Separation of overlapping dental arch objects using digital records of illuminated plaster casts
 Mohammadreza Yadollahi^{1},
 Aleš Procházka^{1, 4}Email author,
 Magdaléna Kašparová^{1, 2},
 Oldřich Vyšata^{1, 3} and
 Vladimír Mařík^{4}
https://doi.org/10.1186/s1293801500669
© Yadollahi et al. 2015
Received: 7 February 2015
Accepted: 29 June 2015
Published: 11 July 2015
Abstract
Background
Plaster casts of individual patients are important for orthodontic specialists during the treatment process and their analysis is still a standard diagnostical tool. But the growing capabilities of information technology enable their replacement by digital models obtained by complex scanning systems.
Method
This paper presents the possibility of using a digital camera as a simple instrument to obtain the set of digital images for analysis and evaluation of the treatment using appropriate mathematical tools of image processing. The methods studied in this paper include the segmentation of overlapping dental bodies and the use of different illumination sources to increase the reliability of the separation process. The circular Hough transform, region growing with multiple seed points, and the convex hull detection method are applied to the segmentation of orthodontic plaster cast images to identify dental arch objects and their sizes.
Results
The proposed algorithm presents the methodology of improving the accuracy of segmentation of dental arch components using combined illumination sources. Dental arch parameters and distances between the canines and premolars for different segmentation methods were used as a measure to compare the results obtained.
Conclusion
A new method of segmentation of overlapping dental arch components using digital records of illuminated plaster casts provides information with the precision required for orthodontic treatment. The distance between corresponding teeth was evaluated with a mean error of 1.38% and the Dice similarity coefficient of the evaluated dental bodies boundaries reached 0.9436 with a false positive rate \(FPR=0.0381\) and false negative rate \(FNR=0.0728\).
Keywords
Background
In the fields of orthodontics and dentofacial orthopaedics, the optimal timing with regard to the patient’s age and skeletal maturity is just as important as identification of the most appropriate treatment process. Depending on his or her actual age, it is critical to identify the growth periods that provide an opportunity to correct the existing dentofacial irregularities while minimizing the potential risks of the orthopedics intervention using dental arch analysis. Multidisciplinary dental care [1] and therapy requires close collaboration between the different medical specialists and professionals, including the surgeon, orthodontist, and prosthodontist.
Although dental casts have been used for diagnosis and treatment planning [2, 3] in various fields of dentistry for a long time, the digitalization of plaster casts gives the opportunity for their better analysis, enhancement and classification. Digital models, unlike traditional dental casts, allow sharing the models with other specialists during the therapy and treatment [4] and eliminating the challenges related to their storage and transfer. Application of computer science and digital technologies, such as digital data acquisition, virtual models, computed tomography, and video image processing [5], help in the diagnosis and treatment of orthodontic patients and in surgery as well. Digital data can be further improved by the study of their evolution by registration methods in selected regions of interest.
Digital data acquisition
For more than a century, traditional film radiographs were used at most dental clinics before digital dental radiography was firstly introduced [11] in the late 1980s. The traditional film radiography has been replaced by digital dental radiography as it has more advantages, such as clinical accuracy, better resolution, reduced radiation exposure of the patient, easy storage, communication and transfer of data.
Devices for the digital imaging of dental casts include 3D scanners, 3D printers, and digital cameras in general. For the purpose of this paper, the 2D digital images of a standard plaster cast were acquired by a digital camera using different directions of illumination sources to obtain images with different shadow sizes related to the shape of the plaster cast.
The experimental environment included the camera placed at a fixed position above the observed orthodontic plaster cast. The source of illumination was installed at the side of the plaster cast to obtain an image with a shadow and reflection to improve the location of the boundary of the object. Instead of using a single image, a series of images was acquired and combined for the following segmentation process. The location of the illumination source was defined by its azimuth (\(\varphi\)) and its elevation (\(\theta\)) angle and a symmetric kind of illumination was selected. The illumination angles were selected experimentally to produce different shadows of the object. A digital camera using a CMOS sensor was used to obtain the set of greylevel images \({\mathbf{A}}_i(\varphi _i,\theta _i)\), \(i=1,2, \ldots\) as a function of the illumination source position [16]. Figure 1 displays selected images obtained.
