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The Classification of HEp-2 Cell Patterns Using Fractal Descriptor Rudan Xu, Yuanyuan Sun*, Member, IEEE, Zhihao Yang, Senior Member, IEEE, Bo Song, and Xiaopeng Hu
Abstract—Indirect immunofluorescence (IIF) with HEp-2 cells is considered as a powerful, sensitive and comprehensive technique for analyzing antinuclear autoantibodies (ANAs). The automatic classification of the HEp-2 cell images from IIF has played an important role in diagnosis. Fractal dimension can be used on the analysis of image representing and also on the property quantification like texture complexity and spatial occupation. In this study, we apply the fractal theory in the application of HEp-2 cell staining pattern classification, utilizing fractal descriptor firstly in the HEp-2 cell pattern classification with the help of morphological descriptor and pixel difference descriptor. The method is applied to the data set of MIVIA and uses the support vector machine (SVM) classifier. Experimental results show that the fractal descriptor combining with morphological descriptor and pixel difference descriptor makes the precisions of six patterns more stable, all above 50%, achieving 67.17% overall accuracy at best with relatively simple feature vectors. Index Terms—Automatic classification, fractal dimension, HEp-2 cells, morphological, pixel difference.
I. INTRODUCTION
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NDIRECT immunofluorescence (IIF) with HEp-2 cells is considered as a powerful, sensitive, and comprehensive technique for analyzing antinuclear autoantibodies (ANAs). To perform the diagnosis approaching to the truth, it has to identify the staining pattern of the samples. Among the many observed staining patterns, six classes are relevant to the diagnostic purpose. They are centromere, coarse speckled, cytoplasmatic, fine speckled, homogeneous, and nucleolar. However, the IIF method has some disadvantages which have bad effect on diagnosis repeatability [1]. The major ones are: the low level of standardization, the interobserver variability, which limits the reproducibility of IIF readings and the lack of resources and adequately trained personnel. Another problem Manuscript received March 30, 2015; accepted March 31, 2015. Date of publication May 21, 2015; date of current version August 05, 2015. This research is supported by the National Natural Science Foundation of China(No. 61103147, 61272373, 61272523), Trans-Century Training Program Foundation for the Talents by the Ministry of Education of China(NCET-13-0084), the National Key Project of Science and Technology of China(No. 2011ZX05039-003-4), Scientific Research Fund of Liaoning Provincial Education Department(No. L2014025), and the Fundamental Research Funds for the Central Universities(No. DUT15QY33) Asterisk indicates corresponding author. R. Xu, Z. Yang, B. Song, and X. Hu are with the College of Computer Science/ Technology, Dalian University of Technology, 116204 Dalian, China. *Y. Sun is with the College of Computer Science and Technology, Dalian University of Technology, CO 116024 Dalian, China (e-mail:
[email protected]. cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TNB.2015.2424243
is the similarity between some abnormal and normal structures, causing the interpretational errors. The standardized evaluation of HEp-2 cell assays by automated interpretation systems can pave the way for reproducible [2]. Computer-aided diagnosis (CAD) system supports the physician's decision and overcome current method limitations. Indeed, pattern recognition technique serves for CAD system effectively in this field. In recent years, much research on HEp-2 cell classification utilizing this technique has been carried out. Ponomarev, Arlazarov, Gelfand, and Kazanov used the difference in number, size, shape, and localization of cell regions for image classification [3]. Nosaka and Fukui presented a novel method for classifying six categories using rotation invariant co-occurrence among local binary patterns by support vector machine (SVM) classifier [4]. Liu and Wang proposed a multi-projection-multi-codebook scheme which creates multiple linear projection descriptors and multiple image representation channels with each channel corresponding to one descriptor [5]. It has been proved that the fractal dimension can be used on the analysis of images representing and also on the properties quantification like texture complexity and spatial occupation. In many works, fractal dimension was used to identify the plant leaf [6], to distinguish breast pathologies [7], to evaluate fractal characteristics of urban landscape [8], and so on. In this study, we try to explore the fractal characteristics of the HEp-2 cell images. To the best of our knowledge, it is the first time that fractal theory is applied to the HEp-2 cell pattern classification. The remainder of the paper is organized as follows: Section II gives a brief statement of the dataset; Section III describes three proposed feature descriptors; the experimental results are reported in Section IV, which is followed by the conclusions II. DATA SET We use the data set from the HEp-2 Cells Classification contest [9] hosted by the International Conference on Pattern Recognition 2012. The dataset is constituted by 28 images, which, as a whole, contain 1457 cells, so divided among the different classes are as follows [10]: • Centromere: this class is characterized by large numbers of strong bright spots on a darker background. In a number of intermediate intensity examples of this class none are visible to the eye, even after contrast normalization. • Coarse speckled: An isotropic texture of somewhat larger specks. • Cytoplasmatic: These nuclei are characterized by a strongly irregular shape, as compared to the generally
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difference between the patterns is the cell texture, we design the feature descriptors without the consideration of the background and only do with the cell image within the mask which is provided in the dataset. A. Fractal Descriptor
Fig. 1. The samples from six classes.
