Background

In this section, we will introduce several basic theorems [3] for color image segmentation. For segmentation of color images, the techniques can roughly be categorized into the following four classes [4]: (1) histogram thresholding approaches; (2) edge based approaches; (3) region based approaches; and (4) physics based approaches. A segmentation method may be one of them or a combination of two or more of the mentioned classes.

(1) Histogram thresholding is one of the widely used techniques for monochrome image segmentation [5]. It assumes that images are composed of regions with different gray level ranges. The histogram of an image can be separated into a number of peaks, each corresponding to one region, and there exists a threshold value corresponding to valley between the two adjacent peaks. Gray level thresholding is the simplest segmentation process.

Chapter 1. Introduction

Many objects or image regions are characterized by constant reflectivity or light absorption of their surface. A threshold can be determined to segment objects and background.

Thresholding is computationally inexpensive and fast. It is the oldest segmentation method and is still widely used in simple applications. It can easily be implemented in real time. A

Complete segmentation can result from thresholding in simple scenes. Thresholding is the transformation of an input image f to an output segmented binary image g as follows:

g( i, j) = 1 for f( i, j) ≧ T

g( i, j) = 0 for f( i, j) < T (1.2)

where T is the threshold, g( i, j) = 1 for image elements of objects, and g( i, j) = 0 for image elements of the background. The basic thresholding algorithm is shown below:

Basic thresholding algorithm:

Search all the pixels f( i, j) of the image f. An image element g( i, j) of the segmented image is an object pixel if f( i, j) ≧ T, and is a background pixel otherwise.

If objects do not overlap each other, and if their gray-levels are clearly distinct from background gray levels, thresholding is a suitable segmentation method. There are many thresholding algorithms. How to choose a proper threshold is shown in detail in [6]. As for color images, the situation is different from monochrome image because of multi-features.

Multiple histogram thresholding divided color space by thresholding each component histogram. Since the color information is represented by tristimulus R, G, and B color space or their linear or nonlinear transformations, representing the histogram of a color image in a 3-dimensional array and selecting threshold in this histogram is not a trivial job [7]. The advantage of a histogram thresholding technique is that it does not need a priori information

Chapter 1. Introduction

of the image. One of the disadvantages of the histogram-based technique is it can’t guarantee that regions are continuous if it does not consider the spatial details. This problem can be solved by a combination of a histogram-based method and other segmentation methods [8].

(2) Edge based detection is another approach to image segmentation. It is extensively utilized for gray level image segmentation which is based on the detection of discontinuity in gray level trying to locate points with abrupt changes in gray level. Edge detection techniques are usually classified into two categories: sequential and parallel [2] [9]. A parallel edge detection technique means that the decision of whether or not a set of points are on an edge is not dependent on whether other sets of points lie on an edge or not. One technique is high emphasis spatial frequency filtering. Since high spatial frequencies are associated with sharp changes in intensity, one can enhance or extract edges by performing high pass filtering using the Fourier operator. The problem here is how to design a relevant filter. There are many types of parallel differential operators such as Roberts, Sobel, and Prewitt operators which are called the first-difference operators, and the Laplacian operator is called the second-difference operator. The main differences between these operators are the weights assigned to each element of the mask. These operators require that there is a distinct change in gray level between two adjacent points and only very abrupt edges between two regions could be detected. They cannot detect ill-defined edges that are formed by a gradual change in gray level across the edge. Since the computation is based on a small window, the result is quiet susceptible to noises. The noise may cause an edge presence in locations where there is no border and no edge presence where a real border exists. Sequential edge detection means that the result at a point is dependent on the result of the previously examined points. There are a number of sequential techniques utilizing heuristic search and dynamic programming. The performance of a sequential edge detection algorithm will depend on the choice of a good initial point and it is not easy to define a termination criterion.

In a monochrome image, edge is defined as a discontinuity in the gray level and can be

Chapter 1. Introduction

detected only when there is a difference of the brightness between two regions. However, in color images, the information about edge is richer than in monochrome case. For example, edges between two objects with the same brightness but different hue can be detected in color images [10]. So an edge should be defined by a discontinuity in a three-dimensional color space in a color image. There are three alternatives for the definition of a color edge [11]: (i) Define a metric distance in some color space and use discontinuities in the distance to determine edges. This makes color edge detection still be performed in 1-D space. Hence the result cannot be expected to be better than that achieved by edge detection in an equivalent monochrome image. (ii) Regard a color image as composed of three monochrome images formed by the three color components, respectively, and perform gray level edge detection on these three images separately. Then the edges detected in the three images might be merged by some specified procedures. This is still essentially a gray level edge detection technique and may be unsatisfactory in some cases, for example, when gradient edge detectors are employed, the three gradients for one pixel may have the same strength but in opposite directions [12] [13]. (iii) Impose some uniformity constraints on the edges in the three color components to utilize all of the three color components simultaneously, but allow the edges in the three color components to be largely independent. Actually, these constraints directly affect the computation of the three color components which makes definition (iii) essentially different from definition (ii).

