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The impact of image dynamic range on texture classification of brain white matter

The impact of image dynamic range on texture classification of brain white matter Background: The Greylevel Cooccurrence Matrix method (COM) is one of the most promising methods used in Texture Analysis of Magnetic Resonance Images. This method provides statistical information about the spatial distribution of greylevels in the image which can be used for classification of different tissue regions. Optimizing the size and complexity of the COM has the potential to enhance the reliability of Texture Analysis results. In this paper we investigate the effect of matrix size and calculation approach on the ability of COM to discriminate between peritumoral white matter and other white matter regions. Method: MR images were obtained from patients with histologically confirmed brain glioblastoma using MRI at 3-T giving isotropic resolution of 1 mm . Three Regions of Interest (ROI) were outlined in visually normal white matter on three image slices based on relative distance from the tumor: one peritumoral white matter region and two distant white matter regions on both hemispheres. Volumes of Interest (VOI) were composed from the three slices. Two different calculation approaches for COM were used: i) Classical approach (CCOM) on each individual ROI, and ii) Three Dimensional approach (3DCOM) calculated on VOIs. For, each calculation approach five dynamic ranges (number of greylevels N) were investigated (N = 16, 32, 64, 128, and 256). Results: Classification showed that peritumoral white matter always represents a homogenous class, separate from other white matter, regardless of the value of N or the calculation approach used. The best test measures (sensitivity and specificity) for average CCOM were obtained for N = 128. These measures were also optimal for 3DCOM with N = 128, which additionally showed a balanced tradeoff between the measures. Conclusion: We conclude that the dynamic range used for COM calculation significantly influences the classification results for identical samples. In order to obtain more reliable classification results with COM, the dynamic range must be optimized to avoid too small or sparse matrices. Larger dynamic ranges for COM calculations do not necessarily give better texture results; they might increase the computation costs and limit the method performance. Page 1 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 image properties on the stability of texture results and on Background Automated statistical and structural methods applied to the performance of the method [9]. Investigations of such digital medical images have shown that the amount of relationships eventually will lead to an optimized and quantitative information available in the image exceeds more reliable method for biomedical image analysis the capacity of the human visual system [1]. These meth- applications, which will require less processing time and ods assume that image greylevel relationships and spatial less extensive calculations. distribution are directly influenced by the properties of the underlying tissue, which themselves, are dynamic and It is commonly assumed in TA applications that increas- depend on biological and chemical composition. There- ing the image dynamic range on which texture is evalu- fore, minor image modifications can be quantified and ated improves textural feature representation; and monitored by appropriate methods even before they are consequently, gives better classification results. However, perceivable by the human eye. Such automated methods there is no evidence in biomedical image analysis litera- are collectively known as Texture Analysis (TA) [1]. ture to confirm or reject this assumption. The objective of the current work is to investigate the dependence of a Since the physical properties of tissues are the basis for commonly used TA method, the Cooccurrence Matrix operating imaging modalities, the reliability of the imag- (COM), on image dynamic range and matrix calculation ing output depends on the ability of the modality to pro- approach for classifying white matter regions. vide contrast between different tissues as well as local contrast that shows early changes in the physical-chemical Methods properties within that tissue. MRI is known to provide the Patients and MRI data best image contrast among the imaging modalities availa- In agreement with the French ethical legislation on clini- ble so far; therefore, MR images are believed to be rich in cal trials, whole brain MRI datasets were acquired in the digital information that can be exploited by TA and would sagittal plane for ten Glioblastoma patients (age = 53 ± be of important analytical and diagnostic utility. In recent 18; histologically confirmed by biopsy) using a Philips 3- years, Texture Analysis on Magnetic Resonance Images T Achieva MR system (Philips Medical System, Best, Neth- (MRI-TA) has been applied successfully in clinical and erlands). The imaging sequence used was Three-Dimen- experimental studies and is regarded as a reliable nonin- sional Gradient Echo (TR = 9.87 ms, TE = 4.56 ms, flip vasive tool of investigation, which combines the high con- angle = 8°). Field of View (FOV) = 256 mm × 256 mm, trast of MRI with the good sensitivity and specificity of TA. matrix size = 256 × 256, and a slice thickness of 1 mm, The quantitative texture data obtained from TA are relative gave isotropic voxel resolution of 1 mm . Transversal sec- rather than absolute; therefore, MRI-TA usually has to be tions were reconstructed from the original sagittal plane. followed by a standard classification method. Imaging procedures and clinical diagnosis were per- formed in Rennes University Hospitals, Rennes, France. It has been demonstrated with laboratory animals that in- vivo MRI-TA of muscles correlates with histology during Each patient showed a tumor mass developed within the degeneration and regeneration processes [2]. Direct rela- brain white matter. Three Regions of Interest (ROI)s were tionships between muscle contents of fat and collagen manually outlined in the normal white matter by a radi- were found using texture classification on high resolution ologist on a first transversal image Slice (S1) according to MRI [3]. MRI-TA has been clinically investigated on sev- relative distance of the region to the tumor: one Peritu- eral tissues such as breast lesions [4], and hepatic fibrosis moral White matter (PtWm) close to the visible margins [5]. Brain tissue also has been studied using