Fractal geometry involves various approaches to define fractal dimension. The most common one in practical applications is the box-counting dimension. In box-counting dimension , an image can be filled with small boxes having sides . When the sides is changed, the number is changed, in other words, the smaller the sides , the greater number of boxes , while the larger the sides , the fewer number of boxes [11]. As the results, the fractal dimension can be calculated by linear approximation. The process of the changing number with the sides r is shown in Fig. 2. The fractal dimension (FD) expression is defined as: (1) In general, however, the proper dimension to use turns out to be the Minkowski-Bouligand dimension as it is based on the correlation between an object interface and the space it occupies. This interfacial/spatial correlation is analyzed based on the circular area the object occupies after successive dilations [11]. The fractal dimension approach can be defined by the following steps: • is the set of sorted Euclidean distances defined by
Fig. 2. The change process of box-counting dimension.
(2) elliptic nature of all other classes. The texture is equally irregular. • Fine speckled: A very fine-grained isotropic texture, not dissimilar to white noise. • Homogeneous: A diffuse pattern, fairly uniform across the whole nucleus. • Nucleolar: A small number (less than 6) of larger bright areas within the nucleus. Fourteen out of the 28 slides are used as the training set. In the training set, the amount of cell images is 721 in which centromere (CE) takes of 208 cell images, coarse speckled (CS) takes of 109 cell images, cytoplasmatic (CY) takes of 58 cell images, fine speckled (FS) takes of 94 cell images, homogeneous (HO) takes of 150 cell images and nucleolar (NU) takes of 102 cell images. The rest images used as testing set is released by MIVIA [1] after the completion of the contest. In the testing set, the amount of cell images is 734 in which CE takes of 149 images, CS takes of 101 images, CY takes of 51 images, FS takes of 114 images, HO takes of 180 images, and NU takes of 139 images. The samples from six classes are shown in Fig. 1. The red curve in Fig. 1 is the outline of the cell. III. FEATURE DESCRIPTORS It can be seen from the cell images that the green channel in all images stands out among the other two channels. In this section, all the discussions are only on the green channel. As the
,
is an element in the set. is the foreground pixels in the image at the coordinates . • is the set of the pixels at the distance.
•
(3) •
, defined by (4), is the set of the influenced pixels after image dilation. (4)
At last, the Minkowski-Bouligand dimension can expressed as: (5) where is the number of dimensions of the space. For 2-D space, is 2, and for 3-D space, is 3. Tables I and II [6] are the distance maps of influence area for two binary images. The zero points in the maps are the interest points. From the above two tables, it can be seen that the influence area will be greatly different even to a little variation of the position.
