Map Segmentation by Colour Cube
Genetic K-Mean Clustering
Vitorino Ramos, Fernando Muge
CVRM - IST Geo-Systems Center, Instituto Superior Técnico,
Avenida Rovisco Pais, 1049-001, Lisboa, Portugal
{vitorino.ramos,muge}@alfa.ist.utl.pt
http://alfa.ist.utl.pt/~cvrm
Abstract. Segmentation of a colour image composed of different kinds of texture regions can be a
hard problem, namely to compute for an exact texture fields and a decision of the optimum number of
segmentation areas in an image when it contains similar and/or unstationary texture fields. In this
work, a method is described for evolving adaptive procedures for these problems. In many real world
applications data clustering constitutes a fundamental issue whenever behavioural or feature domains
can be mapped into topological domains. We formulate the segmentation problem upon such images
as an optimisation problem and adopt evolutionary strategy of Genetic Algorithms for the clustering
of small regions in colour feature space. The present approach uses k-Means unsupervised clustering
methods into Genetic Algorithms, namely for guiding this last Evolutionary Algorithm in his search
for finding the optimal or sub-optimal data partition, task that as we know, requires a non-trivial
search because of its intrinsic NP-complete nature. To solve this task, the appropriate genetic coding
is also discussed, since this is a key aspect in the implementation. Our purpose is to demonstrate the
efficiency of Genetic Algorithms to automatic and unsupervised texture segmentation. Some
examples in Colour Maps are presented and overall results discussed.
1 Introduction
Image segmentation is a low-level image processing task that aims at partitioning an image into
homogeneous regions [11]. How region homogeneity is defined depends on the application. A great
number of segmentation methods are available in the literature to segment images according to various
criteria such as for example grey level, colour, or texture. This task is hard and as we know very
important, since the output of an image segmentation algorithm can be fed as input to higher-level
processing tasks, such as model-based object recognition systems. Recently, researchers have investigated
the application of genetic algorithms (GA, [13,8,15]) into the image segmentation problem. Perhaps the
most extensive and detailed work on GAs within image segmentation is that of Bhanu and Lee [3]. Many
general pattern recognition applications of this particular paradigm can also be found in [16]. One reason
(among others) for using this kind of approach is mainly related with the GA ability to deal with large,
complex search spaces in situations where only minimum knowledge is available about the objective
function. For example, most existing image segmentation algorithms have many parameters that need to
be adjusted. The corresponding search space is in many situations, quite large and there are complex
interactions among parameters, namely if we are seeking to solve colour image segmentation problems.
For instance, this led Bhanu et al. [3] to adopt a GA to determine the parameter set that optimise the
output of an existing segmentation algorithm under various conditions of image acquisition. That was the
case for the optimisation of the Phoenix segmentation algorithm [22], by genetic algorithms,
implementation described also by Bhanu [4]. Another situation wherein GAs may be useful tools is
illustrated by the work of Yoshimura and Oe [23]. In their work, the two authors formulated the
segmentation problem upon textured images as an optimisation problem, and adopt GAs for the clustering
of small regions in a feature space, using also Kohonen’s self-organising maps (SOM). They divided the
original image into many small rectangular regions and extracted texture features from the data in each
small region by using the two-dimensional autoregressive model (2D-AR), fractal dimension, mean and
variance. In other example, Bhandarkar et al. [2] defined a multi-term cost function, which is minimised
using a GA-evolved edge configuration. The idea was to solve medical image problems, namely edge-
detection. In their approach to image segmentation, edge detection is cast as the problem of minimising
an objective cost function over the space of all possible edge configurations and a population of edge
images is evolved using specialised operators. Results comparable with those obtained using simulated
annealing are reported. Fuzzy GA fitness functions were also considered by Chun and Yang [7], mapping

a region-based segmentation onto the binary string representing an individual, and evolving a population
of possible segmentations.Other implementations include the search of optimal descriptors to represent
3D structures [10], or the optimisation of parameters in GA hybrid systems [17] - in this last case, for
finding the appropriate parameters of recurrent neural networks to segment echocardiographic images.
GA applications within elastic-contour models are also possible to find. Cagnoni et al. [6] develop a GA
based on a small set of manually-traced contours of the structure of interest (anatomical structures in 3D
medical data sets). As putted by the authors, the method combines the good trade-off between simplicity
and versatility offered by polynomial filters with the regularisation properties that characterise elastic-
contour models. Another very interesting work, is that one of Andrey [1]. The image to be segmented is
considered as an artificial environment wherein regions with different characteristics according to the
segmentation criterion are as many ecological niches. A GA is then used to evolve a population of
chromosomes that are distributed all over this environment. Each chromosome belongs to one out of a
number of distinct species. The GA-driven evolution leads distinct species to spread over different niches.
Consequently, the distribution of the various species at the end of the run unravels the location of the
homogeneous regions on the original image. Because the segmentation progressively emerges as a by-
product of a relaxation process [9] mainly driven by selection, the method has been called selectionist
relaxation. In model designing terms, this last approach is indeed very close to that one presented by
Ramos and Almeida in [20], using artificial ant colonies. Approaches based on Koza’s genetic
programming paradigm (GP, [14]), i.e., genetic algorithms used for finding appropriate algorithm
structures and strategies, were also applied in image segmentation. Poli’s GP work [18], is perhaps one of
the most interesting to follow, due to is simplicity. Finally, a fairly comprehensive review of other GA
approaches in image processing is available in [5] - references include, animation, classification, feature
extraction, filtering, image analysis, image processing, pattern recognition and naturally, image
segmentation.
(a) (b) (c) (d)
Fig. 1 - (a) Original Luanda (Angola) Colour Map [500x500 pixels] and (b) the respective 1st colour cluster
segmenting train networks (in black), names (in black and dark brown), and parks (in dark green) pointed by the GA;
(c) 2nd colour cluster - sea and rivers (blue); (d) Roads and buildings (red) and topological levels (brown). Other
examples not shown here, reflect darker borders (red, black and brown) and background (whiter regions).
2 Genetic Clustering in Image Segmentation
As putted by Andrey, whether the GA is used to search in the parameter space of an existing segmentation
algorithm [4], or in the space of candidate segmentations [2], an objective fitness function, assigning a
score to each segmentation, has to be specified in both cases. However, evaluating a segmentation result
is itself a difficult task. To date, no standard evaluation method prevails [25], and different measures may
yield distinct rankings [24] (as an aside note, the present authors are nowadays developing image noise
measures by mathematical morphology [21], allowing for instance, his use in image filtering design by
GAs). One possible criterion is to think of homogeneous regions as the result of any appropriate and
optimised clustering process, within the image feature space. Applications of GAs in clustering and
grouping problems are intensively described in [12]. In the present approach, grey level intensities of
RGB image channels are considered as feature vectors, and the k-mean clustering model (J.MacQueen,
1967) is then applied as a quantitative criterion (or GA objective fitness function), for guiding the
evolutionary algorithm in his appropriate search. Since the k-mean clustering model allows to minimise
the internal feature variance of each colour cluster (or the maximisation of the variances between different
colour clusters [19]), natural and homogeneous clusters can emerge if the GA is properly coded. In other
words, the image segmentation problem is simply reformulated as an unsupervised clustering problem,