A fuzzy approach to texture segmentation - IEEE Xplore

A Fuzzy Approach to Texture Segmentation Madasu Hanmandlu

Vamsi Krishna Madasu

Shantaram Vasikarla

Dept. of Electrical Engineering, I.I.T. Delhi, New Delhi-110016, India. [email protected]

School of ITEE, University of Queensland, QLD 4072, Australia. [email protected]

IT Department, American InterContinental University, Los Angeles, CA90066,USA [email protected]

Abstract: The texture segmentation techniques are diversified by the existence of several approaches. In this paper, we propose fuzzy features for the segmentation of texture image. For this purpose, a membership function is constructed to represent the effect of the neighboring pixels on the current pixel in a window. Using these membership function values, we find a feature by weighted average method for the current pixel. This is repeated for all pixels in the window treating each time one pixel as the current pixel. Using these fuzzy based features, we derive three descriptors such as maximum, entropy, and energy for each window. To segment the texture image, the modified mountain clustering that is unsupervised and Fuzzy C-means clustering have been used. The performance of the proposed features is compared with that of fractal features.

Voss [15] have pointed out that different textures may have the same fractal dimension (FD). This may be due to combined differences in coarseness and directionality (dominant orientation and degree of anisotropy). The spectral approach is the transform domain approach that is used to detect global periodicity in an image by finding high energy, narrow peaks in the spectrum. This approach is not popular due to high computational cost. However, a combination of spectral and spatial approaches such as Gabor filters [7], and wavelet transform [8] are becoming popular.

1. Introduction

In this paper, we present a fuzzy approach for the characterization of texture. This approach is spurred by the fact that a Texel has an ambiguity in the spatial arrangement of gray levels of pixels. Moreover, all the pixels do not have the same property and there is uncertainty in the property as well. Here, we explore the possibility of using interaction type model to evolve texture features. Next, these features are utilized to cluster the image. We will use modified mountain clustering [10, 16] and fuzzy C-means clustering [9].

Image segmentation is the process of grouping homogeneous pixels into one region. The homogeneity of the image pixels can be characterized by the spatial arrangement of the gray levels. An image has inherent fuzziness in the gray levels over spatial regions. We use fuzzy logic framework to derive texture features for segmenting the image such that each segment contains a similar texture distinct from its neighbors.

The organization of this paper is as follows: Section 2 gives the extraction of fuzzy features and Section 3 gives the descriptors. Section 4 deals with the clustering of texture image on the basis of these features using both modified mountain clustering and fuzzy C-means clustering techniques. Results of clustering are presented in Section 5 on different texture images. Finally, conclusions are given in Section 6.

Texture features can be based on the three approaches: (1) Statistical approach (2) Structural approach and (3) Spectral approach. In statistical approach, moments of different order in a localized window represent smooth, coarse, grainy, etc. textures [1], co-occurrence statistics can also be used [2], [3]. In structural approach, spatial structure descriptors are used to identify geometric primitives and their arrangement in an image. Some techniques using this approach are: local interaction models like auto regressive moving average model [4], the Gauss - Markov random field model [5] and the fractal model [6]. Mandelbrot and Van Ness [14] and

2. Extraction of Fuzzy Features

Keywords: Texture, fractal dimension, modified mountain clustering, potential, validity, segmentation.

Here, the spatial arrangement of gray levels over a window is considered. The choice of the window size is made such that the texture pattern or texel must exist in the window. Since we do not know a priori how the gray levels are distributed to form texture, we need to consider each pixel with its relative response over all the neighboring pixels in the specified window. A membership function to this effect is defined by the Gaussian type function.

Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC’04) 0-7695-2108-8/04 $ 20.00 © 2004 IEEE

P j (i )

ª x( j ) x(i ) ½ 2 º exp « ® ¾ » b ¿ »¼ «¬ ¯

where (1)

x(i ) for i

j

(2)

That is, response is maximum if the gray level of current pixel is treated as that of the neighboring pixel. Next, we obtain the cumulative response of the current pixel by the weighted sum method. This is defined by n

y (i )

¦ j 1

P j (i ) x(i ) n

¦P

j

gives the strongest response of the pixel.