Combination of the images acquired with the different side illuminations was used to improve the contours of the separate orthodontic plaster cast objects. The proposed method combined four greyscale images obtained for the left, right and two top illuminations for further processing. Identical images acquired with the lefthand side and righthand side illumination were divided into two parts using the central vertical axis. The combination of the separated subimages formed two new images having outside and central illumination. The two images illuminated from the top were multiplied pixel by pixel to form one output image. The resulting combined image was then obtained after the pixel by pixel mutliplication of all these images. Figure 2 illustrates the entire process of image combination.
For further image analysis, the quality of the image needs to be improved by digital signal processing tools, including digital filters to remove blurring, to increase the contrast, and to achieve higher accuracy in the separation of the image components.
Methods of orthodontic data processing
Figure 3 presents the proposed methodology that consists of (a) image acquisition using different kinds of illumination and data fusion, (b) image processing including its denoising and the use of Hough transform for detection of individual objects, (c) segmentation based on the region growing method followed by local segmentation and object separation, and (d) estimation of dental arch parameters.
Image denoising
Image denoising, representing an important concept in image processing, is one of the main tools for the enhancement of (orthodontic) image quality. The noise of the image negatively affects the quality of the image, changing the true greylevel values of each its pixel. Such noise can be caused by a number of factors, including image acquisition conditions, illumination level, positioning of illumination sources, and scene environment.
The initial analysis of the image noise components allows designing the appropriate filter to reduce the noise and to keep the desired information. Noise components of the digital camera (using CCD or CMOS sensors) can be classified into two main categories: the fixed pattern noise caused by sensor nonuniformities and temporal noise. Temporal noise is a nonideality noise in an image sensor which varies randomly over time. In fact, this type of noise varies from frame to frame and is independent across pixels. The sources of noise related to the camera include photon shot noise, dark current, readout noise, reset noise, and quantization noise.
The Wiener filter was applied as a type of lowpass filter [17] that adapts itself to the local image variance. It allows better smoothing results in case the variance is small owing to statistics estimating the local mean and variance around each pixel. The Wiener filter is especially suitable for reducing speckle, Poisson, and Gaussian noise.
Object detection by the circular Hough transform
The determination of the curvature and location of circular objects in an (orthodontic) image are important tasks [20] in machine intelligence, computer vision, and image analysis [21].
The circular Hough transform used in the present paper obtains satisfactory results in the detection of circle patterns within an image [22] in noisy environments. It transforms the feature points in the image space into the Hough space. In this paper, the circular Hough transform of the Tao Peng algorithm is used. It is is based on the gradient field with an input orthodontic greyscale image. The proposed algorithm operates without any loop [23], which makes its operation faster but consumes more memory. The proposed algorithm runs with a specified range of radii (minimum to maximum) to be detected in the orthodontic image and with a threshold for the greylevel gradient.
Image segmentation using region growing
The segmentation [24–26] of an (orthodontic) image can be performed [27] employing different characteristics, which results in the identification of the boundary or region of interest related to an object. Main approaches to image segmentation include: threshold techniques, boundary based methods, region based methods, and hybrid techniques that combine boundary and region criteria [28].
The proposed algorithm is based upon the region growing method using multiple seed points for segmentation of orthodontic images based on partitioning of an image into regions [28–30] using the properties of the image pixels and their distribution. The application of specific preprocessing techniques prior to the regionbased method usually improves the results and makes them more reliable. The regionbased method clusters similar pixels into a region by taking into account the neighbourhood of each pixel according to selected properties or certain characteristics, including texture, colour or intensity [31].
