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- Publisher
- Taylor & Francis
- Copyright
- © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
- ISSN
- 2469-9322
- DOI
- 10.1080/24699322.2018.1560100
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Abstract
COMPUTER ASSISTED SURGERY 2019, VOL. 24, NO. S1, 53–61 https://doi.org/10.1080/24699322.2018.1560100 RESEARCH ARTICLE A novel technique for analysing histogram equalized medical images using superpixels a,b a Li Yao and Sohail Muhammad a b School of Computer Science and Engineering, Southeast University, Nanjing, P.R. China; Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, Nanjing, P.R. China KEYWORDS ABSTRACT SLIC; Superpixel; Quick shift; We present a novel technique to distinguish between an original image and its histogram Watersheds; Felzenszwalb; equalized version. Histogram equalization and superpixel segmentation such as SLIC (simple lin- AHE; CLAHE ear iterative clustering) are very popular image processing tools. Based on these two concepts, we introduce a method for finding whether an image (grayscale) is histogram equalized or not. Because sometimes we see images that look visually similar but they are actually processed or changed by some image enhancement process such as histogram equalization. We can merely infer whether the image is dark, bright or has a small dynamic range. Moreover, we also com- pare the result of SLIC superpixels with three other superpixel segmentation algorithms namely, quick shift, watersheds, and Felzenszwalb’s segmentation algorithm 1. Introduction on the histogram approach, for the enhancement of medical images using Gaussian Mixture Modeling Histogram equalization is an image enhancement GMM. Chen et al. [6] used SLIC superpixels to elimin- method used in image processing. Histogram equaliza- ate the effect of constructed defects and noise by tion techniques are used for contrast enhancement in means of the feature similarity in the preprocess- a wide range of image types ranging from general, ing stage. medical to satellite images. There are numerous varia- Medical image analysis is a broad field and provides tions of histogram equalization but in essence, they a forum for a lot of research in the medical and bio- are divided into global and local histogram equaliza- logical research areas. There are different techniques tion. The algorithm proposed in [1] uses Gaussian available for the analysis of medical images. Machine Mixture Model to model the gray level distribution of learning (ML) approaches are successful in image- images. Moreover, the intersection points of the based diagnosis, disease prognosis, and risk assess- Gaussian model are used to model the dynamic range ment, such as Machine Learning for medical image of the images into input gray level intervals. Eunsung analysis [7], the semiotics of image segmentation [8] Lee et al. [2] proposed a method to compute bright- and machine learning approaches in medical image ness-adaptive intensity transfer functions by using the analysis from detection to diagnosis [9]. E. Goceri et al. low-frequency luminance component in the wavelet [10] have done a comprehensive survey on recent domain and transforms intensity values according to advances and future trends of Deep Learning (DL) in the transfer function. medical image analysis and stated that segmentation Automatic transformation is a method that is the most common technique applied in medical improves the brightness of dim images via the gamma image analysis using deep learning. Moreover [11], has correction and probability distribution of luminance discussed state-of-the-art methods for brain tissue pixels. It also works very well for videos [3]. segmentation like manual, region-based, thresholding- Segmentation algorithms are widely used for the seg- mentation of medical images [4], proposed a method based, clustering-based, and feature extraction meth- for the medical image segmentation using watershed ods. A comprehensive review is done by [12] algorithms. Moreover [5], describes a method based about the medical image segmentation on GPUs CONTACT Li Yao yao.li@seu.edu.cn School of Computer Science and Engineering, Southeast University, Nanjing, P.R. China. 