Descriptor 2: Entropy

where x(i) is the gray level of current pixel with respect to which gray levels of all the neighboring pixels x(j) are compared and b is the fuzzifier which is taken to be the size of the window. Note that

P j (i ) 1 when x( j )

Dij is the element in matrix D . This descriptor

w

f2

(5)

i 1 j 1

This descriptor is a measure of randomness present in the neighborhood of current pixel. It also gives the information content as mentioned above. A high value of f2 indicates that all elements of D are equal.

Descriptor 3: Uniformity; this is the lowest when all elements of D are equal. It is computed as: w

(3)

w

¦¦ Dij2

f3

w

¦¦ D

2 ij

(6)

i 1 j 1

(i )

j 1

The effectiveness of the above descriptors in the segmentation will be ascertained after clustering.

This is the defuzzified response of the current pixel. This process is repeated for all pixels in the window, giving rise to a texture subimage consisting of defuzzified values. If the image is of size MxM, it is partitioned into sub images of size wxw where w 0 , 1@ .

on

overlapping

windows

of

size

(2W 1) u (2W 1) . Thus, at point (i, j ) the first feature value F1 (i, j ) is defined as F1 (i, j )

FD^(i l ), ( j k )`

g min av 2 and L2

wdl,k d w

(A.4) where FD is the fractal dimension. Since 2 d F1 (i, j ) d 3 , we define the normalized

We take images smoothed in their horizontal and vertical direction and compute their FD as the fourth and the fifth feature. Horizontally and vertically smoothed versions of the image are defined as:

I 4 (i, j )

w 1 ¦ I (i, j k ) (2w 1) k w

Features 2-3: Consider two modified images called

I 5 (i, j )

w 1 ¦ I (i k , j ) (2w 1) k w

as

f1 (i, j )

F1 (i, j ) 2

so

0 d f1 (i, j ) d 1 . the high and low gray-valued images I2 and I3 respectively, defined as

I 2 (i, j )

I 3 (i, j )

I 1 (i, j ) L1 if I 1 (i, j ) ! L1 0 otherwise

255 L1

(A.5)

Table 1. Fuzzy Feature Range Feature 1 0.3320-0.9922 0.3516-0.9961 0.6484-0.9961 0.6172-0.9961

Feature 2 0.0-0.5201 0.0-0.4856 0.0-0.5787 0.0-0.2847

Feature 3 0.0-0.6890 0.0-0.8250 0.0-0.2270 0.0-0.6584

Table 2. Intermediate Values for 4-Texture Image

Potential (P) 1.0e+019* Cluster Center (C) d Separation Compactness Validity (S)

Texture 1 -9.979 0.3555 0.4688 0.0084 0.2569 0.1202

(A.7)

(A.8)

The normalized FD features f4 and f5 are computed from I 4 and I 5 respectively.

if I 1 (i, j ) ! (255 L2 )

Texture 1 Texture 2 Texture 3 Texture 4

g max av 2

roughness and hence by the gray value smoothing. For a highly oriented texture, the FD will be affected least if the texture is smoothed along the direction of its dominant orientation. But if the smoothing direction is perpendicular, the FD will be substantially reduced.

that

feature

(A.6)

Features 4-5: The FD of an image is related to its

Feature 1: The FD of the original image I1 is computed

where L1

otherwise

while gmax, gmin and av denote the maximum, minimum and the average gray value in I1, respectively. If two images have the same FD, their high gray-valued images do not have an identical roughness and their FDs would be different. The normalized features f2 and f3 are computed from I2 and I3 .

the original image the high gray-valued image the low gray-valued image the horizontally smoothed image the vertically smoothed image

For any feature value

I 1 (i, j )

Texture 2 -7.3597 0.9922 1.3468 1.10E-03 0.2641 0.914

Texture 3 -9.6867 0.6094 0.6248 1.58E-04 0.3469 8.5839


Texture 4 -9.9712 0.5923 0.7571 0.1084 0.3105 0.0112

Fig. 1

Fig. 2

Fig. 4

Fig. 5

Fig.7

Fig.9


Fig. 3

Fig. 6

Fig.8

Fig.10