Pixels that have similar properties form a region and are grouped together. The purpose of image segmentation [32] is to divide the whole image \({\mathbf{A}}=\{a(i,j)\}_{i,j=1}^{M,N}\) into Q connected subregions \({\mathbf{R}}_{1},\,{\mathbf{R}}_{2},\ldots,{\mathbf{R}}_{Q}\) covering the whole image, which means that \(\bigcup _{k=1}^{Q} {\mathbf{R}}_{k}={\mathbf {A}}\) and \({\mathbf{{R}}}_{k}\bigcap {\mathbf{{R}}}_{l}=\) Ø for all \(k \ne l.\)
The region growing method is initiated with the appropriate selection of a set of seed points. When there exists a priori information about the image properties, such starting points can be defined directly. Otherwise, selected properties should be evaluated for each pixel and after the initial clustering process, seeds can be defined in the centroids of the obtained clusters. The growing starts from the initial seed points and using predefined criteria makes it possible to group pixels with similar properties into larger regions.
The iteration process of the regiongrowing method can be stopped in case all pixels are distributed into regions according to the predefined criteria but some additional conditions can be added, such as region sizes or their shapes. According to the threshold values selected and the sensitivity, the extracted region may grow over the actual region boundary. The suitable selection of seed points, stopping rules, thresholding, and sensitivity [33] are very important for the efficiency of the whole process. Where the borders of the object are extremely difficult to detect, the result of segmentation by region growing is often very satisfactory [34].
Detection of image components
The region growing method applied to one object results in several subareas. Their merging can be done using computational geometry and detection of a convex hull \(C({\mathbf{Z}})\) of an object \(\mathbf{Z}\) [35, 36] composed of T components in twodimensional space. The associated morphology algorithm can then be used to define the convex hull by \(C({\mathbf{Z}})=\bigcup _{k=1}^{T} {\mathbf{R}}_{k}\) where \({\mathbf{R}}_k\) is the kth convex hull component for \(k=1,2,\ldots,T\).
The separation of two connected neighbouring regions when their common boundaries were removed during data processing is an important issue in image analysis and machine vision applications. The identifying of a common boundary between two regions or two overlapping objects is usually challenging, as one segment is incorrectly detected by the segmentation process. Several studies and algorithms [37] have been developed to overcome this problem using different methods, including watersheds, the Otsu method, and adaptive thresholding, for the separation of two overlapping objects. Among these methods, watersheds and their modifications are methods commonly used, although for complex areas, watersheds often result in oversegmentation.

Application of a number of morphological operators, such as dilation performed for boundary extraction, filling the holes to remove unwanted regions in the binary image, and shrinking for reducing the objects on the boundary to a single point. Dilation aims to expand objects in a binary image [40] where the pixels of the objects are expanded to neighbouring pixels. The magnitude of the enlargement of the objects is controlled by different shapes [41] and values as structuring elements.

The application of boundary tracing of two connected neighbouring regions and smoothing of the traced boundary by a moving average filter. In the binary image, the foreground pixels are labelled by ‘one’ and the background pixels are labelled by ‘zero’ [42] so that in the boundary tracing, the pixels of the foreground are detected.

Calculation of the second derivative at each point on the smoothed boundary of two connected neighbouring regions.

Determination of specific zones that contain the intersection points of two connected regions based on the second derivative that are situated inside of the object.

Evaluation of the absolute extreme of the two zones obtained in the previous step which will mark the position of the intersection points of the two connected regions.
The proposed methodology
 1.
Image acquisition with the proposed illumination strategy and fusion of image matrices obtained;
 2.
Wiener and median filtering of image data to reduce their noise components;
 3.
The use of circular Hough transform to apply local segmentation for individual teeth;
 4.
Application of the region growing method with multiple seed points to find boundaries of individual subimages provided by the circular Hough transform;
 5.
Merging of corresponding subareas using computational geometry and convex hull regions to separate overlapping objects as well;
 6.
Evaluation of dental arch parameters and measures using centers of mass of individual objects detected by the previous segmentation process.
Results
Figure 5 shows the fundamental steps of the complete algorithm for dental arch analysis. In Figure 5a it is possible to see the application of the circular Hough transform for the original image to crop the image to subimages for feeding to the region growing method applying multiple seed points in Figure 5b. The result of the convex hull method used to merge the regions resulting from the region growing method for a selected object is displayed in Figure 5c. Figure 5d, e show segmentation results for the whole dental arch.