MRI-TA [6-8]. of the tumor; and two Distant White matter (DWm) taken These studies recommended MRI-TA as a potential tool far from the tumor on both hemispheres (figure 1). Each for non-invasive investigations of cerebral tumors as well ROI contains of about 100–200 pixels. Volumes of Inter- as for healthy white and grey matter. In a previous work est (VOI)s were constructed by copying the ROI position on brain gliomas, we investigated peritumoral white mat- to the next two adjacent transversal slices (S2 and S3) pro- ter in regions defined by the radiologists as normal non- ducing volumes of about 300–600 voxels each. The VOI pathological tissues, but which were in the proximity of boundaries were inspected carefully to avoid overlapping visible tumor margins. MRI-TA classified these regions as structures. Only for one patient the location of the tumor a homogenous texture class, separate from the other white did not allow for outlining a PtWM. A total number of 89 matter regions which clustered in one broad class [8]. We ROIs and 29 VOIs were available for this study. suggested that this different texture could be due to invis- ible proliferation by tumoral cells [8]. Cooccurrence Matrices The Cooccurrence Matrix (COM) was first introduced by Since TA is based on calculations with image greylevels, it Haralick [10] along with 14 derived features; most of becomes crucial to understand the impact of changing them quantitatively describe image homogeneity and Page 2 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 DWm Rescaling to 32 greylevels PtWm MR image of Figure 1 brain glioblastoma and the surrounding white matter MR image of brain glioblastoma and the surrounding white matter. Transversal slice of MRI of brain glioblastoma showing Tumor, T; and the normal white matter regions (solid lines): PtWm, Peritumoral; and DWm, Distant White matter. An ROI and the corresponding matrix are linked (red dashed lines) to illustrate the rescaling process. Matrix A represents the original ROI which has a dynamic range from 0 to 255 greylevels. The matrix B shows the same ROI after multiplying each pixel with the ratio of the maximum greylevel value allowed in B (31 in this case) to the actual maximum greylevel value of A. Page 3 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 greylevels correlations. Some COM features have been 7.0, Math-Works Inc., Natick, MA, USA), on a PC with ® ® found to be discriminative, and therefore, can be used for Intel Pentium 4.0 processor and 1.24 Gb RAM. texture classification [10]. In a digital image, the number of bits-per-pixel (bp) coding determines the maximum Features Selection and Classification bp number of greylevels (N) in the image (2 = N). Hence, Features selection aims to identify the most discriminat- the allowed dynamic range of greylevels is from 0 to (N- ing parameters from each matrix that separate the differ- 1). ent classes most efficiently. Fisher-coefficient (F- coefficient) was calculated for this purpose, giving the The Classical approach of COM calculation (CCOM) sam- ratio of between class variance to within class variance [11] ples the probability density function P (i, j), which gives for each parameter. The ten parameters of the highest F- d, the probability of finding the two greylevels i and j at a coefficient were entered to Linear Discriminant Analysis distance d (d = 1,2,3,...) in the direction of angle ( = (LDA) for classification. LDA aims to find a linear trans- xy xy 0°, 45°, 90°, and 135°), on a two dimensional image form matrix such that the ratio of within-class scatter defined on the x- and y- axes. This calculation approach matrix to between-class scatter matrix is maximized. Such ignores useful spatial information that can be obtained a transform is composed of eigenvectors corresponding to from relationships between slices. Therefore, recent the largest eigenvalues of this ratio of matrices; more approaches try to maximize the usefulness of COM by details about the classification method can be found in including data at various angles on the z-axis. One of these [12]. Cross validation was performed using "leave-one- approaches is known as Three Dimensional Cooccurrence out" criterion, which works by leaving one observation Matrix (3DCOM) [8]. 3DCOM is calculated on image vol- (i.e one ROI) out of the classifier each time the classifica- umes composed of several adjacent slices, and involves tion model is recalculated and then project this observa- nine angles on the z-axis ( = 0°, 45°, 90°, 135°, 180°, tion into the model to test its validity. This process is 225°, 270°, 315°, and co-linear) in addition to angles . carried out for all observations. The percentages of False xy More details can be found in [8]. A Direction Independent Negatives (FN) and False Positives (FP) were evaluated. (DI) matrix results from summing COM over all angles. The Receiver Operating Characteristic (ROC) curve was This indicated in the notation below by = DI. analyzed, which represents the relationship between the '1-Specificity' and the 'Sensitivity' of the test. The Area In this work, both approaches are calculated: i) CCOM on Under the ROC Curve (AUC) is used to judge the separa- ROIs of the three adjacent slices (S1, S2, S3) giving three bility of the two classes for the given dataset and classifier. matrices CCOM-S1, CCOM-S2, and CCOM-S3, respec- An AUC of 1.0 represents a perfect classifier, while an AUC tively; and ii) 3DCOM on the VOI given by the three of 0.5 represents a random classifier. slices. For both approaches, the resulting matrix is always symmetric about its diagonal and of NxN size with N Features Selection was performed using B11 software (ver- number of entries. Five parameters were calculated from sion 3.2, 1999–2002 by Michal Strzelecki), which is each matrix: Angular Second Moment, Inverse Difference developed under the auspices of COST action B11 Euro- Moment, Entropy, Contrast and Correlation [10]. These pean project [12]. Linear Discriminant Analysis (LDA) five parameters were selected because they were found to was followed by cross validation and was performed using be good descriptors of white matter texture in a previous the software Minitab 15 ( 2007 Minitab Inc). The ROC curve was analyzed and AUC were calculated using SPSS work [8]. They provide the main information about image homogeneity and the existence of correlated patterns in 15.0 ( 1989–2006 SPSS Inc). the image. Results and discussion The original MR images are usually digitized over 16 bits- LDA classification on PtWm and DWm white matter per-pixels (65536 greylevels). It