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TABLE I EXAMPLE OF INFLUENCE AREA CALCULATION FOR A BINARY IMAGE. CELLS MARKED WITH ZERO CORRESPOND TO POINTS OF THE IMAGE. THE VALUE OF SOME INFLUENCE AREA FA(R) ACCORDING TO RADIUS R:
TABLE II EXAMPLE OF INFLUENCE AREA CALCULATION FOR A BINARY IMAGE. CELLS MARKED WITH ZERO CORRESPOND TO POINTS OF THE IMAGE. THE VALUE OF SOME INFLUENCE AREA FA(R) ACCORDING TO RADIUS R:
In order to apply the Minkowski-Bouligand dimension onto the gray scale images, the following approach is proposed based on the traditional 3-D Minkowski-Bouligand dimension. A 3-D surface can be generated by an image with its coordinates representing 2-D position and its gray intensity representing the third coordinate. In this definition, the distance between the interest point and other point is calculated as follows:
Fig. 3. The surface of six Hep-2 cell patterns.
(6) where represents the distance between the 2-D position of the interest point and the coordinate position of other points. Like the influence area mentioned above, the influence volume (FV) can also be calculated as (4). So the dimension for gray scale image is:
Fig. 4. The average area of connected components of centromere when the threshold is 60, 68, 76. TABLE III A SQUARE RANGE OF THE HOMOGENEOUS SAMPLE. THE POINTS SQUARE ARE THE INTEREST POINTS
IN THE
(7) The (6) demonstrates that the influence volume has direct relationship not only with positions of the interest points but also with the surrounding gray intensity. It can be concluded that the influence volume for gray scale image contains more image features than the influence area for binary image. The main difference between the six Hep-2 cell patterns is the texture feature. So we believe that the 3-D surface of each pattern should be different as well. It is further verified by Fig. 3. In the proposed method, the points with maximum intensity are regarded as the interest points. As the surrounding near the peak of the surface has great difference between the six classes, a series of squares with the maximum gray intensity in the center are extracted. The distance map of influence volume only on
maximum intensity and the distance map of influence volume on both maximum and minimum intensity in the square are calculated respectively, as the same way with Tables I and II. Suppose that the Table III shows a square of a homogeneous sample with the highest intensity in the center, Table IV is the distance map of influence volume only on the maximum intensity and Table V is the distance map of influence volume on both maximum and minimum intensity in the square. As the above discussed, it can be found that the proposed fractal dimension is calculated around the maximum intensity space, which means the dimension proposed in this paper can
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TABLE IV THE DISTANCE MAP OF INFLUENCE VOLUME ONLY ON MAXIMUM INTENSITY. THE VALUE OF SOME INFLUENCE VOLUME FV(R) ACCORDING TO RADIUS R:
TABLE V THE DISTANCE MAP OF INFLUENCE VOLUME ON BOTH MAXIMUM AND THE MINIMUM INTENSITY. THE VALUE OF SOME INFLUENCE VOLUME FV(R) ACCORDING TO RADIUS R:
only represent the local texture complexity. Therefore, another fractal dimension, which was presented by Peleg et al. [12] with the fractal signature from blanket surfaces and describes the global texture complexity, is also joined. For this fractal dimension, the images are resized in different scales and we calculate its dimension by [12] for each scale. The fractal data for dimension is collected at different square scales before linear approximation. For the proposed dimension, the average and variance of each square scale are recorded. So, the final fractal descriptor is composed by three arrays of fractal dimensions at different scales. One array are the productions by influence volume only on the maximum intensity, one array are the productions on both the maximum and the minimum intensity and the others are the productions by [12]. B. Morphological Feature Descriptor Morphological measurement of image slices at different thresholds is another way of comparing texture. As centromere image has strong bright spots on a darker background and homogeneous is fairly uniform, we can imagine that centromere image usually has many connected components and homogeneous image has less connected components. In addition, the average area of connected components of homogeneous may be bigger than that of centromere. In this paper, the image is first on binary process at each threshold . Then the whole area of connected components and the number of the connected components of the binary image are recorded with threshold . At last, a vector of average area of connected components (AACC) can be defined as follows: (8) where is the cell area used for normalization. Fig. 5 is the average area of connected components of the centromere cell in Fig. 1 at different thresholds and Fig. 6 is the results of the homogeneous cell. From Figs. 5 and 6, it can be seen that the AACC variation of centromere is bigger than that of homogeneous for different threshold. That is to say, the AACC of the centromere is more
Fig. 5. The average area of connected components of homogeneous when the threshold is 60, 68, 76.