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 54 L. YAO AND S. MUHAMMAD (Graphical Processing Unit). The image processing and for a given image X and intensity X , p(X ), is k k visualization time are greatly reduced by using given by: GPU platforms. pXðÞ ¼ ; for k ¼ 0; 1; .. . ; L1 (2) In this paper, firstly, we make use of two techni- ques to equalize the histograms of low contrast gray- Whereas, N equals the total number of samples or scale images and then we use four superpixel pixels and n is the number of times k-th gray level algorithms to segment the histogram-equalized appears in the image. If we compare Equations (1) images into superpixels. Finally, we extract the super- and (2) then it is clear that PDF is a normalized histo- pixel segments of the equalized images using four gram. It simply maps the intensities of input images in segmentation algorithms and compare the results. Our such a way that the intensities of output images are results show that SLIC superpixels are compact, grid- spread over the full range of intensities. In order to shaped and equal to the k number of superpixels that achieve this, the Cumulative Distribution Function we extracted before the histogram equalization. We (CDF) of the input image is used as the mapping func- have tested grayscale medical images for experiments. tion. A normalized histogram can be identified as the Figure 1 shows the original image, two histogram probability density function of the random signal. So equalized images, and histograms of each image. The according to the Probability Distribution Function flowchart of the proposed method is shown in (PDF) Equation (2), the Cumulative Distribution Figure 2. Where GHE and CLAHE stands for Global Function (CDF) for an intensity X , c (X ) is defined as: k k Histogram Equalization and Contrast Limited Adaptive Histogram Equalization respectively. Moreover, cXðÞ ¼ for k ¼ 0; 1; .. . ; L 1 (3) Figure 3 illustrates the superpixels of original images as well as a comparison between the superpixels gen- erated before and after histogram equalization. 2.1. Adaptive histogram equalization Subsequent sections of this paper contain a discussion Global histogram equalization does not work effect- of the histogram equalization techniques in section 2, ively for images that contain local regions of low con- a brief introduction of superpixel segmentation algo- trast and bright or dark regions. In this case, local rithms in section 3, our proposed technique in section histogram equalization LHE comes into action. It works 4, comparison of the results of segmentation is shown by taking into account only small regions and based in section 5 and finally, section 6 concludes the paper. on their local CDFs, performs contrast enhancement of those regions. Examples of LHE method include 2. Histogram equalization (HE) Adaptive Histogram Equalization (AHE) [17,18], Contrast Limited Adaptive HE (CLAHE) [17], It is one of the most celebrated techniques of image Interpolated Adaptive HE (IAHE), Weighted Adaptive enhancement since it is simple and produces visually HE (WAHE) [17], Non-Overlapped Block HE (NOBHE) pleasing results out of noisy or dark images. Basic [19], Partially Overlapped Sub-Block HE (POSHE) [20], histogram equalization is called Global Histogram Cascaded Multistep Binomial Filtering HE (CMBFHE) Equalization (GHE) because it does enhancement glo- [21], Fast Local Histogram Specification (FLHS) [22] bally. It is known with different names such as and Conditional Sub-Block Bi-HE (CSBHE) [23]. Pizer Classical HE [13], Traditional HE [14], Conventional HE et al. have defined the AHE using a tiled window with and Typical HE [15]. Suppose that X ¼ {X(i,j)} is a given interpolated mapping in their paper. This method image, which consists of L number of discrete gray enhances the global contrast but at the cost of levels. {X , X , … , X } represents the intensity of the 0 1 L1 enhancing the noise in regions with small inten- image at some spatial location (i,j), assuming that X(i,j) sity range. 2 {X , X , … , X }. 0 1 L1 A discrete function is the histogram of digital image and can be written as: 2.2. Contrast limited adaptive histogram equalization (CLAHE) hXðÞ ¼ n ; f or k ¼ 0; 1; .. . ; L1 (1) k k In order to overcome the noise enhancement artifact where X is the k-th gray level and n denotes the k k of AHE, this method takes one extra step to clip the number of times that gray level (X ) appears in the image. Moreover, as discussed by Wang and Ye [16]in histogram before computing the CDF as a mapping statistical terms it is the probability distribution of function. It also introduces an additional parameter each gray level. The Probability Density Function (PDF) that defines the level where to clip the histogram. COMPUTER ASSISTED SURGERY 55 Figure 1. Original image, global histogram equalized image, CLAHE equalized image, and