is computationally exten- regions always separated PtWm into a distinct homoge- sive and time consuming to calculate COM over such a nous class. This class was well distinguished for small as large dynamic range. Therefore, it is a standard procedure well as for large dynamic ranges for all matrices. However, in medical image analysis to apply a quantization process the number of classification errors between the two in order to reduce the original range to a user-defined classes depended remarkably on the dynamic range along value of N. This is done by scaling the original pixel values with COM approach used. Table 1 represents the percent- with the ratio between the maximum greylevel allowed in age of False Negatives (FN: PtWm classified as DWm) and the rescaled image and the actual maximum greylevel in False Positives (FP: DWm classified as PtWm) for each the original image (figure 1). Prior to COM calculations, number of greylevels N and matrix calculation approach. each ROI is rescaled for five different values of N, (N = 16, The average errors and standard deviation (Mean ± SD) 32, 64, 128, and 256). All texture calculations and image for CCOM-S1, CCOM-S2, and CCOM-S3 over the three processing methods were implemented using Matlab (ver Page 4 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 Table 1: Classification results using cross-validated LDA and for Peritumoral White matter (PtWm) classified as Distant White matter (DWm) (False Negative: FN). 16-GL 32-GL 64-GL 128-GL 256-GL FN% FP% AUC FN% FP% AUC FN% FP% AUC FN% FP% AUC FN% FP% AUC CCOM-S1 22.00 15.00 0.82 33.00 5.00 0.81 33.00 10.00 0.785 11.00 5.00 0.915 22.00 15.00 0.815 CCOM-S2 55.00 25.00 0.60 25.00 44.00 0.655 33.00 20.00 0.735 33.00 10.00 0.785 22.00 10.00 0.84 CCOM-S3 33.00 20.00 0.735 33.00 10.00 0.785 11.00 15.00 0.87 11.00 10.00 0.895 22.00 10.00 0.84 Mean ± 36.67 ± 20.00 ± 0.71 30.33 ± 19.67 ± 0.75 25.67 ± 15.00 ± 0.8 18.33 ± 8.33 ± 0.87 22.00 ± 11.67 ± 0.83 SD 16.80 5.00 5 4.62 21.22 12.70 5.00 12.70 2.89 0.00 2.89 3DCOM 22.00 10.00 0.84 22.00 20.00 0.79 33.00 10.00 0.785 11.00 10.00 0.895 44.00 5.00 0.755 DWm classified as PtWM (False Positive: FP); using five dynamic ranges (N = 16, 32, 64, 128, and 256). FN and FP are represented as percentage errors. AUC for each ROC curve is also demonstrated. CCOM: Classical Cooccurrence Matrix calculated on slices: -S1, -S2, and -S3. 3DCOM: Three Dimensional Cooccurrence Matrix. Mean ± SD the average and standard deviation of results for CCOM-S1, CCOM-S2, and CCOM-S3. GL: Greylevels. LDA: Linear Discriminant Analysis. AUC : Area Under the Receiver Operating Characteristic (ROC) Curve. slices is also presented and will be used for comparison former (figure 2a). This balance is lost at other values of N with 3DCOM. (figure 2b). The Mean CCOM method on the three slices (-S1,-S2,-S3) shows the highest sensitivity and specificity Analyzing table 1 shows that the Mean FN or FP of CCOM at N = 128 (figure 2b). For either CCOM or 3DCOM, fig- (-S1,-S2,-S3) decreases progressively with increasing N ure 2 demonstrates that the specificity of the method is until reaching N = 256 for which it increases again (table always higher than its sensitivity. The Area Under the ROC 1). For 3DCOM, the lowest value of FN occurs at N = 128, Curve (AUC) represents a comprehensive measure for which was less than those obtained from Mean CCOM for evaluating the accuracy of the classifier (table 1). By com- any other N. The most discriminating parameters for this paring AUCs of the Mean value of the three CCOMs and analysis and their F-Coefficients are presented in table 2. those of 3DCOM, it can be shown that the highest AUC The percentage of FN shows a considerable increase when value was obtained for 3DCOM at N = 128, while the low- 3DCOM is calculated for N = 256; however, FP represents est was obtained for Mean CCOMs at N = 16 (figures 3a the lowest percentage obtained (table 1). and 3b, respectively). It can also be shown that the highest value of AUC among Mean CCOMs was obtained also at The bar graph of test outcomes measures (sensitivity and N = 128 (table 1). specificity) (figure 2) demonstrates a balanced tradeoff between the sensitivity and specificity of the 3DCOM In this study, PtWm clustering as a separate white matter method at N = 128 and N = 32 with higher values at the region is consistent with previous findings [8]; however, we demonstrate in the current work that classification accuracy is highly dependent on the dynamic range of Table 2: The ten most discriminating parameters, according to image quantization for both COM calculation approaches the Fisher (F-) coefficient, between the two white matter classes (Peritumoral white matter and distant white matter). (CCOM and 3DCOM). Also, we can see that classification results among different slices might give diverse results in Most Discriminating Parameters F-Coefficient spite of carrying out the analyses on identical positions. This can be demonstrated for FN at N = 16 that gave 22% Entropy_ = 0° 3.0972 on CCOM-S1 and 55% on CCOM-S2. Angular Second Moment_ = 135° 2.2651 Entropy_ = DI 1.9090 Entropy_ = 135° 1.8852 It can be also shown that calculating 3DCOM on small Angular Second Moment_ = 0° 1.8002 dynamic ranges (N = 12, 32 and 64) does not enhance Angular Second Moment_ = 45° 1.7164 classification as long as the dynamic range remains rela- Angular Second Moment_ = 90° 1.6279 tively small. In contrast, 3DCOM on a larger dynamic Angular Second Moment_ = DI 1.5740 range (N = 128) enhances classification remarkably, but a Entropy_ = 45° 1.4461 further increase of N worsens the method's sensitivity. Contrast_ = DI 1.0305 Although method's specificity has increased at N = 256, the tradeoff between sensitivity and specificity remains an Using Three-Dimensional Cooccurrence Matrix (3DCOM) for a number of greylevels N = 128. important factor to take into account when evaluating the DI: Direction Independent method's performance. Therefore, N = 256 is probably : The angle of the parameter. not a good choice for 3DCOM analysis. Page 5 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 (a) (b) Sen Figure 2 sitivity and specificity bar graphs Sensitivity and specificity bar graphs. Sensitivity and specificity bar graphs for (a) 3DCOM on white matter VOIs; and, (b) The Mean value of (CCOM) on the individual slices ROIs (-S1, -S2, and -S3). CCOM: Two Dimensional Classical Cooccurrence Matrix. 