sensitive to the threshold, which implies that the variance of the AACC at different thresholds can be used as another feature. As the cytoplasmatic class is also characterized by shape, we include circularity of the connected components (calculated as area divided by square of the perimeter) [10], circularity of the mask, the area of the mask, as well as the variance of the cell image as a part of morphological descriptor in every feature set. At last, the morphological feature descriptor is composed by six features which are AACC, variance of AACC, the variance of the cell image, the circularity of the connected components, circularity of the mask, and the area of the mask. C. Pixel Difference Feature Descriptor Pixel difference statistics at different scales are another way to represent the textural feature. The expression is defined as follows:
(9) where is the offset at both horizontal and vertical direction, and is the mask of the cell. In order to remove the image individual influence on the sampled data such as the influence by the brightness and contrast of image, we calculate pairwise ratios between measurements at different scales. As the ratios are free from dependency on overall brightness and contrast of the image, they present the feature of the texture for each pattern [10]. Finally, the pixel difference feature descriptor is consisted of the ratios between the near two . IV. EXPERIMENT RESULTS In this section, the prediction derived from each feature set is in its corresponding subsection. All the features are scaled for normalization and are tested by grid.py tool in SVM [13] for the best training parameter maximizing the overall accuracy before classification. The experiment was conducted by two protocols: the first one is the contest protocol which the 28 images are partitioned into training group and test group with 14 images per group. The second one follows the leave-one-out protocol, i.e., each slide is chosen as the test set and the remaining slides are as the training set. According to the contest protocol, features are extracted from the training set for prediction in the testing set. For the sake of brevity, hereafter we will use confusion matrix containing each
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TABLE VI THE CONTENT FOR EACH SLIDE
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TABLE VII THE CONFUSION MATRIX OF FRACTAL DESCRIPTOR. THE TRAINING PARAMETERS: -C 8.0, -G 0.125
TABLE VIII THE CONFUSION MATRIX OF MORPHOLOGICAL DESCRIPTOR WITH SEVEN THRESHOLDS. THE TRAINING PARAMETERS: -C 8.0, -G 0.125
pattern's precision for analysis. The “ ” in the lower left corner of the confusion matrix represents the precision of one pattern. In the following sections, the overall accuracy is achieved by the following: (10) is the whole correct prediction in the test set and where is the whole number of the test set. In our experiments, . In the confusion matrix, equals to the sum of the elements at diagonal of the matrix. The precision is achieved by the following: (11) where is the number of correct prediction of class , is the prediction number of this class. In the confusion and matrix, equals to the sum of the elements at the th column. For the leave-one-out protocol, Table VI provides an overview of the content for each slide out of 28. All the experiments were conducted on a Core(TM) i5 (2.40 GHz) PC. A. Fractal Descriptor In the fractal descriptor, the size of extracted square with the highest peak in the center is set ranging from 2 to 14 with one increment for the fractal dimension produced by influence volume only on the maximum intensity. For fractal dimension produced by both the maximum and the minimum intensity, the size is set ranging from 2 to 6 with one increment. For fractal dimension proposed by [12], the reshaped size is set ranging
from 0.5 to 7.5 with one increment. For [12], we recode its dimension, intercept, and correlation coefficient additionally. As the consequence, the vector length of the fractal descriptor is . Table VII is the confusion matrix using fractal descriptor. It can be calculated from Table VII that the overall accuracy is 54.5%. From the results, the recognition to the centromere images is weakest, which has only 41.8% precision, while the recognition to the cytoplasmatic images is the best, which achieves 79.37% precision. B. Morphological Descriptor The image is first converted to a binary image at the threshold . In the experiment, we set seven thresholds whose baseline is the minimum value in the cell. The increment for thresholds is assigned as two. The morphological feature descriptor is composed of six features, AACC, variance of AACC, the circularity of the connected components, the circularity of the mask, the variance of the cell image, the variance of the cell image, and the area of the mask, so the vector length of the morphological . Table VIII is the confusion matrix descriptor is using morphological descriptor. The overall accuracy of the morphological descriptor at image level is 54.22%. It can be seen from Table VIII that the morphological descriptor works better on cytoplasmatic as the precision on cytoplasmatic achieves 97.78%. However, the lowest precision is produced by fine speckled, which is 35.8%. C. Pixel Difference Descriptor Considering that the sampling process is done only in the cell within the mask that the dataset provides and the sampled data is in too small amount to retain any relevant information, the offset at both horizontal and vertical direction should not be a big value. The scales of pixel difference feature descriptor are assigned ranging from 1 to 14 with one increment. So there are
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TABLE IX THE CONFUSION MATRIX OF PIXEL DIFFERENCE DESCRIPTOR WITH ONE INCREMENT. THE TRAINING PARAMETERS: -C 512.0, -G 0.125
TABLE X THE CONFUSION MATRIX OF HYBRID DESCRIPTOR . THE TRAINING PARAMETERS: -C 8.0, -G 0.03125
ratios as a vector. Table IX is the confusion matrix using pixel difference descriptor. The overall accuracy by the pixel difference descriptor is only about 33.51%. This descriptor has an obvious weakness when recognizing the cytoplasmatic images. Although it is not satisfying, this feature descriptor can be combined with other descriptors, helping enhance the performance, which will be seen in the following.
