Oct 25, 1984 - T.L. HUNTSBERGER, C. L. JAcoas and R. L. CANNON. No ..... L. JACOBS received a B.S. degree in Biology in 1972 from Mary Washington.
Pattern Ret~alnirion Vol. 18. No. 2, pp. 131 131¢, 1985. Printed in Great Britain.
I;I)31 3203 X5 S3(I0+ 00 Pergamon Press Lid. ( IttS5 I);Itlt'll) Recoglllii~m ~;,~.'l¢l)
ITERATIVE FUZZY IMAGE SEGMENTATION T. L. HtlNI:';III!R(;I!R,C. L. JAt'()Ils and R. L. CANNON Intelligent Systems Laboratory, Department of Computer Science, University of South Carblina, Columbia, SC 29208, U.S.A. (Receited 24 Au~.lust 1984; receired for publication 25 October 1984)
Abstract--The multispectral signature of features has been used for identification of objects in remotely sensed scenes for a number of years. Recently these techniques have been applied to feature selection in natural scenes. Due to the inherent noise and degradation of the input cues to the algorithms, meaningful image segmentation is a difficult process. In an effort to reduce the sensitivity of a system to these problems, we have been led to the development of a iterative fuzzy clustering technique for image segmentation. It is believed that this method represents an image segmentation scheme which can be used as a preprocessor for a multivalued logic based computer vision system. Image processing
Pattern recognition
Image segmentation
I. I N T R O D U C T I O N
The multispectral characteristics of remotely sensed objects are routinely used for image segmentation purposes. (1"2) Recently these remote sensing techniques have been applied to the analysis of natural color scenes, o 5) Image segmentation in an unsupervised environment tends to be noisy and objects sometimes lose their boundaries. Since these effects cause errors in segmentation when compared with a hand segmented image, anot.her study compared various techniques as to their ability for error reduction in supervised image segmentation. (6) The probabilistic approach (see Eklundh et al. (6)) gave the best results. It is based on the assignment of class 'probabilities' to each pixel combined with a relaxation technique. (7) There are primarily three classes of image segmentation techniques. (s) These include characteristic feature thresholding and clustering, edge detection, and region growing. Whereas thresholding, clustering and region growing segment using similarities of the pixels within regions, edge detection is usually reliant upon discontinuities between regions. Edge models tend to be operators in local neighborhoods of the image. A more global view of the data can be maintained using similarities between measurements in the feature space of the image. However, choice of the optimal feature space for distinct clusters needed for meaningful segmentation is quite difficult. (9.~°) The technique generally employed is to perform image segmentation using a variety of feature spaces, the optimal features being those giving the best segmentation for the image.(5, t t. ~2) Recently, there has been an increasing use of fuzzy set theory and fuzzy algorithms for image processing applications. "-~ ~x) This is motivated by a desire to model the ambiguity and noise contained in digitally defined images.
Fuzzy clustering
This paper presents an iterative algorithm for image segmentation, based on clustering in an image feature space. If the clustering in feature space is done with a fuzzy cluster, such as the fuzzy c-means algorithm, (9) non-uniformity of the characteristics of regions can be included in the initial image segmentation process. Such a technique allows the generation of a detailed feature space view of the original image without the bias introduced by a hard segmentation. (t9) The next section reviews the details of the fuzzy cmeans algorithm. (9) The following section discusses adaptation of the algorithm for image segmentation, which involves the inclusion of methods for iterative processing of an image. This is followed by the application of the approach to a natural color scene using various color feature spaces. A final section discusses the results of these experiments. 2. F U Z Z Y C - M E A N S A L G O R I T H M
The fuzzy ISODATA or fuzzy c-means algorithm was initially developed by Dunn (2°) and generalized by Bezdek. tg) Fuzzy c-means uses iterative optimization ofan objective function based on a weighted similarity measure between the pixels in the image and each ofc cluster centers. Local extrema of this objective function are indicative of an 'optimal' clustering of the input data. The objective function is defined as
J.(u,
(l) k=l i=l
where/~ik is the fuzzy membership value of pixel k in cluster center i and dik is any inner product induced norm metric. In contrast to hard clustering, the fuzzy membership value ranges from 0 to 1. The exponent m varies the nature of the clustering, ranging from 131
132
T.L. HUNTSBERGER,C. L. JAcoas and R. L. CANNON
j
¢ InitioLize portit.ion
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I Set x,m,_,L, aLph__o,#uncl, rem J
J Compute k cluster centers
Obtaintestset set
Compute distances
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k - _x
I
I
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I Compute singles
! Compute k J aLpha-cores 8 J classify, se't #uncLJ
1
JC°mputea I new partition
No No
o+
No
Yes I Fig. 1. Block diagram of iterative fuzzy image segmentation algorithm. absolute 'hard' clustering at m = 1 to increasingly fuzzier clustering as m increases. Since the image is analyzed in terms of pixels with multiple attributes in feature space, U is the fuzzy c-partition of the image over the set v of c cluster centers treated as vectors. The fuzzy c-means algorithm relies on the appropriate choices of U and v to minimize the objective function given above. This can be accomplished using the algorithm given below.(v) 1. Fix the number ofclusters c, 2 < c < n, where n = number of data items. Fix m, 1 < m < ~ . Choose any inner product induced norm metric II* II. 2. Initialize the fuzzy c-partition, U co). 3. A t s t e p b , b - - 0 , 1 , 2 . . . . : ~.,(b)~ with U °) and 4. Calculate the c cluster centers ~,~ the formula: cluster center for cluster i =
~ (~,k)"xk v+ = k =l~,
k=l
(2)
5. Update U°): calculate the memberships in U