Figure 6 presents a comparison of the dental arch segments obtained by the proposed process and the boundaries of real objects, in order to numerically evaluate the results.

Sensitivity as the truepositive rate of the correct positive classification in the positive set$$\begin{aligned} TPR=\frac{TP}{TP+FN}; \end{aligned}$$(4)

Specificity as the truenegative rate of the correct negative classification in the negative set$$\begin{aligned} TNR=\frac{TN}{FP+TN}; \end{aligned}$$(5)

Probabilities of false classifications in the positive set (falsenegative rate) and negative set (falsepositive rate)$$\begin{aligned} FNR&= \frac{FN}{TP+FN}, \end{aligned}$$(6)$$\begin{aligned} FPR= \frac{FP}{FP+TN}; \end{aligned}$$(7)

Accuracy as the measure of correct classification$$\begin{aligned} Accuracy=\frac{TP+TN}{TP+TN+FP+FN}; \end{aligned}$$(8)

Jaccard similarity index and Dice coefficient$$\begin{aligned} JaccInd= \frac{TP}{FP+TP+FN}, \end{aligned}$$(9)used to evaluate set agreements and the results of the segmentation process [46–48] with their values inside the range [0, 1] and individual coefficients close to one for a complete correspondence between evaluated and real object boundaries.$$\begin{aligned} DiceCoef= \frac{2\;\;TP}{(FP+TP)+(TP+FN)}; \end{aligned}$$(10)
Evaluation of the proposed segmentation by the Jaccard similarity index and Dice coefficient showing their largest values in italics
Similarity measures  

Jaccard  Dice  Accuracy  FPR  FNR  
Teeth rightside  
1R  0.9330  0.9653  0.9993  0.0627  0.0086 
2R  0.9211  0.9589  0.9994  0.0649  0.0192 
3R  0.9606  0.9799  0.9996  0.0285  0.0120 
4R  0.9344  0.9661  0.9994  0.0512  0.0178 
5R  0.9466  0.9726  0.9989  0.0363  0.0190 
6R  0.9217  0.9593  0.9986  0.0308  0.0499 
7R  0.8933  0.9436  0.9988  0.0198  0.0891 
Teeth leftside  
1L  0.8786  0.9354  0.9998  0.0611  0.0677 
2L  0.8224  0.9025  0.9998  0.0146  0.1656 
3L  0.7285  0.8429  0.9974  0.0654  0.2238 
4L  0.8360  0.9106  0.9983  0.0455  0.1261 
5L  0.8593  0.9243  0.9971  0.0427  0.1040 
6L  0.8964  0.9454  0.9983  0.0248  0.0813 
7L  0.8986  0.9466  0.9990  0.0309  0.0737 
Similarity measures evaluated for the whole dental arch include the Jaccard index \(JaccInd=0.8931\) and Dice coefficient \(DiceCoef=0.9436\) and \(Accuracy=0.9828.\) Regions incorrectly classified are represented by the false positive rate \(FPR=0.0381\) and false negative rate \(FNR=0.0728.\)
Distances (mm) between mass centres of symmetric regions for manual and proposed segmentation
Distances (mm)  Error  

Manual seg.  Proposed seg.  mm  %  
Teeth number  
11  32.68  32.14  0.54  1.65 
22  85.86  84.69  1.17  1.36 
33  124.15  121.38  2.77  2.23 
44  147.82  145.39  2.43  1.64 
55  168.63  166.44  2.19  1.30 
66  206.01  203.77  2.24  1.09 
77  227.72  226.87  0.85  0.37 
Conclusion
This paper presented an innovative approach to the segmentation of orthodontic plaster cast images. The proposed method is based on processing the image constructed from separate images acquired with different illumination sources reflecting different edges of the object. The combined image with its increased contrast and enhanced object boundaries is then used for the detection of separate object.
The results of segmentation of a digital image of the orthodontic plaster cast by the method proposed in this paper show that the convex hull followed by the separation of two connected objects form effective complementary techniques to improve the segmentation by the region growing method.
