1. Texture

2. What is Texture?

3. What is Texture No formal definition
There is significant variation in intensity levels between nearby pixels
Texture is a homogeneous property at some spatial scale
A characteristic of the human visual system is that textures are perceived as homogeneous regions by a human observer even though textures do not have uniform intensity

4. Texture Apparent homogeneous regions: Sand on a beach A brick wall
In both cases the HVS will interpret areas of sand or bricks as a ‘region’ in an image
But, close inspection will reveal strong variations in pixel intensity

5. Texture A single pixel does not have texture.
Texture is the property of a ‘group of pixels’
The ‘group of pixels’ can define a
Texture Primitive
Texture Element
Texture is scale dependent – at different scales texture will take on different properties

6. Scale Dependency Scale is important – consider sand Close up -
“small rocks, sharp edges”
“rough looking surface”
“smoother”
Far Away
“one object  brown/tan color”

7. Terms (Properties) Used to Describe Texture
Coarseness
Roughness
Direction
Frequency
Uniformity
Density
How would describe dog fur, cat fur, grass, wood grain, pebbles, cloth, steel??

8. “The object has a fine grain and a smooth surface”
Can we define these terms precisely in order to develop a computer vision recognition algorithm?

9. Features Tone – based on pixel intensity in the texture primitive
Structure – spatial relationships between primitives
A pixel can be characterized by its Tonal/Structural properties of the group of pixels it belongs to

10. Spatial Relationship of Primitives:
Tonal:
Average intensity
Maximum intensity
Minimum intensity
Size, shape
Spatial Relationship of Primitives:
Random
Pair-wise dependent

11. Artificial Texture
OO OX OX OX XX
OOOOOOOOXXXXXXXXXXX

12. Artificial Texture OO OX OX OX XX OOOOOOOOXXXXXXXXXXX
Segmenting into regions based on texture

13. Color Can Play an Important role in Texture
OO OX OX OX XX
OOOOOOOOXXXXXXXXXXX

14. Color Can Play an Important Role in Texture
OO OX OX OX XX
OOOOOOOOXXXXXXXXXXX

15. Statistical and Structural Texture
Consider a brick wall:
Statistical Pattern – close up pattern in bricks
Structural (Syntactic) Pattern – brick pattern
OX on previous slides can be represented by a grammar,
such as, ababab )

16. Most current research focuses on statistical texture
Edge density is a simple texture measure
- edges per unit distance
Segment object based on edge density
HOW DO WE ESTIMATE
EDGE DENSITY??

17. Move a window across the image
and count the number of edges in
the window
ISSUE – window size?
How large should the window be?
What are the tradeoffs?
How does window size affect
accuracy of segmentation?
Segment object based
on edge density

18. Move a window across the image
and count the number of edges in
the window
ISSUE – window size?
How large should the window be?
Large enough to get a good estimate
Of edge density
What are the tradeoffs?
Larger windows result in larger overlap
between textures
How does window size affect
Accuracy of segmentation?
Smaller windows result in better region
segmentation accuracy, but poorer
Estimate of edge density
Segment object based
on edge density

19. Average Edge Density Algorithm
Smooth image to remove noise
Detect edges by thresholding image
Count edges in n x n window
Assign count to edge window
Feature Vector  [gray level value, edge density]
Segment image using feature vector

20. Run Length Coding Statistics
Runs of ‘similar’ gray level pixels
Measure runs in the directions 0,45,90,135 1 2 3
Y( L, LEV, d)
Where L is the number of runs of
length L
LEV is for gray level value and
d is for direction d
Image

21. 1 2 3 1 2 3 4 1 2 3 4 Image 45 degrees 0 degrees Run Length, L1 2 3
Image
45 degrees
0 degrees
Run Length, L
Run Length, L 1 2 3 4 1 2 3 4
Gray Level, LEV
Gray Level, LEV

22. 1 2 3 1 2 3 4 1 2 3 4 Image 45 degrees 0 degrees Run Length, L1 2 3
Image
45 degrees
0 degrees
Run Length, L
Run Length, L 1 2 3 4 1 2 3 4
Gray Level, LEV
Gray Level, LEV

23. Run Length Coding
For gray level images with 8 bits 256 shades of gray  256 rows
1024x1024  1024 columns
Reduce size of matrix by quantizing:
Instead of 256 shades of gray, quantize each 8 levels into one resulting in 256/8 = 32 rows
Quantize runs into ranges; run 1-8  first column, 9-16 the second…. Results in 128 columns

24. Gray Level Co-occurrence Matrix, P[i,j]
Specify displacement vector d = (dx,dy)
Count all pairs of pixels separated by d having gray level values i and j
Consider simple image with gray level values 0,1,2
Let d = (1,1)
One pixel right
One pixel down 2 1 x y

25. 2 1
Count all pairs of pixels in which the
first pixel has value i and the second
value j displaced by d.
P(1,0) 1
P(2,1) 2 1
Etc.
There are 16 pairs, so normalize by 16

26. Co-occurrence Matrix, P[i,j]2 1 1 2 3 i
P[i,j]

27. Uniform Texture x d=(1,1) y Let Black = 1, White = 0 P[i,j] P(0,0)=

28. Uniform Texture x d=(1,1) y Let Black = 1, White = 0 P[i,j] P(0,0)= 24

29. Uniform Texture x d=(1,0) y Let Black = 1, White = 0 P[i,j] P(0,0)= ?

30. Uniform Texture x d=(1,0) y Let Black = 1, White = 0 P[i,j] P(0,0)= 0

31. Randomly Distributed Texture
What if the Black and white pixels where randomly distributed?
What will matrix P look like??

