TEXTURE

I.)

In this Assignment, we focus on texture analysis using Co-occurrence matrices. We investigate features extracted from the matrices, as possible characterization of the textures:

Part I - coding co-occurrence m-function

Code a Matlab function that calculates the co-occurrence matrix:

Building the co-occurrence matrix P is done by computing for each pair of gray-levels (usually 0-255), the number of adjecent pixels that hold this pair in the image, for different directions and distances.

For image of size MxN, for distance d=1pixel, in the horizontal direction, the co-occurrence matrix P will be defined as follows:

where i,j=0. . . 255, (number of possible gray-levels), k,m=1 . . . M (image width), l,n=1 . . . N (image height).
 
 

Input arguments:

A two dimensional matrix X, containing the gray-level values of an image.

The distance d for the co-occurrence calculations.

Output argument:

A 256*256 co-occurrence matrix P, summed on all directions.
 
 

Part II - Building Feature space for a training set

• Open the four texture-types from the given Brodatz texture images (image01, image02, image03, image04).
• Create five samples, 50*50 pixels (by dividing each image to four), from each selected texture-type, to create a training set.
• Apply your m-file on the twenty samples, to calculate their co-occurrence matrices.
• Pick two (or three) texture-features from the following list, or suggest your own.

 
where  are the co-occurrence matrix entries, ,  is the mean gray-level, and  is the gray-level variance.

• Plot the feature-vectors of each one of the twenty samples, in feature space (Feature1 vs. Feature2). Is there a visible clustering? Discuss.

• Create a table of mean and standard deviation for each texture-type, for the two selected features.

• Open the test image, "test.bmp". Calculate the same two or three features for the test image and determine its Euclidean distance from each of the twenty samples of the training set.
• Sort the distances by proximity order. To which tissue type does "test.bmp" belong?

II.)

   A. Obtain the gray-level co-occurrence matrix (GLCM)  of a 5 x 5 image of
        alternating 1’s and 0’s. Top left pixel has a value 0.
       (a) d = 1 pixel to the right
       (b) d = 2 pixels to the right.

    B.  Explain the following observation:

•         For a coarse texture with large elements the co-occurrence matrix has large values on the diagonal.
•         For a fine texture the co-occurrence matrix is more spread out.

I.)   (a)   Show that redefining the starting point of a chain code so that the resulting  sequence of numbers
        forms an integer of minimum magnitude makes the code independent of the initial starting point on the boundary.
        (b)   Find the normalized starting point of the code 11076765543322.
        (c) Show that the first difference of a chain code normalizes it to rotation.
        (d) Compute the 1st difference of the code 0101030303323232212111.
 

II.)     Find the Euler number of the characters: 0, 1, 8, 9, X.