The illumination from different sides highlights shadows of the object, converting each region into several subregions: hence, region growing, based on the application of multiple seed points, is a suitable tool to extract individual bodies. However, the method (1) does not produce satisfactory results in the common boundary of two regions that have similar properties and (2) the identified subregions related to the same region are not always recognized as one region.
The final evaluation of the segmentation process points to the efficiency of the proposed method with a Dice similarity coefficient of 0.9436 and a mean error of real and estimated distances between corresponding teeth of 1.38%.
Further studies will be devoted to further more sophisticated methods based upon threedimensional convex hulls, used for the separation of individual bodies, as well as to a more detailed analysis of the shapes of the separate dental arch components.
Declarations
Authors’ contributions
The paper presents results of the close interdisciplinary collaboration of three research groups. Authors from the Department of Paediatric Stomatology of the Second Medical Faculty of Charles University were responsible for data acquisition resulting from their own medical treatment and for correct interpretation of results. Authors from the Department of Computing and Control Engineering of the University of Chemistry and Technology and from the Neurological Department of Charles University belonging to the Digital Signal and Image Processing Research Group were responsible for mathematical analysis of biomedical data and their statistical evaluation. Authors from the Czech Institute of Informatics, Robotics and Cybernetics contributed to the methodological part of the study. All authors read and approved the final manuscript.
Acknowledgements
Real orthodontic data were kindly provided by the Department of Paediatric Stomatology of the Second Medical Faculty of Charles University in Prague, Czech Republic. The authors would like to thank all the patients who signed the informed consent to participate in the project approved by the local ethics committee.
Compliance with ethical guidelines
Competing interests The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
 Opheij DG, Opdebeeck H, Steenberghe DV, Quirynen M. Age as compromising factor for implant insertion. Periodontol. 2003;2000(33):172–84.View ArticleGoogle Scholar
 Kasparova M, Grafova L, Dvorak P, Dostalova T, Prochazka A, Eliasova H, et al. Possibility of reconstruction of dental plaster cast from 3D digital study models. Biomed Eng Online. 2013;12(49):1–11.Google Scholar
 Kasparova M, Prochazka A, Grafova L, Yadollahi M, Vysata O, Dostalova T. Evaluation of dental morphometrics during the orthodontic treatment. Biomed Eng Online. 2014;13:1–13.View ArticleGoogle Scholar
 Keating AP, Knox J, Bibb R, Zhurov AI. A comparison of plaster, digital and reconstructed study model accuracy. J Orthod. 2008;35(3):191–201.View ArticleGoogle Scholar
 Ogodescu AS, Sinescu C, Ogodescu EA, Negrutiu M, Bratu E. Digital tools in the interdisciplinary orthodontic treatment of adult patients. NAUN Int J Biol Biomed Eng. 2010;4(3):97–105.Google Scholar
 Chang YB, Xia JJ, Gateno J, Xiong Z, Zhou X, Wong STC. An automatic and robust algorithm of reestablishment of digital dental occlusion. IEEE Trans Med Imaging. 2010;29(9):1652–63.View ArticleGoogle Scholar
 Yaqi M, Zhongke L. Computer aided orthodontics treatment by virtual segmentation and adjustment. In: International conference on image analysis and signal processing (IASP); 2010. pp. 336–39.Google Scholar
 Chapuis J, Schramm A, Pappas I, Hallermann W, SchwenzerZimmerer K, Langlotz F, et al. A new system for computeraided preoperative planning and intraoperative navigation during corrective jaw surgery. IEEE Trans Inf Technol Biomed. 2007;11(3):274–87.View ArticleGoogle Scholar