32. Randomly Distributed Texture
What if the Black and white pixels where randomly distributed?
What will matrix P look like??
No preferred set of gray level
pairs, matrix P will have
approximately a uniform
population

33. Co-occurrence Features
Gray level co-occurrence matrices are referred to as GLCM
Typically GLCM are calculated at four different angles, 0, 45,90 and 135 degrees
For each angles different distances can be used, d=1,2,3, etc.
Each matrix will be 256x256 for an 8 bit image. Quantizing the image will result in smaller matrices. A six bit image will result in 64x64 matrices
14 features can be calculated from each GLCM. The features are used for texture calculations

34. Co-occurrence Features
P(ga,gb,d,t) :
ga  gray level pixel ‘a’
gb  gray level pixel ‘b’
d  distance d
t  angle t (0, 45,90,135
In many applications the transition ga to gb and gb to ga are
both counted. This results in symmetric GLCMs:
For P(0,0,1,0)
results in an entry of 2 for the ‘0 0’ entry

35. Co-occurrence Features
The data in the GLCM are used to derive the features, not the original image data
Contrast =  Pi,j * (i-j)2
How do you interpret the contrast equation?

36. Co-occurrence Features
The data in the GLCM are used to derive the features, not the original image data
Contrast =  Pi,j * (i-j)2
How do you interpret the contrast equation?
The (i-j)2 term is a weighing factor, values along the diagonal where i=j are multiplied by zero. These values represent adjacent image pixels that do not have a gray level difference. Entries further away from the diagonal represent pixels that have a greater gray level difference, that is more contrast, and are multiplied by a larger weighing factor.
NOTE: The weighing factor is a squared term

37. Co-occurrence Features
Dissimilarity =  Pi,j * |i-j|
Dissimilarity is similar to contrast, except the weights increase linearly

38. Co-occurrence Features
Inverse Difference Moment
IDM =  Pi,j / [ 1+(i-j)2 ]
IDM has smaller numbers for images with high contrast, larger numbers for images low contrast

39. Co-occurrence Features
Angular Second Moment measures orderliness. Orderliness measures how regular or orderly the pixel values are in the window
ASM =  Pi,j 2
Energy is the square root of ASM, E =   Pi,j 2
Entropy =  Pi,j 2 * ( -ln Pi,j ) with the assumption ln(0)=0

40. Regional Descriptors
Texture

41. Random texture is analyzed by statistical methods.
Regional Descriptors
Texture
Texture is usually defined as the smoothness or roughness of a surface.
In computer vision, it is the visual appearance of the uniformity or lack of uniformity of brightness and color.
There are two types of texture: random and regular.
Random texture cannot be exactly described by words or equations; it must be described statistically. The surface of a pile of dirt or rocks of many sizes would be random.
Regular texture can be described by words or equations or repeating pattern primitives. Clothes are frequently made with regularly repeating patterns.
Random texture is analyzed by statistical methods.
Regular texture is analyzed by structural or spectral (Fourier) methods.

42. Statistical Approaches
Regional Descriptors
Statistical Approaches
Let z be a random variable denoting gray levels and let p(zi), i=0,1,…,L-1, be the corresponding histogram, where L is the number of distinct gray levels.
The nth moment of z:
The measure R:
The uniformity:
The average entropy:

43. Statistical Approaches
Regional Descriptors
Statistical Approaches
Smooth
Coarse
Regular

44. Structural Approaches
Regional Descriptors
Structural Approaches
Structural concepts:
Suppose that we have a rule of the form S→aS, which indicates that the symbol S may be rewritten as aS.
If a represents a circle [Fig (a)] and the meaning of “circle to the right” is assigned to a string of the form aaaa… [Fig (b)] .

45. Regional Descriptors
Spectral Approaches
For non-random primitive spatial patterns, the 2-dimensional Fourier transform allows the patterns to be analyzed in terms of spatial frequency components and direction.
It may be more useful to express the spectrum in terms of polar coordinates, which directly give direction as well as frequency.
Let is the spectrum function, and r and are the variables in this coordinate system.
For each direction , may be considered a 1-D function
For each frequency r, is a 1-D function.
A global description:

46. Regional Descriptors
Spectral Approaches

47. Regional Descriptors
Spectral Approaches

48. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
For a 2-D continuous function f(x,y), the moment of order (p+q) is defined as
The central moments are defined as

49. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
If f(x,y) is a digital image, then
The central moments of order up to 3 are

50. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
The central moments of order up to 3 are

51. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
The normalized central moments are defined as

52. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
A seven invariant moments can be derived from the second and third moments:

53. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
This set of moments is invariant to translation, rotation, and scale change.

54. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions

55. Moments of Two-Dimensional Functions
Regional Descriptors
Moments of Two-Dimensional Functions
Table Moment invariants for the images in Figs (a)-(e).