their respective histograms. (a) Original Image (b) Histogram of Original Image. (c) Global Histogram Image (d) Histogram of GHE Image. (e) CLAHE Image (f) Histogram of CLAHE Image. As explained by the Pizer et al. [17,18], contrast ðÞ Cumulative Histogram i miðÞ ¼ Display Range ðÞ enhancement is also known as the slope of the func- Region Size tion mapping input intensities to the output inten- (4) sities. If we limit the height of the histogram to a specific level, we can infer that we can also limit slope We will make use of global histogram equalization of the CDF mapping function as well as the level of GHE and CLAHE to equalize the histogram of input contrast enhancement. Thus, the mapping image first and then we will perform the superpixel function m(i) is proportional to the cumulative segmentation using four techniques that are discussed histogram. in section 4. Figure 1 shows the original image (a), its 56 L. YAO AND S. MUHAMMAD Figure 2. Flowchart of the proposed method. (a) Segmentation of Original Image. (b) Segmentation of GHE Image. (c) Segmenatation of CLAHE Image. global histogram equalized image (c) and the contrast limited adaptive histogram equalized image (e). The histogram of each image is also shown in Figure 1(b), (d) and (f) respectively. 3. Superpixel segmentation Superpixels are gaining popularity in the various com- puting applications because of their perceptual mean- ingfulness and computational efficiency. They significantly decrease the complexity of certain image processing tasks. Variety of features is available for grouping pixels into superpixels, such as brightness, intensity, texture, contour and good continuation. Superpixels are used in several fields such as image segmentation [24], skeletonization [25], object localiza- tion [26], recognition, image indexing and body model estimation [27]. Each superpixel in an image is a con- sistent unit of similar pixels, such as, similar in color or texture. They are the result of over-segmentation. Figure 3. Comparison of segmentation results using four superpixel segmentation algorithms (a) superpixels of the ori- Broadly speaking, Achanta et. al. [28] categorized ginal image (b) shows the superpixels generated for GHE them into two classes, gradient-ascent based and image and (c) shows the superpixel segments of CLAHE graph-based algorithms. Graph-based algorithm treats image. (a) Input image (b)superpixel segmentation (c) GHE each pixel as a node in a graph, and edge weights (d) CLAHE. between two nodes are set proportional to the similar- ity between pixels, Felzenszwalb’s algorithm is an example of graph-based algorithms. However, gradi- segmentation until convergence is achieved. SLIC, ent-ascent based algorithms start by operating over Quick shift, and Watersheds are of this class. These an initial rough clustering. It is an iterative process algorithms behave differently when an original image where during each iteration new clusters are refined and histogram equalized image is subjected to them, from the previous iteration to obtain better we will make use of all of these four algorithms. COMPUTER ASSISTED SURGERY 57 In this section, we will briefly look into these segmen- taking a color image as input, it takes a grayscale gra- tation algorithms. Since we are not primarily con- dient image, where bright pixels represent boundaries cerned with the number of superpixels, we will not among segments or regions. It obtains watersheds or explicitly control the number of superpixels. lines that separate catchment basins [30]. It takes gray level images as topographic reliefs and each of the reliefs is flooded from its minima. A dam is built when 3.1. Felzenszwalb’s algorithm two lakes merge, the set of all dams define the so- This efficient and fast image segmentation algorithm called watershed. This representation of watersheds proposed by Felzenszwalb, P.F. and Huttenlocher is simulates the natural flooding process [31]. It takes prevalent in the computer vision field. It has only one the input image as a landscape, where bright pixels scaling factor that affects the size of a segment. The form high peaks. Each individual basin ultimately number and actual size of segments may vary signifi- makes a unique segment. Just like SLIC. It is also a sin- cantly, depending on the local contrast of images. gle parameter algorithm but there is another compact- However, it does not provide explicit control over the ness parameter that makes it tougher for markers to number of segments. This algorithm provides segmen- flood