1. COMP 9517 Computer Vision
Texture
6/22/2018
COMP 9517 S2, 2009

2. Why texture?
Texture is another feature that help image segmentation and classification
Texture provides information about the spatial arrangement of the colours or intensities in an image
spatial distribution beside colour/intensity level distribution
Texture descriptor provides measures of properties such as smoothness, coarseness, and regularity
6/22/2018
COMP 9517 S2, 2009

3. Texture, texels and statistics
It is usually difficult to describe the irregular spatial arrangements
There is some quality of the image that would make on argue that there is a noticeable arrangement in each image
Properties as playing an important role in describing texture: uniformity, density, coarseness, roughness, regularity, linearity, directionality, direction, frequency, and phase.
6/22/2018
COMP 9517 S2, 2009

4. Texture, texels and statistics
Structural approach:
A set of primitive texels in some regular or repeated relationship
Statistical approach:
A quantitative measure of the arrangement of intensities in a region
A description of smooth, coarse and grainy
More general, easier to compute and popular in practice
Spectral approach:
Based on properties of the Fourier spectrum by itentifying high-energy, narrow peaks in the spectrum
Primarily to detect global periodicity
6/22/2018
COMP 9517 S2, 2009

5. Structural Texture Description
A simple “texture primitive” can be used to form more complex texture patterns by means of some rules that limit the number of possible arrangements of the primitives.
Descriptors:
A description of the texels
A specification of the spatial relationship
Suitable for man-made and regular patterns
6/22/2018
COMP 9517 S2, 2009

6. Structural Texture Description
Geometry-based description(Tuceryan & Jain)
The characterisation of the spatial relationships is obtained from a Voronoi tessellation of the texels
Process steps:
Segment the image to extract texels
Construct the Voronoi tessellation
Calculate shape feature of the polygons to group the polygons into clusters that define uniformly textured regions
6/22/2018
COMP 9517 S2, 2009

7. Structural Texture Description
Construction of Voronoi tessellation
Let S be the set of centroids of texels
For any pair of points P and Q in S, create the perpendicular bisector of the line joining them
Let HQ(P) be the half plane that is closer to P with respect to the perpendicular bisector of P and Q. The Voronoi Polygon of P is defined by:
6/22/2018
COMP 9517 S2, 2009

8. Statistical Texture Description
Motivations:
Segmenting out the texels is often difficult in real images
Numeric quantities or statistics of a texture from the colours/intensity themselves can be computed
Advantages:
Computationally efficient
Work well for both segmentation and classification
6/22/2018
COMP 9517 S2, 2009

9. Statistical Texture Description
Methods for statistical texture description
Edge Density and Direction
Local Binary Partition
Histogram and Features
Co-occurrence Matrices and Features
Autocorrelation and Power Spectrum
6/22/2018
COMP 9517 S2, 2009

10. Edge Density and Direction
Edge detection is simple and easy to apply
The number of edge pixels in a give fixed-size region gives some indication of the busyness of that region
The directions of the edges also describe the characteristics of the texture pattern
6/22/2018
COMP 9517 S2, 2009

11. Edge Density and Direction
The outputs for each point from edge detector:
The gradient magnitude Mag(p)
The gradient direction Dir(p)
Edgeness Per Unit Area (EPUA)
EPUA measures the busyness, but not the orientation of the texture
6/22/2018
COMP 9517 S2, 2009

12. Edge Density and Direction
Extended to include both busyness and orientation
Let Hmag(R) denote the normalised histogram of gradient magnitudes of region R
Let Hdir(R) denote the normalised histogram of gradient orientations of region R
The quantitative texture description of region R is
L1 distance for comparison
6/22/2018
COMP 9517 S2, 2009

13. Local Binary Partition (LBP)
For each pixel p in the image, create an 8-bit number B=b0b1b2b3b4b5b6b7
Check the eight neighbour of p
Texture is represented by a histogram of B
L1 distance can be used to compare two image/region 1 2 3 * 4 5 6 7
6/22/2018
COMP 9517 S2, 2009

14. Local Binary Partition (LBP)
An example
110
200
198 30 64
147
137 75 47 89 56 27 6 9 11 73
112
167 1 3
143
186
6/22/2018
COMP 9517 S2, 2009

15. Histogram and Features
Use statistical moments of the gray-level histogram of an image or region
Let z be a random variable denoting gray levels and let p(zi), i=0,1,2,…,L-1, be the corresponding histogram, where L is the number of distinct gray levels
The mean
The nth moment of z about the mean is
6/22/2018
COMP 9517 S2, 2009

16. Histogram and Features
The second moment
is of particular importance in texture description since it measures the gray-level contrast that can be used to establish descriptions of relative smoothness
For example, a measure of constant intensity
The standard deviation σ is used frequently
6/22/2018
COMP 9517 S2, 2009

17. Histogram and Features
The third moment
is a measure of the skewness of the histogram
The fourth moment is a measure of its relative flatness
The fifth and higher moments are not so easily related to histogram shape, but they do provide further quantitative discrimination of texture content
6/22/2018
COMP 9517 S2, 2009

18. Histogram and Features
Some other texture measures based on histogram
Uniformity
U is maximum for an image in which all gray levels are equals (maximally uniform)
Average entropy
Entropy is a measure of variability and is 0 fro a constant image
6/22/2018
COMP 9517 S2, 2009