3DCOM: Three Dimensional Cooccurrence Matrix. VOI: Volume of Interest. ROI: Region of Interest. Page 6 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 a) b) ROC curves showing the highest and lowest A Figure 3 UC ROC curves showing the highest and lowest AUC. Receiver Operating Characteristic (ROC) curves showing: a) the highest Area Under the Curve (AUC) (= 0.895) which was obtained using 3DCOM at N = 128; and, b) the lowest AUC (= 0.715) obtained using the Mean CCOMs at N = 16. CCOM: Two Dimensional Classical Cooccurrence Matrix. 3DCOM: Three Dimensional Cooccurrence Matrix. Page 7 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 The relationship between the dynamic range and classifi- Authors' contributions cation accuracy can be related to COM characteristics. This DMG has designed the study, implemented the texture 7.0, acquired data, analyzed matrix, by definition, is a probability density matrix of analysis methods on Matlab unit sum. Decreasing the dynamic range means that the results, and drafted the manuscript. MKA has participated original ROI will be reduced to smaller adjoining values in the programming procedures. JDC has set and super- of greylevels as shown in figure 1; therefore, cooccurrence vised the protocol of MR image acquisition in Rennes matrix will be smaller and the joint probabilities will be University Hospitals according to rules and regulations set estimated for a limited number of matrix entries (eg. N = by Ethics Committees. FMG has participated in results 16, COM size = 16 × 16 = 256 entry). This could be insuf- analysis and critical revision of the manuscript. ficient to represent texture features and may result in higher classification errors. On the other hand, increasing Acknowledgements This work has been achieved in coordination with COST European project the dynamic range will spread the greylevels over a larger Action B21 "Physiological modelling of MR image formation". It has been scale producing matrices with sufficient number of presenting during COST B21 Meeting in Bled, Slovenia, 2007. entries; and then, discriminating texture features would have more chance to appear; consequently, this would A part of this work has been funded by United Arab Emirates University, reduce the percentage error. Further increase of N values Research Grant number: 01-02-2-11/07. produces sparse matrices with probabilities broken down over a huge number of entries (65535 for N = 256); in The authors would like to thank Biatrice Carsin, for MRI acquisition (CHRU Pontchaillou), and Pierre-Antoine Eliat for technical assistance (Rennes I other words, feature representation would be weakened University). and classification errors increased. It merits to mention that the processing time for calculating 3DCOM using N References = 128 was within a fraction of a second, while it took 1. Castellano G, Bonilha L, Li LM, Cenes F: Texture analysis of med- almost 30 seconds for calculating the same matrix using N ical images. Clinical Radiology 2004, 59:1061-1069. = 256. The increase in processing time is even more signif- 2. Mahmoud-Ghoneim D, Cherel Y, Lemaire L, de Certaines JD, Mani- ere A: Texture analysis of Magnetic Resonance Images of rats icant for larger VOIs. muscles during atrophy and regeneration. Magn Reson Imaging 2006, 24:167-171. 3. Mahmoud-Ghoneim D, Bonny JM, Renou JP, de Certaines JD: Ex- From these results, we recommend quantizing image vivo Magnetic Resonance Imaging Texture Analysis Can Dis- ROI/VOI to a number of N = 128 greylevels prior to tex- criminate Genotypic Origin in Bovine Meat. J Sci Food Agr 2005, ture analysis of white matter. This value represents a com- 85:629-632. 4. Chen W, Giger ML, Li H, Bick U, Newstead GM: Volumetric tex- promise for applying cooccurrence matrix calculations in ture analysis of breast lesions on contrast-enhanced mag- white matter texture studies for the two dimensional netic resonance images. Magn Reson Med 2007, 58:562-71. approach as well as for the three dimensional one. 5. Kato H, Kanematsu M, Zhang X, Saio M, Kondo H, Goshima S, Fujita H: Computer-aided diagnosis of hepatic fibrosis: preliminary evaluation of MRI texture analysis using the finite difference Conclusion method and an artificial neural network. AJR Am J Roentgenol 2007, 189:117-22. In this work we have demonstrated that the dynamic 6. Schad LR, Blüml S, Zuna I: MR tissue characterization of intrac- range on which texture features are evaluated, particularly ranial tumors by means of texture analysis. Magn Reson Imaging when using the cooccurrence matrix, can directly influ- 1993, 11:889-896. 7. Herlidou-Même S, Constans JM, Carsin B, Olivier D, Eliat PA, Nadal- ence the accuracy of classification of white matter regions. Desbarats L, Gondry C, Le Rumeur E, Idy-Peretti I, de Certaines JD: We found that rescaling the ROI to a dynamic range of MRI Texture Analysis on Texture Test Objects, Normal greylevels from 0 to 127 (i.e. N = 128) gives the best clas- Brain and Intracranial Tumors. Magn Reson Imaging 2003, 21:989-993. sification results using two dimensional cooccurrence 8. Mahmoud-Ghoneim D, Toussaint G, Constans JM, de Certaines JD: matrix CCOM represented by the mean value of the three "Three Dimensional Texture Analysis in MRI: a preliminary evaluation in gliomas". Magn Reson Imaging 2003, 21:983-987. slices (S1, S2, and S3). It also gives the best balance 9. Collewet G, Strzeleck M, Mariette F: Influence of MRI acquisition between sensitivity and specificity, using the three dimen- protocols and image intensity normalization methods on sional cooccurrence matrix 3DCOM. For both types of texture classification. Mag Reson Imaging 2004, 22:81-91. 10. Haralick RM, Shanmugam K, Dinstein I: Textural Features for matrices, the AUC of the ROC curve was maximum at N = Image Classification. IEEE T Syst Man Cy 1973, 3:610-621. 128. We conclude that a reduced user-defined dynamic 11. Swets W: Using discriminant eigenfeatures for image retrieval. IEEE PAMI 1996, 18(8):831-836. range can be faster, computationally less extensive, and 12. Materka A: MaZda and B11 User's Manual 1999–2002. [http:/ more efficient in separating texture classes. /www.eletel.p.lodz.pl/merchant/mazda/order1_en.epl]. Competing interests Pre-publication history The authors declare that they have no competing interests. The pre-publication history for this paper can be accessed here: http://www.biomedcentral.com/1471-2342/8/18/prepub Page 8 of 8 (page number not for citation purposes) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BMC Medical Imaging Springer Journals

The impact of image dynamic range on texture classification of brain white matter

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Copyright © 2008 by Mahmoud-Ghoneim et al; licensee BioMed Central Ltd.