faraway pixels. This results in the uniform and tation of both real and synthetic images and widely compact watershed regions or segments. known as a segmentation algorithm rather than a superpixel algorithm. We will see that it works nor- 3.4. SLIC superpixels mally with original as well as histogram equalized images. In general, the input to the graph based algo- The SLIC uses k-means clustering for superpixel gener- rithms is a graph G ¼ (V, E), with n vertices and m ation, which makes it relatively easy and fast. In add- edges [29]. The output is a segmentation of V into ition, by default, k is the lone parameter for setting S ¼ (C ,C , … , C ) components. Dijkstra’s algorithm is the required number of superpixels. Hence, we can 1 2 r used for computing the shortest paths in the undir- control the size indirectly by choosing the appropriate ected graph defined on these grid positions. It has a number of superpixels. SLIC works for both color and complexity of O(NlogN). grayscale images, and this provided us the opportun- ity to use SLIC on grayscale images before and after histogram equalization to test their original and histo- 3.2. Quick shift algorithm gram equalized nature. Most of the superpixel gener- It is a mode seeking two dimensional (2D) algorithm ation methods do not provide explicit control over the used for image segmentation. The algorithm relies on compactness and even the number of superpixels the approximation of kernelized mean-shift. It which we wish to generate. Nevertheless, in SLIC we makes use of the Parzen density estimation. Let us have firm control over the number, size as well as the consider N number of data points denoted as compactness of the superpixels. In this paper, we x ; x ; ... ; x 2 X ¼ R , then a mode-seeking algorithm 1 2 N make use of the compactness parameter to show that like quick shift begins by computing the Parzen dens- superpixels generated for a given image before and ity estimate: after histogram equalization are different for the same compactness parameter setting. We have used the PxðÞ ¼ kxx ; x 2 R (5) ðÞ proposed method on various medical images. i¼1 Moreover, as discussed in section 5, we also show that other superpixel segmentation methods work normally Similar to the SLIC algorithm, quick shift is also without differentiating between original and histo- applied to the 5 D space, which not only consists of gram equalized image. SLIC algorithm [32] is divided image location but also color information. However, into three main steps. First is the initialization step in contrary to SLIC, it cannot control the number or size which clusters are initialized; in the second assignment of superpixels explicitly. One of the advantages of step each pixel is associated with the nearest cluster quick shift algorithm is that it simultaneously com- center if search region overlaps its location. Finally, in putes ordered segmentation on multiple scales. the third step cluster centers are updated to become the mean vector of all the pixels belonging to the 3.3. Watersheds algorithm cluster. Nevertheless, the literature shows that by It makes intelligent use of the watershed transform- selecting small values of the compactness parameter ation and topological gradient approach. Instead of spatially more compact (square shaped) superpixels 58 L. YAO AND S. MUHAMMAD could be obtained. In our method, we select the value image and Figure 3(c) shows the superpixel segmenta- of compactness parameter to be the same for image tions for CLAHE image. As one can clearly see that segmentation before and after equalization. Whereas only SLIC superpixels (Figure 3(b) top left) are compact the number of superpixels k can be selected arbitrar- and uniform if the given image is histogram equalized ily. The resulting superpixels of histogram equalized as compared to the Figure 3(a) top left image which is images will be the same as corresponding superpixels SLIC superpixel segmentation before histogram equal- in the original image. ization. It should be noted here that the shape of superpixels clearly varies even for the same parameter settings of SLIC. The resulting SLIC superpixels in 4. Proposed technique Figure 3(b) and (c) are spatially more compact but In this section, we present the basic steps used for spectrally they are more heterogeneous. Pixels belong- analyzing histogram equalized images(as Figure 2 ing to the same superpixel are of similar nature, it also shown), these steps includes: histogram equalization, simplifies their nature as compared to individual pix- superpixel