5 Comparison of Two Pixel based Segmentation Algorithms of Color Images by Histogram Dr. Goutam Chatterjee, Professor, Dept of ECE, KPR Institute of Technology, Ghatkesar, Hyderabad, India ABSTRACT The image segmentation techniques are essentially categorized into edge based, region based and pixel based. The experimental and research works in this field have given best results in pixel based image segmentation techniques. The pixel of colour images apart from RGB information; involve hue and intensity, compared to a grey level image. The current paper analyses the two pixel based algorithms involving histograms. The analysis has been carried out on the metrics of performance, segment level, segmentation effect, complexity and ease of utility. The right choice of image segmentation technique would be particularly beneficial for the applications such as MRI scan, satellite imagery, deforestation mapping and water body discovery. Keywords Segmentation; Thresholding; Histogram; Bimodal; Multimodel I. INTRODUCTION An image is partitioned into meaningful regions by an image segmentation process with respect to a particular application. The segmentation process involves measurements taken from the image which might be grey level, colour, texture, depth or motion. To understand an image in its entirety generally image segmentation is an initial and vital step in a series of processes. In many applications, the image segmentation plays a vital role. For example, an object can be identified in a scene for object-based measurements such as size and shape. In another application, objects can be identified in a moving scene for object-based video compression technique like MPEG4. In yet another application, it can also help identification of objects which are at different distances from a sensor using depth measurements from a laser range finder. In this case, path planning may be carried out for mobile robots. In the pixel based image segmentation techniques, the two methods that are commonly employed are thresholding and clustering. However, in this paper we would discuss two methods that are based on Histogram thresholding and Histogram acceptable segmentation techniques. II. METHODOLOGY In the research process, two separate algorithms for Histogram Thresholding and Histogram Acceptable segmentations were developed, tested and compared. Acceptable Segmentation. The aim of the given segmentation was to split the histogram in separated modes. The mode can be defined as an interval on which the histogram follows the increasing hypothesis on a first part and the decreasing hypothesis on the second part. [1] Let us say that a histogram h follows the unimodal hypothesis on the interval [y, z]. If x [y, z] exists such that r follows the increasing hypothesis on [y, x] and r follows the decreasing hypothesis on [x, z] then it may be surmised that such a segmentation exists. Of course, the segmentation defined by all the minima of the histogram as separators would obviously follow the unimodal hypothesis on each segment. Reasonable segmentation can be assumed only if there are no fluctuations, however small they may be. In the next paragraph a procedure is presented that finds segmentation much more reasonable than the segmentation defined by all the minima. The objective is to build a minimal (in terms of numbers of separators) segmentation, which leads us to introduce the notion of acceptable segmentation. Let h be a histogram on {1,...,N}. We will say that segmentation S of h is acceptable if it verifies the following properties: h follows the unimodal hypothesis on each interval [Si, Si+1].
6 There is no interval [Si, S k ] with k > i+1, on which h follows the unimodal hypothesis. The above two stated requirements allow us to avoid under-segmentations and over-segmentations, respectively. It is obvious that in the discrete case such a segmentation exists. Now we can start with the limit segmentation containing all the minima of h and gather the consecutive intervals together until both properties are verified. This is the principle that is used in the next algorithm:- Fine to Coarse (FTC) Segmentation Algorithm. It is explained as given below:- (a) Define the finest segmentation (i.e. the list of all the minima) M = {M1,..., Mn} of the histogram. (b) Repeat: Choose i randomly in [2, length(m) 1]. If the modes on both sides of Mi can be gathered in a single interval [Mi 1, Mi+1] following the unimodal hypothesis, group them. Update M. Stop when no more unions of consecutive intervals follow the unimodal hypothesis. (c) Repeat step 2 with the unions of k intervals, k going from 3 to length (M). Now that the algorithm has been set up and which ensures the construction of an acceptable segmentation, the next section can be devoted to the application of the proposed method to colour image segmentation. Colour Image Segmentation. The FTC algorithm is applied on the hue histogram of a colour image, in order to obtain a first segmentation. By this step, a lot of colour information, contained in the saturation and intensity components, has been lost. Then, the same process is followed by applying the algorithm to the saturation and intensity histograms of each mode obtained previously. For the practical implementation of the algorithm, it must be taken into account that, in the discrete case, a quantization problem appears when we try to assign hue values to quantized colour points in the neighbourhood of the grey axis. A solution to this problem is found by discarding the points that have saturation smaller than Q/2π, where Q is the number of quantized hue values. The stated solution defines a cylinder in the HSI colour space called the grey cylinder, since all the points contained in it will be treated as grey values. [4] The algorithm is described through the following steps:- (a) The FTC algorithm is applied on the hue histogram of the image. Let S g be the obtained segmentation. (b) Each pixel of the grey cylinder is linked to its corresponding interval Sg i = [s gi, s gi +1], according to its hue value. (c) For each i, construct the saturation histogram in respect of all the pixels of the image whose hue belongs to S g i. The pixels of the grey cylinder are not taken in to the account. Apply the FTC algorithm on the corresponding saturation histogram. For each i, let {S g i,i1, S g i,i2,...