THE CONFUSION MATRIX
TABLE XI OF HYBRID DESCRIPTOR . THE TRAINING PARAMETERS: -C 32.0, -G 0.03125
TABLE XII THE CONFUSION MATRIX BY THE MULTI-PROJECTION-MULTI-CODEBOOK SCHEME [5] WITH 200 VECTOR LENGTH
TABLE XIII THE CONFUSION MATRIX B USING ROTATION INVARIANT CO-OCCURRENCE [4] WITH 408 VECTOR LENGTH
D. Hybrid Descriptor From above discussions, we can see that the fractal descriptor and the morphological descriptor work better, with the higher overall accuracy. However, for morphological descriptor, the values of six classes precision vary largely from the maximum 97.78% to the minimum 35.8%, resulting the predictions for some classes such as fine speckled are not convinced. Comparing morphological descriptor with fractal descriptor, the latter one has the advantage over the former because it has milder changes in precision. A good classification system should have small change in precisions between the classes as well as a high overall accuracy. Since a single feature classification has its own drawback and increasing the feature vectors only cannot enhance the classification performance generally, we mix the above three descriptors together to make up for one's own weak points. Table X is the confusion matrix results by hybrid descriptor without the fractal descriptor. Table XI is the confusion matrix . results by hybrid when the vector length is It can be seen that the overall accuracy of hybrid descriptor is 67.17% in Table XI, and overall accuracy of hybrid descriptor without the fractal descriptor is 63.49% in Table X. Comparing Table X with Table VIII which is the result of single morphological descriptor, although the overall accuracy by hybrid descriptor without fractal descriptor is improved by 9.27%, the problem of the morphological feature descriptor with large precision variation is not solved yet. The precision still
ranges from the minimum 45.16% of fine speckled to the maximum 96% of cytoplasmatic. The classification on fine speckled from Table X shows that the prediction on the fine speckled has 124 samples in which only 56 samples taking of 45.16% are correct. The classification by hybrid descriptor including the fractal descriptor works better than both that of hybrid descriptor excluding the fractal descriptor and that of single morphological descriptor. For the overall accuracy, the hybrid descriptor achieves 67.17%, which is 3.68% higher than that of hybrid descriptor without fractal descriptor and 12.95% higher than that of single morphological descriptor. What's more, the fractal descriptor makes the results distribute more evenly in the prediction of each class. As we can see from Tables X and XI, the precision of each class in Table XI keeps above 52%, not varying so much than that of Table X. Besides, the predictions on some of the patterns are enhanced. For instance, the prediction on the fine speckled has 102 samples in which 61 samples taking of 59.8% are correct. It is 14.64% higher than the corresponding precision in Table X. As the consequence, the classifier of the hybrid descriptor serves better for each class in general. It is obvious that the fractal descriptor plays an important role in the classifier.