segmentation and analyzing the histogram els, which we had before histogram equalization. equalized images. Yellow colored lines superimposed on the segmented The flowchart in Figure 2. illustrates the steps used images are called the superpixel boundaries and they in our method. The original grayscale image is input- separate one superpixel or segment from the other. ted to both the superpixel segmentation (SLIC, quick They are shown here in the output image as we are shift, watersheds, and Felzenszwalb) and histogram not interested in the result of image enhancement or equalization (GHE and CLAHE) algorithms for relevant histogram equalization but we want to know the segmentation and equalization respectively. In the nature of images based on superpixels. Without these next step, only histogram equalized images are boundaries, image will look similar to the image again inputted to all four superpixel segmentation obtained after histogram equalization process. algorithms and resultant images are acquired Experiments show that SLIC superpixels for original for comparison. low contrast images are of arbitrary shape. However, At this point, we have four superpixelized images for histogram equalized images it produces compact in Figure 3(a), and four global histogram images with and uniform superpixels. superpixels in Figure 3(b) and four CLAHE images with Moreover, other three algorithms work normally on superpixels as shown in Figure 3(c). In the final stage, both original and histogram equalized images as a comparison is done among original image, global shown in Figure 3. Thus, SLIC superpixels clearly dis- histogram equalized GHE images and adaptive histo- tinguish between an original image and its histogram gram equalized CLAHE images with superpixel seg- equalized version. The comparison is done to show ments. The resultant image is the histogram equalized the robustness of the SLIC superpixels and our tech- image with compact SLIC superpixels. nique. A Quantitative comparison is also shown in Table 1. 5. Comparison In this section, we compare superpixels generated by 5.1. Additional test images four publicly available algorithms, namely, SLIC, Quick With the following experiments, by using different shift, Watersheds and Felzenszwalb. In general, super- images we want to show the performance and effi- pixels are used at a pre-processing stage in vision ciency of the proposed method. Figure 4. shows some applications. In this paper, we have used superpixels of the medical test images and generated results. at post-processing stage. Firstly, the output images Original images are placed in column (a), segmenta- obtained from two histogram equalization processes tion of original images is in column (b) and column (c) i.e. GHE and CLAHE are segmented into superpixels by shows the segmentation of global histogram (GHE) using four segmentation algorithms. Figure 3(a) at images and column (d) shows the segmentation of top-right is the result of SLIC, at top-left is the result CLAHE images. Our proposed method analyses differ- of the quick shift, at bottom-left is the result of Felzenszwalb and figure at bottom-right shows the ent test images and gives satisfactory results to distin- guish between original and histogram equalized superpixels generated by the watersheds algorithm for the original image. Figure 3(b) is the result of super- image. Further, in order to show the robustness of pixel segmentations for globally histogram equalized proposed method, we have tested some additional COMPUTER ASSISTED SURGERY 59 Table 1. Comparison of superpixels. Before HE SLIC Quick shift Felzenszwalb Watershed No. of Superpixels 100 163 195 100 Compactness Non-uniform Non-uniform Non-uniform Non-uniform Parameters 1 2 1 2 After GHE SLIC Quick shift Felzenszwalb Watershed No. of Superpixels 100 186 219 100 Compactness Uniform Non-uniform Non-uniform Non-uniform Parameters 1 2 1 2 After CLAHE SLIC Quick shift Felzenszwalb Watershed No. of Superpixels 100 190 266 100 Compactness Uniform Non-uniform Non-uniform Non-uniform Parameters 1 2 1 2 Figure 4. Some test images: An input image (column (a)), its superpixel segmentation by using four segmentation algorithms (b). Our work is focused on generating superpixel segments of GHE image (c), of CLAHE image (d) and compare their results. 60 L. YAO AND S. MUHAMMAD Table 2. 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Journal
Computer Assisted Surgery – Taylor & Francis
Published: Oct 1, 2019
Keywords: SLIC; Superpixel; Quick shift; Watersheds; Felzenszwalb; AHE; CLAHE