19. Histogram and Features
6/22/2018
COMP 9517 S2, 2009

20. Histogram and Features
Measures of texture based on histogram suffer from the limitation that they carry no information regarding the relative position of pixels with respect to each other
One way to bring this type of information into the texture analysis process is to consider not only the distribution of intensities, but also the positions of pixels with equal or nearly equal intensity values
6/22/2018
COMP 9517 S2, 2009

21. Co-occurrence Matrices
A co-occurrence matrix is a 2-D array C in which both the rows and the columns represent a set of possible image values V.
The value of C(i, j) denotes how many times value I co-occurs with value j in some designated spatial relationships R.
V can be the set of possible gray tones for gray-level images or the set of possible colours for colour images
6/22/2018
COMP 9517 S2, 2009

22. Co-occurrence Matrices
Let d = (dr, dc) be a displacement vector where dr is a displacement in rows and dc is a displacement in columns.
Let V be a set of gray tones
The gray-level co-occurrence matrix Cd for image I is defined by
6/22/2018
COMP 9517 S2, 2009

23. Co-occurrence Matrices
An example
C[0,1] C[1,0] C[1,1] 1 2 1 2 1 2 1 2 1 2 2 1 1 2 3 1 4 2 1 2 1 2 i j i j i j
6/22/2018
COMP 9517 S2, 2009

24. Co-occurrence Matrices
Two variations of the standard gray-level co-occurrence matrix
Normalised gray-level co-occurrence matrix
Symmetric gray-level co-occurrence matrix
6/22/2018
COMP 9517 S2, 2009

25. Co-occurrence Matrices
Features based on co-occurrence matrix
where μi, μj are the mean and σi, σi are the standard deviations of the row and column sums
6/22/2018
COMP 9517 S2, 2009

26. Co-occurrence Matrices
Features based on co-occurrence matrix
Maximal probability gives an indication of the strongest response
The second one has a relatively low value when the high values of N are near the man diagonal
The third one has the opposite effect
6/22/2018
COMP 9517 S2, 2009

27. Co-occurrence Matrices
One problem for co-occurrence matrices is how to choose the displacement vector d
Use χ2 statistical test to select the value of d that have the most structure, i.e. to maximise the value
6/22/2018
COMP 9517 S2, 2009

28. Co-occurrence Matrices
The co-occurrence matrix features suffer from a number of difficulties
There is no well established method of selecting the displacement vector
Computing co-occurrence matrices for different values of d is not feasible
Some sort of feature selection methods must be used to select the most relevant ones from a large number of features
Primarily used in texture classification tasks and not in segmentation tasks
6/22/2018
COMP 9517 S2, 2009

29. Laws Texture Energy Measures
Use local masks to detect various types of textures
Define vectors:
L5 (Level) = [ ]
E5 (Edge) = [ ]
S5 (Spot) = [ ]
R5 (Ripple) = [ ]
Masks are obtained by outer products of pairs of these vectors
Texture Energy Map
Average certain symmetric pairs to form nine energy maps:
9 standard energy map: L5E5/E5L5, L5S5/S5L5, L5R5/R6L5, E5S5/S5E5,E5R5/R5E5,S5R5/R5S5,E5E5,S5S5,R5R5
6/22/2018
COMP 9517 S2, 2009

30. Laws Texture Energy Measures
Steps of creating Laws Texture Energy Measures
Moving a small window around the image and subtracting the local average from each pixel
Apply the 16 filters to the pre-processed image
Calculate the texture energy map for each filter
Create 9 energy map images by averaging certain symmetric pairs
6/22/2018
COMP 9517 S2, 2009

31. Autocorrelation
Autocorrelation function of an image can be used to detect repetitive patterns of texture elements and fineness/coarseness of the texture
The autocorrelation function ρ(dr,dc) of an (N+1)x(N+1) image for displacement d = (dr,dc) is defined by
If the texture is coarse, then the autocorrelation function drops off slowly
6/22/2018
COMP 9517 S2, 2009

32. Spectral Approach
Fourier spectrum is ideally suited for describing the directionality of periodic or almost periodic 2-D patterns
Global texture patterns can be detected as concentrations of high-energy bursts in the spectrum, but quite difficult to be detected with spatial methods
6/22/2018
COMP 9517 S2, 2009

33. Spectral Approach Three features of the Fourier spectrum:
Prominent peaks in the spectrum – principal direction of the texture patterns
The location of the peaks in the frequency plane – the fundamental spatial period of the patterns
Eliminating any periodic components via filtering leaves non-periodic image elements – to be described by statistical techniques
6/22/2018
COMP 9517 S2, 2009

34. Spectral Approach
Detection and interpretation of the spectrum features
Express the spectrum in polar coordinates: S(r, θ)
For each direction θ: Sθ(r) is a 1-D function
For each frequency r: Sr(θ) is a 1-D function
A more global descriptor
6/22/2018
COMP 9517 S2, 2009

35. Spectral Approach
6/22/2018
COMP 9517 S2, 2009

36. Texture Segmentation
Any texture measure that provides a value or vector of values at each pixel, describing the texture in a neighbourhood of that pixel, can be used to segment the image into regions of similar textures
Segmentation based on both colour and texture can do better
Segmentation of natural scenes is an unsolved problem
6/22/2018
COMP 9517 S2, 2009

37. References
Tuceryan, M., and A.K. Jain Texture analysis. In Handbook of Pattern Recognition and Vision. World Scientific Publishing Co., Singapore,
6/22/2018
COMP 9517 S2, 2009

38. Acknowledgement
Some material, including images and tables, were drawn from the textbook and Stockman’s online resources.
6/22/2018
COMP 9517 S2, 2008