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Medicine & Public Health; Imaging / Radiology
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Abstract

Background: The Greylevel Cooccurrence Matrix method (COM) is one of the most promising methods used in Texture Analysis of Magnetic Resonance Images. This method provides statistical information about the spatial distribution of greylevels in the image which can be used for classification of different tissue regions. Optimizing the size and complexity of the COM has the potential to enhance the reliability of Texture Analysis results. In this paper we investigate the effect of matrix size and calculation approach on the ability of COM to discriminate between peritumoral white matter and other white matter regions. Method: MR images were obtained from patients with histologically confirmed brain glioblastoma using MRI at 3-T giving isotropic resolution of 1 mm . Three Regions of Interest (ROI) were outlined in visually normal white matter on three image slices based on relative distance from the tumor: one peritumoral white matter region and two distant white matter regions on both hemispheres. Volumes of Interest (VOI) were composed from the three slices. Two different calculation approaches for COM were used: i) Classical approach (CCOM) on each individual ROI, and ii) Three Dimensional approach (3DCOM) calculated on VOIs. For, each calculation approach five dynamic ranges (number of greylevels N) were investigated (N = 16, 32, 64, 128, and 256). Results: Classification showed that peritumoral white matter always represents a homogenous class, separate from other white matter, regardless of the value of N or the calculation approach used. The best test measures (sensitivity and specificity) for average CCOM were obtained for N = 128. These measures were also optimal for 3DCOM with N = 128, which additionally showed a balanced tradeoff between the measures. Conclusion: We conclude that the dynamic range used for COM calculation significantly influences the classification results for identical samples. In order to obtain more reliable classification results with COM, the dynamic range must be optimized to avoid too small or sparse matrices. Larger dynamic ranges for COM calculations do not necessarily give better texture results; they might increase the computation costs and limit the method performance. Page 1 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 image properties on the stability of texture results and on Background Automated statistical and structural methods applied to the performance of the method [9]. Investigations of such digital medical images have shown that the amount of relationships eventually will lead to an optimized and quantitative information available in the image exceeds more reliable method for biomedical image analysis the capacity of the human visual system [1]. These meth- applications, which will require less processing time and ods assume that image greylevel relationships and spatial less extensive calculations. distribution are directly influenced by the properties of the underlying tissue, which themselves, are dynamic and It is commonly assumed in TA applications that increas- depend on biological and chemical composition. There- ing the image dynamic range on which texture is evalu- fore, minor image modifications can be quantified and ated improves textural feature representation; and monitored by appropriate methods even before they are consequently, gives better classification results. However, perceivable by the human eye. Such automated methods there is no evidence in biomedical image analysis litera- are collectively known as Texture Analysis (TA) [1]. ture to confirm or reject this assumption. The objective of the current work is to investigate the dependence of a Since the physical properties of tissues are the basis for commonly used TA method, the Cooccurrence Matrix operating imaging modalities, the reliability of the imag- (COM), on image dynamic range and matrix calculation ing output depends on the ability of the modality to pro- approach for classifying white matter regions. vide contrast between different tissues as well as local contrast that shows early changes in the physical-chemical Methods properties within that tissue. MRI is known to provide the Patients and MRI data best image contrast among the imaging modalities availa- In agreement with the French ethical legislation on clini- ble so far; therefore, MR images are believed to be rich in cal trials, whole brain MRI datasets were acquired in the digital information that can be exploited by TA and would sagittal plane for ten Glioblastoma patients (age = 53 ± be of important analytical and diagnostic utility. In recent 18; histologically confirmed by biopsy) using a Philips 3- years, Texture Analysis on Magnetic Resonance Images T Achieva MR system (Philips Medical System, Best, Neth- (MRI-TA) has been applied successfully in clinical and erlands). The imaging sequence used was Three-Dimen- experimental studies and is regarded as a reliable nonin- sional Gradient Echo (TR = 9.87 ms, TE = 4.56 ms, flip vasive tool of investigation, which combines the high con- angle = 8°). Field of View (FOV) = 256 mm × 256 mm, trast of MRI with the good sensitivity and specificity of TA. matrix size = 256 × 256, and a slice thickness of 1 mm, The quantitative texture data obtained from TA are relative gave isotropic voxel resolution of 1 mm . Transversal sec- rather than absolute; therefore, MRI-TA usually has to be tions were reconstructed from the original sagittal plane. followed by a standard classification method. Imaging procedures and clinical diagnosis were per- formed in Rennes University Hospitals, Rennes, France. It has been demonstrated with laboratory animals that in- vivo MRI-TA of muscles correlates with histology during Each patient showed a tumor mass developed within the degeneration and regeneration processes [2]. Direct rela- brain white matter. Three Regions of Interest (ROI)s were tionships between muscle contents of fat and collagen manually outlined in the normal white matter by a radi- were found using texture classification on high resolution ologist on a first transversal image Slice (S1) according to MRI [3]. MRI-TA has been clinically investigated on sev- relative distance of the region to the tumor: one Peritu- eral tissues such as breast lesions [4], and hepatic fibrosis moral White matter (PtWm) close to the visible margins [5]. Brain tissue also has been studied using MRI-TA [6-8]. of the