However, edge based detection for image segmentation has difficulties because it does not work well with images in which the edges are ill-defined or where there are too many edges, and it is difficult to link edges into closed boundaries. It can only provide useful information about the region boundaries for the higher level systems. It is possible to obtain a good segmentation result with other approaches, such as region based segmentation combine with edge detection to complete the segmentation tasks.

(3) Region based approaches including region growing, region splitting, region merging

Chapter 1. Introduction

and their combination attempt to separate regions on the basis of a homogeneity predicate defined on groups of connected pixels [14]. The regions must satisfy the following conditions:

( )_i

H R =TRUE i = 1, 2, …, S ( _{i j})

H R



where S is the total number of regions in an image and H(Ri) is a homogeneity evaluation of the region Ri. Resulting regions of the segmented image must be homogeneous. Homogeneity is an important property of regions, and is used as the main segmentation criterion in region based approaches, whose basic idea is to divide an image into zones of maximum homogeneity. The criteria for homogeneity can be based on gray level, color, texture, and etc.

In the region growing approach, a seed region is first selected then expanded to include all homogeneous neighbors and this process is repeated until all pixels in the image are classified.

Region growing techniques are generally better in noise images where borders are extremely difficult to detect. A problem with region growing is its inherent dependence on the selection of the seed region and the order in which pixels and regions are examined. In the region splitting approach, the initial seed region is simply the whole image. If the seed region is not homogeneous, it is usually divided into four squared sub-regions which become new seed regions. This process is repeated until all sub-regions are homogeneous. The major disadvantage of region splitting is that the resulting image tends to mimic the data structure used to represent the image and comes out too square. The region merging approaches are often combined with region growing or region splitting to merge the similar regions for making a homogeneous region as large as possible. These techniques work best on images with an obvious homogeneity criterion and tend to be less sensitive to noise because homogeneity is typically determined statistically. They are better than thresholding by taking into account both feature space and the spatial relation between pixels simultaneously.

However, all region based approaches are by nature sequential, and another problem with

Chapter 1. Introduction

these techniques is their inherent dependence on the selection of seed region and the order in which pixels and regions are examined. The other disadvantage is that they are more expensive in computing time. But the region based approach is widely used in color image segmentation because it considers the color information and spatial details at the same time. It is a quiet strong point.

(4) Physics based segmentation approaches aim at solving this problem by employing physical models to locate the objects’ boundaries while eliminating the spurious edges of shadow or highlights in a color image. Two models, the “dichromatic reflection model” [15]

and the “approximate color-reflectance model (ACRM)” [16] are the most common ones.

Reflection is highly related to the nature of the materials. Reference [16] divided materials into different classes: optically homogeneous materials like metals, glass and crystals, and optically inhomogeneous materials such as plastics, paper, textiles and paints. Usually it is very helpful to identify or classify the material in the scene of an image before the algorithm is applied. For example, we should distinguish metals from dielectrics since they interact with lights in different ways and require different algorithms for image understanding. Reference [15] created a method to determine the amount of interface reflection and body reflection in a color image pixel by pixel and represented an algorithm for analyzing color values which is very useful in color image understanding based on “dichromatic reflection model.” “ACRM”

[16] demonstrated the independence of the spectral composition and geometrical scaling of the light reflected. This model is consistent with dichromatic reflection model when the materials are inhomogeneous dielectrics.

The existing physics based models are efficient only in image processing for the materials whose reflection properties are know and easy to model. There are too many rigid assumptions of these physics models regarding the material type, the light sources and illumination. These conditions may not be satisfied in the real world. Therefore, these models can be used only in a very limited scope of applications. The comparisons of these

Chapter 1. Introduction

Chapter 1. Introduction separating regions in color image. Some disadvantages of one technique can be overcome by the advantages of other techniques. So if we combine several techniques together properly, maybe we can get a better segmentation result. In this thesis, we combine several segmented method like clustering method for smoothing, which is pre-processing stage of a region based approach, relaxation labeling for region assignment of the pixels, and addition to proper color space to get the better results. In our case, the outcome of a relaxation step can be viewed as a

Chapter 1. Introduction

relaxation of the constraint of the triangle inequality which is much different from classical probabilistic relaxation schemes. The computation complexity of the proposed algorithm is lower than those of other methods.