1

Texture analysis

5554 - Packet 18 - Page 2

Can you identify these materials?

2

5554 - Packet 18 - Page 3

More examples

5554 - Packet 18 - Page 4

Synthetic examples

3

5554 - Packet 18 - Page 5

Even very simple textures can convey depth information

5554 - Packet 18 - Page 6

Different textures can indicate different 3D objects

Texture 1

Texture 3

Texture 4

Texture 5

Texture 2

4

5554 - Packet 18 - Page 7

Main topics in texture analysis

• Definitions• Applications• Texture primitives• Statistical texture analysis• Structural texture analysis• Shape from texture

5554 - Packet 18 - Page 8

What is texture?

• Visual texture is something that everyone understands, but it is difficult to define– "Despite its importance and ubiquity in image data, a formal

approach or precise definition of texture does not exist."(R. M. Haralick, 1979)

– Texture is "something composed of closely interwoven elements."(Webster's dictionary)

• Texture is "repeating patterns of local variations in image intensitywhich are too fine to be distinguished as separate objects at the observed resolution."(Jain, Kasturi, and Schunck, 1995)

5

5554 - Packet 18 - Page 9

Why should we study texture?

• Texture analysis has been used in– industrial inspection– image segmentation

(especially satellite imagery, for such applications as distinguishing forests from urban areas, etc.)

– shape analysis– estimation of object range and orientation

• Texture holds important information about image content(but that information can be difficult to extract!)

5554 - Packet 18 - Page 10

Application: find the defects in this image

6

5554 - Packet 18 - Page 11

Application: recognize different types of wood

maple

oak

oak

oak

5554 - Packet 18 - Page 12

• Humans often use qualitative descriptions of texture:– "coarse texture" or "fine texture"– "regular texture" or "irregular texture"– "uniform" or "nonuniform"– "granular"– "periodic"– . . .

• We need to perform a quantitative analysis, but how?

• (The relationship between texture and image intensity is complicated, much like particles and waves in physics)

7

5554 - Packet 18 - Page 13

Texture primitives

• One approach is to identify texture primitives(sometimes called "texels", or "texture elements")and then describe the spatial relations between them

• Examples using circular disks as the texture primitives:

Example of regular texture Example of irregular texture

5554 - Packet 18 - Page 14

Example with nonuniform size and nonuniform positioning of circular texture elements

8

5554 - Packet 18 - Page 15

Texture can exist at different scales

5554 - Packet 18 - Page 16

Statistical texture analysis

• Try to characterize the texture of an image region using statistical measures

• Common examples of this capture information about intensity levels in the image:– mean– standard deviation– moments– . . .– histogram– Gray-Level Co-occurrence Matrix (GLCM)– . . .– Fourier transform– autocorrelation . . .

9

5554 - Packet 18 - Page 17

Histograms for different surfaces

5554 - Packet 18 - Page 18

Notice that all 3 images belowhave the same histogram Is that a problem?

10

5554 - Packet 18 - Page 19

Higher-order statistics

• In a histogram, information about one pixel value is independent of all other pixel values

• We call it a "first-order statistic", and it is similar to the marginal probability

• It is possible to consider n pixels simultaneously, and these are called "nth-order statistics"

• A common second-order statistic resembles the following joint probability

( )( )icrI =,Pr

( ) ( )( )� jccrrIicrI =∆+∆+= ,,Pr

5554 - Packet 18 - Page 20

GLCM

• The Gray-Level Co-occurrence Matrix (GLCM)captures intensity information about pairs of pixels

• First, one needs to specify a particular distance and direction between pixel pairs; usually this is done with a displacement vector

• Example: to capture information about each pixel and its neighbor at the right, use displacement vector d= (0, 1)

• The GLCM contains information about all pixel pairs that lie at p=(r, c) and

( )cr ∆∆= ,d

( )ccrr ∆+∆+=+ ,dp

11

5554 - Packet 18 - Page 21

• The GLCM is defined as

where M is the number of different pixel pairs in the image(based on displacement vector d), and is the number of times that

and

( )���

�

�

���

�

�

=�

�

ijM ajiC 1,

( ) jccrrI =∆+∆+ ,( ) icrI =,ija

5554 - Packet 18 - Page 22

Simple GLCM example

������

�

�

������

�

�

2332022321322103320033110

Original image

201

3200420012100221

3210

⋅

����

�

�

����

�

�

GLCM C(i, j), using d=(0, 1)

3210i =

j =

12

5554 - Packet 18 - Page 23

Compute the GLCM for each of the 3 images shown below.Use displacement vector d = (0, 1)

5554 - Packet 18 - Page 24

Some observations

• If the original image has randomly distributed intensity values, then the GLCM is will tend to have a constant value (1/M) in every cell

• But if the original image has pixel pairs that correspond to the chosen displacement vector, then the GLCM will contain a large "spike"

• An image with coarse texture will tend to have large valuesalong the diagonal of the GLCM,whereas fine texture will often cause values to spread out from the diagonal

13

5554 - Packet 18 - Page 25

Texture measures based on the GLCM

• Energy

• Entropy

• Contrast

• Homogeneity

• etc.

( ) ( )��−i j

jiCjiC ,log,

( )��i j

jiC ,2

( ) ( )�� −i j

jiCji ,2

( )�� −+i j ji

jiC1

,

5554 - Packet 18 - Page 26

• Notice that the GLCM is not necessarily symmetric• Suppose we wish to consider these 2 cases as being

equivalent

• The symmetric GLCM is defined as

( ) ( ) ( )[ ]dd −+= jiCjiCjiCs ,,, 21

( ) ( )[ ]dd jiCjiC T ,,21 +=

a

b a

b

14

5554 - Packet 18 - Page 27

Structural texture analysis

• For statistical texture analysis, we simply used pixel values as the texture elements

• For a higher-level structural texture analysis, the usual approach is to detect texture elements, and then try to find a compact description of their spatial distribution

• Structural analysis is difficult, and is a topic of on-going research

5554 - Packet 18 - Page 28

Shape from texture

• Consider the following situation

• It seems that we should be able to extract information about the orientation of the flat object by analyzing the image texture

15

5554 - Packet 18 - Page 29

Examples

5554 - Packet 18 - Page 30

16

5554 - Packet 18 - Page 31

5554 - Packet 18 - Page 32

Shape from texture: the basic idea

• Identify texture elements ("texels")• If they lie on a regular grid, then

– Fit lines through the texel centers (possibly using the Hough transform)

– Locate vanishing points in the image– Calculate surface orientation using the vanishing points

• If they do not lie on a grid, then– Compute a "texture gradient" (which indicates the direction and

rate of change of a texel parameter, such as size)– Estimate the surface orientation using the texture gradient

(a greater rate of change suggests a surface that is more steeply inclined with respect to the camera)

17

5554 - Packet 18 - Page 33

Summary

• Visual texture is an important aspect of image analysis• Several statistical texture measures have been defined

(but none of them is perfect)– Image histograms are very common for many image-analysis

tasks – GLCMs are commonly used to characterize texture

• Structural texture measures seem like a good idea, and research is in progress in this area

• Shape from texture is also an important research area