tumor; and two Distant White matter (DWm) taken These studies recommended MRI-TA as a potential tool far from the tumor on both hemispheres (figure 1). Each for non-invasive investigations of cerebral tumors as well ROI contains of about 100–200 pixels. Volumes of Inter- as for healthy white and grey matter. In a previous work est (VOI)s were constructed by copying the ROI position on brain gliomas, we investigated peritumoral white mat- to the next two adjacent transversal slices (S2 and S3) pro- ter in regions defined by the radiologists as normal non- ducing volumes of about 300–600 voxels each. The VOI pathological tissues, but which were in the proximity of boundaries were inspected carefully to avoid overlapping visible tumor margins. MRI-TA classified these regions as structures. Only for one patient the location of the tumor a homogenous texture class, separate from the other white did not allow for outlining a PtWM. A total number of 89 matter regions which clustered in one broad class [8]. We ROIs and 29 VOIs were available for this study. suggested that this different texture could be due to invis- ible proliferation by tumoral cells [8]. Cooccurrence Matrices The Cooccurrence Matrix (COM) was first introduced by Since TA is based on calculations with image greylevels, it Haralick [10] along with 14 derived features; most of becomes crucial to understand the impact of changing them quantitatively describe image homogeneity and Page 2 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 DWm Rescaling to 32 greylevels PtWm MR image of Figure 1 brain glioblastoma and the surrounding white matter MR image of brain glioblastoma and the surrounding white matter. Transversal slice of MRI of brain glioblastoma showing Tumor, T; and the normal white matter regions (solid lines): PtWm, Peritumoral; and DWm, Distant White matter. An ROI and the corresponding matrix are linked (red dashed lines) to illustrate the rescaling process. Matrix A represents the original ROI which has a dynamic range from 0 to 255 greylevels. The matrix B shows the same ROI after multiplying each pixel with the ratio of the maximum greylevel value allowed in B (31 in this case) to the actual maximum greylevel value of A. Page 3 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 greylevels correlations. Some COM features have been 7.0, Math-Works Inc., Natick, MA, USA), on a PC with ® ® found to be discriminative, and therefore, can be used for Intel Pentium 4.0 processor and 1.24 Gb RAM. texture classification [10]. In a digital image, the number of bits-per-pixel (bp) coding determines the maximum Features Selection and Classification bp number of greylevels (N) in the image (2 = N). Hence, Features selection aims to identify the most discriminat- the allowed dynamic range of greylevels is from 0 to (N- ing parameters from each matrix that separate the differ- 1). ent classes most efficiently. Fisher-coefficient (F- coefficient) was calculated for this purpose, giving the The Classical approach of COM calculation (CCOM) sam- ratio of between class variance to within class variance [11] ples the probability density function P (i, j), which gives for each parameter. The ten parameters of the highest F- d, the probability of finding the two greylevels i and j at a coefficient were entered to Linear Discriminant Analysis distance d (d = 1,2,3,...) in the direction of angle ( = (LDA) for classification. LDA aims to find a linear trans- xy xy 0°, 45°, 90°, and 135°), on a two dimensional image form matrix such that the ratio of within-class scatter defined on the x- and y- axes. This calculation approach matrix to between-class scatter matrix is maximized. Such ignores useful spatial information that can be obtained a transform is composed of eigenvectors corresponding to from relationships between slices. Therefore, recent the largest eigenvalues of this ratio of matrices; more approaches try to maximize the usefulness of COM by details about the classification method can be found in including data at various angles on the z-axis. One of these [12]. Cross validation was performed using "leave-one- approaches is known as Three Dimensional Cooccurrence out" criterion, which works by leaving one observation Matrix (3DCOM) [8]. 3DCOM is calculated on image vol- (i.e one ROI) out of the classifier each time the classifica- umes composed of several adjacent slices, and involves tion model is recalculated and then project this observa- nine angles on the z-axis ( = 0°, 45°, 90°, 135°, 180°, tion into the model to test its validity. This process is 225°, 270°, 315°, and co-linear) in addition to angles . carried out for all observations. The percentages of False xy More details can be found in [8]. A Direction Independent Negatives (FN) and False Positives (FP) were evaluated. (DI) matrix results from summing COM over all angles. The Receiver Operating Characteristic (ROC) curve was This indicated in the notation below by = DI. analyzed, which represents the relationship between the '1-Specificity' and the 'Sensitivity' of the test. The Area In this work, both approaches are calculated: i) CCOM on Under the ROC Curve (AUC) is used to judge the separa- ROIs of the three adjacent slices (S1, S2, S3) giving three bility of the two classes for the given dataset and classifier. matrices CCOM-S1, CCOM-S2, and CCOM-S3, respec- An AUC of 1.0 represents a perfect classifier, while an AUC tively; and ii) 3DCOM on the VOI given by the three of 0.5 represents a random classifier. slices. For both approaches, the resulting matrix is always symmetric about its diagonal and of NxN size with N Features Selection was performed using B11 software (ver- number of entries. Five parameters were calculated from sion 3.2, 1999–2002 by Michal Strzelecki), which is each matrix: Angular Second Moment, Inverse Difference developed under the auspices of COST action B11 Euro- Moment, Entropy, Contrast and Correlation [10]. These pean project [12]. Linear Discriminant Analysis (LDA) five parameters were selected because they were found to was followed by cross validation and was performed using be good descriptors of white matter texture in a previous the software Minitab 15 ( 2007 Minitab Inc). The ROC curve was analyzed and AUC were calculated using SPSS work [8]. They provide the main information about image homogeneity and the existence of correlated patterns in 15.0 ( 1989–2006 SPSS Inc). the image. Results and discussion The original MR images are usually digitized over 16 bits- LDA classification on PtWm and DWm white matter per-pixels (65536 greylevels). It is computationally exten- regions always separated PtWm into a distinct homoge- sive and time consuming to calculate COM over such a nous class. This class was well distinguished for small as large dynamic range. Therefore, it is a standard procedure well as for large dynamic ranges for all matrices. However, in medical image analysis to apply a quantization process the number of classification errors between the two in order to reduce the original range to a user-defined classes depended remarkably on the dynamic range along value of N. This is done by scaling the original pixel values with COM approach used. Table 1 represents the percent- with the ratio between the maximum greylevel allowed in age of False Negatives (FN: PtWm classified as DWm) and the rescaled image and the actual maximum greylevel in False Positives (FP: DWm classified as PtWm) for each the original image (figure 1). Prior to COM calculations, number of greylevels N and matrix calculation approach. each ROI is rescaled for five different values of N, (N = 16, The average errors and standard deviation (Mean ± SD) 32, 64, 128, and 256). All texture calculations and image for CCOM-S1, CCOM-S2, and CCOM-S3 over the three processing methods were implemented using Matlab (ver Page 4 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 Table 1: Classification results using cross-validated LDA and for Peritumoral White matter (PtWm) classified as Distant White matter (DWm) (False Negative: FN). 16-GL 32-GL 64-GL 128-GL 256-GL FN% FP% AUC FN% FP% AUC FN% FP% AUC FN% FP% AUC FN% FP% AUC CCOM-S1 22.00 15.00 0.82 33.00 5.00 0.81 33.00 10.00 0.785 11.00 5.00 0.915 22.00 15.00 0.815 CCOM-S2 55.00 25.00 0.60 25.00 44.00 0.655 33.00 20.00 0.735 33.00 10.00 0.785 22.00 10.00 0.84 CCOM-S3 33.00 20.00 0.735 33.00 10.00 0.785 11.00 15.00 0.87 11.00 10.00 0.895 22.00 10.00 0.84 Mean ± 36.67 ± 20.00 ± 0.71 30.33 ± 19.67 ± 0.75 25.67 ± 15.00 ± 0.8 18.33 ± 8.33 ± 0.87 22.00 ± 11.67 ± 0.83 SD 16.80 5.00 5 4.62 21.22 12.70 5.00 12.70 2.89 0.00 2.89 3DCOM 22.00 10.00 0.84 22.00 20.00 0.79 33.00 10.00 0.785 11.00 10.00 0.895 44.00 5.00 0.755 DWm classified as PtWM (False Positive: FP); using five dynamic ranges (N = 16, 32, 64, 128, and 256). FN and FP are represented as percentage errors. AUC for each ROC curve is also demonstrated. CCOM: Classical Cooccurrence Matrix calculated on slices: -S1, -S2, and -S3. 3DCOM: Three Dimensional Cooccurrence Matrix. Mean ± SD the average and standard deviation of results for CCOM-S1, CCOM-S2, and CCOM-S3. GL: Greylevels. LDA: Linear Discriminant Analysis. AUC : Area Under the Receiver Operating Characteristic (ROC) Curve. slices is also presented and will be used for comparison former (figure 2a). This balance is lost at other values of N with 3DCOM. (figure 2b). The Mean CCOM method on the three slices (-S1,-S2,-S3) shows the highest sensitivity and specificity Analyzing table 1 shows that the Mean FN or FP of CCOM at N = 128 (figure 2b). For either CCOM or 3DCOM, fig- (-S1,-S2,-S3) decreases progressively with increasing N ure 2 demonstrates that the specificity of the method is until reaching N = 256 for which it increases again (table always higher than its sensitivity. The Area Under the ROC 1). For 3DCOM, the lowest value of FN occurs at N = 128, Curve (AUC) represents a comprehensive measure for which was less than those obtained from Mean CCOM for evaluating the accuracy of the classifier (table 1). By com- any other N. The most discriminating parameters for this paring AUCs of the Mean value of the three CCOMs and analysis and their F-Coefficients are presented in table 2. those of 3DCOM, it can be shown that the highest AUC The percentage of FN shows a considerable increase when value was obtained for 3DCOM at N = 128, while the low- 3DCOM is calculated for N = 256; however, FP represents est was obtained for Mean CCOMs at N = 16 (figures 3a the lowest percentage obtained (table 1). and 3b, respectively). It can also be shown that the highest value of AUC among Mean CCOMs was obtained also at The bar graph of test outcomes measures (sensitivity and N = 128 (table 1). specificity) (figure 2) demonstrates a balanced tradeoff between the sensitivity and specificity of the 3DCOM In this study, PtWm clustering as a separate white matter method at N = 128 and N = 32 with higher values at the region is consistent with previous findings [8]; however, we demonstrate in the current work that classification accuracy is highly dependent on the dynamic range of Table 2: The ten most discriminating parameters, according to image quantization for both COM calculation approaches the Fisher (F-) coefficient, between the two white matter classes (Peritumoral white matter and distant white matter). (CCOM and 3DCOM). Also, we can see that classification results among different slices might give diverse results in Most Discriminating Parameters F-Coefficient spite of carrying out the analyses on identical positions. This can be demonstrated for FN at N = 16 that gave 22% Entropy_ = 0° 3.0972 on CCOM-S1 and 55% on CCOM-S2. Angular Second Moment_ = 135° 2.2651 Entropy_ = DI 1.9090 Entropy_ = 135° 1.8852 It can be also shown that calculating 3DCOM on small Angular Second Moment_ = 0° 1.8002 dynamic ranges (N = 12, 32 and 64) does not enhance Angular Second Moment_ = 45° 1.7164 classification as long as the dynamic range remains rela- Angular Second Moment_ = 90° 1.6279 tively small. In contrast, 3DCOM on a larger dynamic Angular Second Moment_ = DI 1.5740 range (N = 128) enhances classification remarkably, but a Entropy_ = 45° 1.4461 further increase of N worsens the method's sensitivity. Contrast_ = DI 1.0305 Although method's specificity has increased at N = 256, the tradeoff between sensitivity and specificity remains an Using Three-Dimensional Cooccurrence Matrix (3DCOM) for a number of greylevels N = 128. important factor to take into account when evaluating the DI: Direction Independent method's performance. Therefore, N = 256 is probably : The angle of the parameter. not a good choice for 3DCOM analysis. Page 5 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 (a) (b) Sen Figure 2 sitivity and specificity bar graphs Sensitivity and specificity bar graphs. Sensitivity and specificity bar graphs for (a) 3DCOM on white matter VOIs; and, (b) The Mean value of (CCOM) on the individual slices ROIs (-S1, -S2, and -S3). CCOM: Two Dimensional Classical Cooccurrence Matrix. 