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TABLE XIV PREDICTIONS WITHIN EACH SLIDE USING HYBRID FEATURES, AS NUMBERS OF CELLS AND PERCENTAGES
Table XII is the confusion matrix from [5] by the multi-projection-multi-codebook scheme. Table XIII is the confusion matrix from [4] by using rotation invariant co-occurrence. In [5], the dimension of the learned descriptor is set to 40 and 5 groups are used, so the vector length is 200. In [4], the final feature . Both of them are vector length is much longer than the vector length, 79, in the proposed method. The overall accuracy of [5] is 66.6% and the overall accuracy of [4] is 67.3%. The overall accuracy of the proposed method is 67.17%, which is a comparable result with relatively simple feature vectors. Comparing Table XI with Tables XII and XIII, the precisions of fine speckled and coarse speckled by the hybrid descriptor are higher than the other two precisions in the literature. In addition, the precision on cytoplasmatic is 97.96%, also larger than the other two precisions. It is shown that the prediction results of fine speckled and cytoplasmatic are more convinced than the schemes proposed by the two papers. As discussed above, the fractal descriptor combining with morphological descriptor and pixel difference descriptor makes the precisions of six classes more stable, all above 52%. Tables XII and XIII show that the precisions of the prediction on the fine speckled, 45.70% and 41.80% respectively, are much lower than that of other classes. We believe that the fractal descriptor combining with other feature vectors can help achieve more satisfying results. E. Leave-One-Out Protocol The numbers of cells predicted within each slide by leaveone-out protocol are listed in Table XIV. The dramatic changes of the classification accuracy can be seen from the Table. For some slides, e.g., for the 16th and the 26th slide, the classifica-
tion accuracy can be as high as 100%, and for the 3rd and the 12th slide, the accuracies are above 95%, but for the 8th and the 15th the classification accuracies are extremely low. This phenomenon can be explained by the imbalance data distribution of the training set. Evidently, for some images, the visual appearance is quite different from the other images labeled as belonging to the same category [5]. In addition, for some slides, the cells are quite similar visually, while they are belonged to different patterns, such as the nucleolar in #4 and the homogeneous in #5. V. CONCLUSION In this paper, we proposed an approach for pattern recognition in stained HEp-2 cell IIF images, which is critical for the immune diseases diagnosis. The fractal theory is firstly applied on HEp-2 cell pattern classification. The descriptors carried out in this paper are 42-size fractal descriptor, 24-size morphological feature descriptor, 13-size pixel difference feature descriptor, and 79-size hybrid descriptor. As fractal dimension can be used on the analysis of image representing, the fractal feature is extracted from the HEp-2 cell images. The experiments on fractal descriptor show that the overall accuracy is 54.5% with the highest precision nearly 79.37% of centromere. The experimental results show that the morphological descriptor performs well. The overall accuracy of the classification achieves 54.22% with the highest precision 97.78% on cytoplasmatic. However, the values of six classes precision vary largely from the maximum 97.78% to the minimum 35.8%. The hybrid descriptor combining with the fractal descriptor makes the classification results distribute more evenly, all above
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52%. Its vector length is 79. The experimental results show that the overall accuracy achieves more than 67% with a mildly variation in class precision. Based on the comparison with the previous literature methods, the proposed method works better in some of the class predictions with the least vector length. We arrive the conclusion that the join of the fractal descriptor enhance the overall accuracy and serves better for the hybrid descriptor on each class in general. For some images, the visual appearance is quite different from the other images labeled as belonging to the same category. And, for some slides, the cells are quite similar visually while they are belonged to different patterns. As the result, the recognition rates to some slides are very low, which also appears in other literature schemes. The problem may be solved in the further exploration of fractal feature extraction. Future work will be focused on the improvement and refinement of the fractal descriptor.
Rudan Xu was born in ZhuZhou City, HuNan Province, China, in 1990. She received her B.Sc. degree at the Zhejiang University of Science and Technology, China, in 2008, and her M.Sc. at the DaLian University of Technology, China, in 2015. She is a M.S. candidate at the College of Computer Science and Technology, DaLian University of Technology. Her fields of interest are the fractal applications in computer vision, image analysis, and pattern recognition.