} be the obtained segmentation. (d) For each i, each pixel of the grey cylinder that belonged to the interval S g i is linked to the lower saturation interval S g i,i1 obtained in the previous segmentation step. (e) The intensity histogram is computed and segmented for each i and each k of all the pixels whose hue and saturation belong to S g i and S g i,ik, including those of the grey cylinder. It may be pointed out that the hue histogram is circular, which means that the hue value 0 0 is identified to the hue value 360 0. Results of Acceptable segmentation. For each experiment, five images are shown. The first one is the original image; the second one pertains to the hue histogram with the realized modes marked with a dashed line between them; the third one is the segmented image after the algorithm has been applied to the hue histogram; the fourth one pertains to the segmented image after the algorithm has been applied to the histograms of hue and saturation; and finally, the segmented image after the algorithm has been applied to the histograms of hue, saturation and intensity. The segmented images are displayed with the different modes represented by the mean values of the hue, saturation and intensity of all the pixels in the mode. Figure-1 is the Orange bug image in which we distinguish three different colours corresponding to different objects: background, leaf and orange bug. After the proposed separation approach has been applied to the hue histogram, the three different modes are obtained that correspond to the three referred objects. It is apparent that the modes are detected independently of their relative number of pixels. The detection depends only on the
7 meaningfulness of the mode, allowing the detection of small objects, as in the present example. The total number of colours in the final segmentation is 11, because of the great variety of shades in the background. Figure-1 (e) Resultant image with 11 colours after hue, saturation and intensity segmentation Figure-1 (a) Original image Orange bug sourced from reference [1] Histogram Thresholding. To explain histogram thresholding, which is a very simple simple image segmentation technique, we take a greylevel histogram of an image. A very simple object-background test image is taken for consideration of a zero, low and high noise image and as shown in Figure-2. Figure-1 (b) Hue histogram with the three obtained modes Figure-2 (a) Noise free image Figure-1 (c) Resultant image with 3 colours after hue segmentation Figure-2 (b) Low noise image Figure-1 (d) Resultant image with 4 colours after hue and saturation segmentation Figure-2 (c) High noise image
8 To characterise low noise and high noise, we can consider the histograms of our images. (a) For the noise free image, it s simply two spikes at i=100, i=150 (b) For the low noise image, there are two clear peaks centred on i=100, i=150 (c) For the high noise image, there is a single peak two greylevel populations corresponding to object and background have merged The input image signal-to-noise ratio can be defined in terms of the mean greylevel value of the object pixels, the background pixels and the additive noise standard deviation as per given formula:- S / N b o For the test images, following values of S/N are assigned:- Thresholding Foundation. Any threshold separates the histogram into 2 groups with each group having its own statistics (mean, variance). The homogeneity of each group is measured by the within group variance.the optimum threshold is that threshold which minimizes the within group variance thus maximizing the homogeneity of each group. Let us consider that the gray-level histogram relates to an image, f(x,y), composed of dark objects in a light background, in such a manner that object and background pixels have gray levels grouped into two dominant modes. One simple method to extract the objects from the background is to select a threshold T that separates these modes. Then any point (x,y) for which f(x,y) > T is called an object point, otherwise, the point is called a background point. An Example is given in Figure-4:-[3][5] S/N (noise free) = S/N (low noise) = 5 S/N (high noise) = 2 h(i) 2500.00 2000.00 1500.00 1000.00 Noise free Low noise 500.00 0.00 0.00 50.00 100.00 150.00 200.00 250.00 High noise Figure-3.Greylevel Histogram Based Segmentation As shown in Figure-3, histograms are constructed by splitting the range of the data into equal-sized heaps (called classes). Then for each heap, the number of points from the data set that fall into each heap is counted. The vertical axis in the figure-3 indicates Frequency (i.e., counts for each heap). The horizontal axis displays the response variable or the pixels. In Matlab, image histograms can be constructed using the imhist command. i Figure-4. Greylevel thresholding The image histogram which is characterized by the two dominant modes, it is called a bimodal histogram and only one threshold is enough for partitioning the image. For example, if an image is composed of two types of light objects on a dark background, three or more dominant modes characterize the image histogram. In such a case the histogram has to be partitioned by multiple thresholds. Multilevel thresholding classifies a point (x,y) as belonging to one of the following classes:- If T1 < (x,y) <= T2, Then (x,y) belong to other object class If f(x,y) > T2 Then (x,y) belong to the background If f(x,y) <= T1. Then (x,y) refers to basic Global Thresholding.