3DCOM: Three Dimensional Cooccurrence Matrix. VOI: Volume of Interest. ROI: Region of Interest. Page 6 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 a) b) ROC curves showing the highest and lowest A Figure 3 UC ROC curves showing the highest and lowest AUC. Receiver Operating Characteristic (ROC) curves showing: a) the highest Area Under the Curve (AUC) (= 0.895) which was obtained using 3DCOM at N = 128; and, b) the lowest AUC (= 0.715) obtained using the Mean CCOMs at N = 16. CCOM: Two Dimensional Classical Cooccurrence Matrix. 3DCOM: Three Dimensional Cooccurrence Matrix. Page 7 of 8 (page number not for citation purposes) BMC Medical Imaging 2008, 8:18 http://www.biomedcentral.com/1471-2342/8/18 The relationship between the dynamic range and classifi- Authors' contributions cation accuracy can be related to COM characteristics. This DMG has designed the study, implemented the texture 7.0, acquired data, analyzed matrix, by definition, is a probability density matrix of analysis methods on Matlab unit sum. Decreasing the dynamic range means that the results, and drafted the manuscript. MKA has participated original ROI will be reduced to smaller adjoining values in the programming procedures. JDC has set and super- of greylevels as shown in figure 1; therefore, cooccurrence vised the protocol of MR image acquisition in Rennes matrix will be smaller and the joint probabilities will be University Hospitals according to rules and regulations set estimated for a limited number of matrix entries (eg. N = by Ethics Committees. FMG has participated in results 16, COM size = 16 × 16 = 256 entry). This could be insuf- analysis and critical revision of the manuscript. ficient to represent texture features and may result in higher classification errors. On the other hand, increasing Acknowledgements This work has been achieved in coordination with COST European project the dynamic range will spread the greylevels over a larger Action B21 "Physiological modelling of MR image formation". It has been scale producing matrices with sufficient number of presenting during COST B21 Meeting in Bled, Slovenia, 2007. entries; and then, discriminating texture features would have more chance to appear; consequently, this would A part of this work has been funded by United Arab Emirates University, reduce the percentage error. Further increase of N values Research Grant number: 01-02-2-11/07. produces sparse matrices with probabilities broken down over a huge number of entries (65535 for N = 256); in The authors would like to thank Biatrice Carsin, for MRI acquisition (CHRU Pontchaillou), and Pierre-Antoine Eliat for technical assistance (Rennes I other words, feature representation would be weakened University). and classification errors increased. It merits to mention that the processing time for calculating 3DCOM using N References = 128 was within a fraction of a second, while it took 1. Castellano G, Bonilha L, Li LM, Cenes F: Texture analysis of med- almost 30 seconds for calculating the same matrix using N ical images. Clinical Radiology 2004, 59:1061-1069. = 256. The increase in processing time is even more signif- 2. Mahmoud-Ghoneim D, Cherel Y, Lemaire L, de Certaines JD, Mani- ere A: Texture analysis of Magnetic Resonance Images of rats icant for larger VOIs. muscles during atrophy and regeneration. Magn Reson Imaging 2006, 24:167-171. 3. Mahmoud-Ghoneim D, Bonny JM, Renou JP, de Certaines JD: Ex- From these results, we recommend quantizing image vivo Magnetic Resonance Imaging Texture Analysis Can Dis- ROI/VOI to a number of N = 128 greylevels prior to tex- criminate Genotypic Origin in Bovine Meat. J Sci Food Agr 2005, ture analysis of white matter. This value represents a com- 85:629-632. 4. Chen W, Giger ML, Li H, Bick U, Newstead GM: Volumetric tex- promise for applying cooccurrence matrix calculations in ture analysis of breast lesions on contrast-enhanced mag- white matter texture studies for the two dimensional netic resonance images. Magn Reson Med 2007, 58:562-71. approach as well as for the three dimensional one. 5. Kato H, Kanematsu M, Zhang X, Saio M, Kondo H, Goshima S, Fujita H: Computer-aided diagnosis of hepatic fibrosis: preliminary evaluation of MRI texture analysis using the finite difference Conclusion method and an artificial neural network. AJR Am J Roentgenol 2007, 189:117-22. In this work we have demonstrated that the dynamic 6. Schad LR, Blüml S, Zuna I: MR tissue characterization of intrac- range on which texture features are evaluated, particularly ranial tumors by means of texture analysis. Magn Reson Imaging when using the cooccurrence matrix, can directly influ- 1993, 11:889-896. 7. Herlidou-Même S, Constans JM, Carsin B, Olivier D, Eliat PA, Nadal- ence the accuracy of classification of white matter regions. Desbarats L, Gondry C, Le Rumeur E, Idy-Peretti I, de Certaines JD: We found that rescaling the ROI to a dynamic range of MRI Texture Analysis on Texture Test Objects, Normal greylevels from 0 to 127 (i.e. N = 128) gives the best clas- Brain and Intracranial Tumors. Magn Reson Imaging 2003, 21:989-993. sification results using two dimensional cooccurrence 8. Mahmoud-Ghoneim D, Toussaint G, Constans JM, de Certaines JD: matrix CCOM represented by the mean value of the three "Three Dimensional Texture Analysis in MRI: a preliminary evaluation in gliomas". Magn Reson Imaging 2003, 21:983-987. slices (S1, S2, and S3). It also gives the best balance 9. Collewet G, Strzeleck M, Mariette F: Influence of MRI acquisition between sensitivity and specificity, using the three dimen- protocols and image intensity normalization methods on sional cooccurrence matrix 3DCOM. For both types of texture classification. Mag Reson Imaging 2004, 22:81-91. 10. Haralick RM, Shanmugam K, Dinstein I: Textural Features for matrices, the AUC of the ROC curve was maximum at N = Image Classification. IEEE T Syst Man Cy 1973, 3:610-621. 128. We conclude that a reduced user-defined dynamic 11. Swets W: Using discriminant eigenfeatures for image retrieval. IEEE PAMI 1996, 18(8):831-836. range can be faster, computationally less extensive, and 12. Materka A: MaZda and B11 User's Manual 1999–2002. [http:/ more efficient in separating texture classes. /www.eletel.p.lodz.pl/merchant/mazda/order1_en.epl]. Competing interests Pre-publication history The authors declare that they have no competing interests. The pre-publication history for this paper can be accessed here: http://www.biomedcentral.com/1471-2342/8/18/prepub Page 8 of 8 (page number not for citation purposes)

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Published: Dec 23, 2008

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