 Yadollahi M, Prochazka A, Kasparova M, Vysata O. The use of combined illumination in segmentation of orthodontic bodies. Signal Image Video Process. 2015;9(1):243–50 (Springer).View ArticleGoogle Scholar
 Yamamoto K, Hayashi S, Nishikawa H, Nakamura S, Mikami T. Measurements of dental cast profile and threedimensional tooth movement during orthodontic treatment. IEEE Trans Biomed Eng. 1991;38(4):360–5.View ArticleGoogle Scholar
 Bansal GJ. Digital radiography. A comparison with modern conventional imaging. Med J. 2006;82:425–8.Google Scholar
 Kavalcova L, Skaba R, Kyncl A, Rouskova B, Prochazka A. The diagnostic value of MRI fistulogram and MRI distal colostogram in patients with anorectal malformations. J Pediatr Surg. 2013;48(8):1806–9.View ArticleGoogle Scholar
 Harrell WE, Hatcher DC, Bolt RL. In search of anatomic truth: 3dimensional digital modeling and the future of orthodontics. Am J Orthod Dentofac Orthop. 2002;122(3):325–30.View ArticleGoogle Scholar
 Tomaka A, Tarnawski M, Luchowski L, LisniewskaMachorowska B. Digital dental models and 3D patient photographs registration for orthodontic documentation and diagnostic purposes. In: Kurzynski M, Puchala E, Wozniak M, Zolnierek A, editors. Computer recognition systems 2. Advances in soft computing. New York: Springer; 2007.Google Scholar
 Singh GD. Digital diagnostics: threedimensional modelling. Br J Oral Maxillofac Surg. 2008;46(1):22–6.View ArticleGoogle Scholar
 Lindner C, León FP. Modelbased segmentation of surfaces using illumination series. IEEE Trans Instrum Meas. 2007;56(4):1340–6.View ArticleGoogle Scholar
 Shinde B, Dani AR. Noise detection and removal filtering techniques in medical images. Int J Eng Res Appl. 2012;2(4):311–6.Google Scholar
 Suganthi A, Senthilmurugan M. Comparative study of various impulse noise reduction techniques. Int J Eng Res Appl. 2013;3(5):1302–6.Google Scholar
 Teoh SH, Ibrahim H. Median filtering frameworks for reducing impulse noise from grayscale digital images: a literature survey. Int J Future Comput Commun. 2012;1(4):323–7.View ArticleGoogle Scholar
 Rizon M, Yazid H, Saad P, Shakaff AYM, Saad AR, Sugisaka M. Object detection using circular Hough transform. Am J Appl Sci (2). 2005;2(12):1606–9.View ArticleGoogle Scholar
 Jain L, Mahor D. Application of Hough transform for finding parametric curves. Int J Comput Appl Eng Sci. 2011;1(2):100–3.Google Scholar
 Nitasha SS, Sharma R. Comparison between circular Hough transform and modified cCanny edge detection algorithm for circle detection. Int J Eng Res Technol (IJERT). 2012;1(3):15.Google Scholar
 Ghadiri F, Pourreza H, Banaee T, Delgir M. Retinal vessel tortuosity evaluation via circular Hough transform. In: 18th Iranian conference on biomedical engineering, Tehran, Iran. IEEE; 2011. pp. 181–184.Google Scholar
 Stanescu A, Burdescu DD. Medical image segmentation—a comparison of two algorithms. In: International conference on medical measurements and applications proceedings. IEEE; 2010Google Scholar
 Adams R, Bischof L. Seeded region growing. Int J Pattern Recognit Lett. 1994;16(6):641–7.Google Scholar
 Jung C, Liu J, Sun T, Jiao L, Shen Y. Automatic image segmentation using constraint learning and propagation. Digit Signal Process. 2014;24:106–16 (Elsevier).View ArticleGoogle Scholar
 Iscan Z, Yuksel A, Dokur Z, Korurek M, Olmez T. Medical image segmentation with transform and moment based features and incremental supervised neural network. Digit Signal Process. 2009;19(5):890–901 (Elsevier).View ArticleGoogle Scholar
 Gonzales RC, Woods RE, Eddins SL. Digital image processing using MATLAB. Upper Saddle River, New Jersey: Pearson Education, Inc.; 2004.Google Scholar