9 Accordingly:- An initial estimate for T is selected. The image is segmented using T. This will produce two groups of pixels. G1 consisting of all pixels with gray level values >T and G2 consisting of pixels with values <=T. The average gray level values mean-a and mean-b are computed for the pixels in regions G1 and G2. A new threshold value is computed T= (1/2) (mean-a +mean-b) The steps 2 through 4 are repeated until difference in T in successive iterations is smaller than a predefined parameter In basic adaptive thresholding, images having uneven illumination make it difficult to segment the image using histogram. Therefore, this approach is adopted to divide the original image into sub images and use the above said thresholding process to each of the sub images. [6] Figure-5 (b) Histograph for colour R In colour images each pixel is characterized by three RGB values therefore, a 3D histogram is constructed, and the similar procedure is used as for one variable. Histograms plotted for each of the colour values and threshold points are found. The objects can be distinguished by assigning a arbitrary pixel value or average pixel value to the regions separated by thresholds. In the experiment following type of images were used: [3][7] (a) Colour image having bimodal histogram structure. (b) Colour image having multi-modal histogram structure. Figure-5 (c) Histograph for colour G Figure-5 (a) Colour Image bimodal Source: reference[3] Figure-5 (d) Histograph for colour B
10 Figure-5 (e) Segmented Image giving the outline of her face, hand etc Figure-6 (c) Histograph for colour G Figure-6 (a) Colour Image- Multimodal Figure-6 (d) Histograph for colour B Figure-6 (e) Segmented Image Figure-6 (b) Histograph for c After segmenting the image, the objects can be extracted using edge detection techniques. Image segmentation techniques are extensively used in Similarity Searches. (IDB)
11 III. COMPARISON OF ALGORITHMS AND RESULTS For each of these algorithms, beside the metrics of performance, segment level, segmentation effect, complexity and ease of utility, we examined three more characteristics:- 1. Correctness that is the ability to produce results that is consistent with ground truth. 2. Stability with respect to parameter choice that is the ability to produce segmentations of consistent correctness for a range of parameter choices. 3. Stability with respect to image choice that is the ability to produce segmentations of consistent correctness using the same parameter choice on a wide range of different images. Comparison Table of Acceptable Segmentation and Thresholding Segmentation Metrics Acceptable Thresholding Performance Good Best Colour Space Gray levels and HSI Images, RGB Image combination of YIQ values and RGB and Grayscale Segment level Discontinuity in Homogeneity Homogeneity Segmentation Effect Good Good Complexity Average Very low Quality Based on measurement intensity variation Table-1. Comparison of algorithms IV. CONCLUSION Based on chosen threshold value There is a need of image segmentation because the quality of images is directly affected by the temperature, noise and pressure. The segmentation depends upon many factors such as pixel colour, intensity, texture, similarity of images and image content. According to the above comparison table, it is apparent that the thresholding segmentation algorithm is superior to the acceptable segmentation algorithm. However, one single algorithm type does not guarantee same kind of result for all type of images so we can choose segmentation techniques that give efficient and accurate performance according to the application requirement. ACKNOWLEDGMENT The photographs of Figure-1 are sourced from reference[1] The photographs of Figure-3 are sourced from reference [3] V. REFERENCES [1] Julie Delon et al, Color Image Segmentation Using Acceptable Histogram Segmentation, Math papers, DDLP_IbPRIA. [2] Dr. Mike Spann, http://www.eee.bham.ac.uk/spannm [3] Senthikumaran N, Vaithegi S, Image Segmentation by using Thresholding Techniques for Medical Images, Computer Science & engineering, An International Journal (CSEIT). 2016; Vol. 6, No. 1, DOI: 10.5121/cseij.2016.6101.CIS 601 [4] Khang Siang Tan and Nor Ashidi Mat Isa, Color image segmentation using histogram thresholding Fuzzy C-means hybrid approach, Elsevier, Volume 44, Issue 1, January 2011, Pages 1 15 [5] Matta S. Review: Various Image Segmentation Techniques, International Journal of Computer Science and Information Technologies (IJCSIT). 2014; Vol. 5 (6), ISSN: 0975-9646. [6] Senthikumaran N, Vaithegi S, Image Segmentation by using Thresholding Techniques for Medical Images, Computer Science & engineering:an International Journal (CSEIT), 2016; Vol. 6, No. 1, DOI: 10.5121/cseij.2016.6101. [7] Pantofaru, C., and Hebert, M.: Comparison of Image Segmentation Algorithms, tech. report CMU-RITR-05-40, Robotics Institute, Carnegie Mellon University, 2005.