1100Example: •co-occurrence matrix of I(x,y) and I(x+1,y) •Normalize the matrix to get probabilities.

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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 P[A|B,C] means probability of A given B and C

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 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

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

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”

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.