Yuanyuan Sun was born in Feicheng, Shandong Province, China, in 1979. She received the M.S. and Ph.D. degrees in computer science from the Dalian University of Technology, China, in 2003 and 2009, respectively. From 2006 to 2011, she was a Lecturer with the Department of Computer Science and Technology. Since 2012, she has been an Associate Professor with the College of Computer Science and Technology, Dalian University of Technology. Her research interests include fractal theory, and its applications in image processing and complex networks.
REFERENCES [1] “MIVIA HEp-2 images dataset” [Online]. Available: http://mivia. unisa.it/datasets/biomedical-image-datasets/hep2-image-dataset/ [2] K. Egerer et al., “Automated evaluation of autoantibodies on human epithelial-2 cells as an approach to standardize cell-based immunofluorescence tests,” Arthritis Res. Therapy, vol. 12, 2010. [3] G. V. Ponomarev, V. L. Arlazarov, M. S. Gelfand, and M. D. Kazanov, “ANA HEp-2 cells image classification using number, size, shape and localization of targeted cell regions,” Pattern Recognit., vol. 47, pp. 2360–2366, 2014. [4] R. Nosaka and K. Fukui, “HEp-2 cell classification using rotation invariant co-occurrence among local binary patterns,” Pattern Recognit., vol. 47, pp. 2428–2436, 2014. [5] L. Q. Liu and L. Wang, “HEp-2 cell image classification with multiple linear descriptors,” Pattern Recognit., vol. 47, pp. 2400–2408, 2014. [6] A. R. Backes, D. Casanova, and O. M. Bruno, “Plant leaf identification based on volumetric fractal dimension,” Int. J. Pattern Recognit. Artif. Intell., vol. 23, pp. 1145–1160, 2009. [7] A. Eguizabal et al., “Fractal analysis of scatter imaging signatures to distinguish breast pathologies,” in Proc. Conf. Biomed. Appl. Light Scattering VII, 2013, vol. 8592. [8] B. Q. Liang, Q. H. Weng, and X. H. Tong, “An evaluation of fractal characteristics of urban landscape in Indianapolis, USA, using multisensor satellite images,” Int. J. Remote Sensing, vol. 34, pp. 804–823, 2013. [9] [Online]. Available: http://mivia.unisa.it/hep2contest/ [10] V. Snell, W. Christmas, and J. Kittler, “HEp-2 fluorescence pattern classification,” Pattern Recognit., vol. 47, pp. 2338–2347, 2014. [11] O. M. Bruno, R. de Oliveira Plotze, M. Falvo, and M. de Castro, “Fractal dimension applied to plant identification,” Inf. Sci., vol. 12, pp. 2722–2733, 2008. [12] S. Peleg, J. Naor, R. Hartley, and D. Avnir, “Multiple resolution texture analysis and classification,” IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, pp. 518–523, 1984. [13] “LIBSVM—A library for support vector machines” [Online]. Available: http://www.csie.ntu.edu.tw/~cjlin/libsvm/
Zhihao Yang received his Ph.D. degree in computer science from Dalian University of Technology, Dalian, China, in 2008. He is currently a professor in the College of Computer Science and Technology at Dalian University of Technology. He has published over 20 research papers on topics in biomedical literature data mining. His research interests include biomedical literature data mining and information retrieval. His research projects are funded by the Natural Science Foundation of China.
Bo Song received the B.S. degree in biomedical engineering from Northeastern University, Shenyang, China, in 2010 and the M.S. degree in biomedical engineering from Drexel University, Philadelphia, PA, USA, in 2012. He is currently pursuing the Ph.D. degree in information science at Drexel University. Since 2013, he was a Research Assistant with the College of Computing and Informatics (CCI) at Drexel University. He had also worked as a Research Associate with Drexel Center for Integrated Bioinformatics. His research interests include the biomedical image processing, bioinformatic studies, and data mining and analysis. Xiaopeng Hu is currently a Professor in computer science at Department of computer science and technology, Dalian University of Technology, Dalian, China. His research interests include computer vision, machine learning, pattern recognition, and sensor fusion.