 Ansari MA, Anand RS. Region based segmentation and image analysis with application to medical imaging. In: IETUK international conference on information and communication technology in electrical sciences, Dr. M.G.R. University, Chennai, Tamil Nadu, India; 2007. pp. 724–729.Google Scholar
 Kunte A, Bhalchandra A. Effective region based segmentation technique for high resolution aerial imagery. In: Fifth international conference on image and graphics, Xi’an, Shanxi. IEEE; 2009. pp. 272–275.Google Scholar
 Praveena SM, IlaVennila D. Optimization fusion approach for image segmentation using kmeans algorithm. Int J Comput Appl. 2010;2(7):18–25.Google Scholar
 Zhu SC, Yuille A. Region competition: unifying snakes, region growing, and Bayes/MOL for multiband image segmentation. Int J Pattern Anal Mach Intell. 1996;18(9):884–900.View ArticleGoogle Scholar
 Kaganami HG, Beiji Z. Regionbased segmentation versus edge detection. In: Fifth international conference on intelligent information hiding and multimedia signal processing, Kyoto. IEEE; 2009. pp. 1217–1221.Google Scholar
 Srinivasan GN, Shobha G. Segmentation techniques for ATDR. NAUN Int J Comput. 2008;2(9):165–71.Google Scholar
 Böhm C, Kriegel HP. Determining the convex hull in large multidimensional databases, vol. 2114. In: International conference on data warehousing and knowledge discovery. Munich: Springer; 2001. pp. 294–306.Google Scholar
 Nagabhushana S. Computer vision and image processing. New York: New Age International; 2009.Google Scholar
 Xia R, Wang P, Zhang W, Xiong Q. A novel overlapping mice macrophages images segmentation method. In: International conference on image analysis and signal processing, Linhai. IEEE; 2009. pp. 40–43.Google Scholar
 Yang J, Li X. Boundary detection using mathematical morphology. Pattern Recognit Lett. 1995;16(12):1277–86.View ArticleGoogle Scholar
 Stein SC, Schoeler M, Papon J, Worgotter F. Object partitioning using local convexity. In: Conference on computer vision and pattern recognition. IEEE, Columbus; 2014.Google Scholar
 Hafizah WM, Soh JZE, Supriyanto E, Nooh SM. Automatic classification of muscle condition based on ultrasound image morphological differences. Int J Biol Biomed Eng. 2012;6(1):87–96.Google Scholar
 Zhang XQ, Yang K, Baoqing H. Celledge detection method based on canny algorithm and mathematical morphology. In: International congress on image and signal processing CISP2010. IEEE, Yantai; 2010.Google Scholar
 Kim D, Uk CJ, Cong PT, Wook JJ. Realtime object boundary tracing circuit based on FPGA. In: International conference on control, automation and systems, Seoul. IEEE; 2007. pp. 2307–2312.Google Scholar
 Fawcett T. An introduction to ROC analysis. Pattern Recognit Lett. 2006;27:861–74.View ArticleGoogle Scholar
 Byrd KA, Zeng J, Chouikha M. A validation model for segmentation algorithms of digital mammography images. J Appl Sci Eng Technol. 2007;1:41–50.Google Scholar
 Prochazka A, Vysata O, Tupa O, Yadollahi M, Valis M. Discrimination of axonal neuropathy using sensitivity and specificity statistical measures. Neural Comput Appl. 2014;25(6):1349–58 (Springer).View ArticleGoogle Scholar
 Shattuck DW, Prasad G, Mirza M, Narr KL, Toga AW. Online resource for validation of brain segmentation methods. NeuroImage. 2009;45(2):431–9 (Elsevier).View ArticleGoogle Scholar
 Chao A, Chazdon RL, Colwell RK, Shen TJ. A new statistical approach for assessing similarity of species composition with incidence and abundance data. Ecol Lett. 2005;8:148–59.View ArticleGoogle Scholar
 Zou KH, Warfield SK, Bharatha A, Tempany CMC, Kaus MR, Haker SJ, Wells WM, Jolesz FA, Kikinis R. Statistical validation of image segmentation quality based on a spatial overlap index. Acad Radiol. 2004;11(2):178–89.View ArticleGoogle Scholar