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It was demonstrated that statistical analysis of bacteria colonies Fresnel patterns recorded in the optical system with converging spherical wave illumination is suitable for highly effective bacteria species classification. The proposed method includes Fresnel patterns recording followed by image processing and the statistical analysis based on feature extraction, feature selection, classification and classification performance methods. Examination performed on various bacteria species (Salmonella enteritidis, Staphylococcus aureus, Staphylococcus intermedius, Escherichia coli, Proteus mirabilis, Pseudomonas aeruginosa and Citrobacter freundii) revealed that the proposed method achieved very high accuracy of over 98%.
©2013 Optical Society of America
1. Introduction
Increasing number of microbes identified as possible food and waterborne pathogens is present in the surrounding environment. Therefore, the early detection and classification of bacteria is an important issue in life sciences, health safety and food protection. The risk of microbial contamination, increasing bacterial resistance to the commonly used antibacterial agents, as well as possible biohazard cause that the new modalities to detect and combat pathogenic microbes are in focus of many international and national projects [1–6]. It is also important in agriculture [7].
The identification of bacteria species is a difficult, time and resources consuming task. There are some attempts to identify bacteria by means of biochemical, molecular or immunological techniques. However in spite of their high sensitivity, they are also time-consuming, need high quality reagents and very pure samples, which makes them expensive. Moreover, the most sensitive methods as the PCR (Polymerase Chain Reaction) can take up to seven days to identify particular bacteria species, what for example in hospital condition may lead in extreme cases even to patient’s death [8].
Various optical methods as e.g. bacterial cells detection in water suspension by forward and backward light scattering [9,10], infrared [11] and fluorescence spectroscopy [12–15], flow cytometry, chromatography, chemiluminescence [16], bioconjugated biomolecules [17,18] or surface plasmon resonance (SPR) [19,20] were proposed, as well. Although they offer the possibility of non-invasive, non-destructive and non-contact examination of bacterial samples, they exhibit similar disadvantages as previous techniques, including demanding time-consuming preparation of high quality samples and necessity to use equipment with high sensitivity and spectral resolution.
Recently, it was demonstrated that the analysis of forward light scattering on bacterial colonies grown on solid nutrient media can be used for identification of different bacteria species [21–27]. Contrary to the other methods, there is no need for special and labor intensive preparation of bacteria samples. Based on these predictions, in our previous works we have demonstrated that the analysis of bacterial colonies Fourier spectra, considered in general as diffraction patterns, can be used to evaluate the bacterial colonies number [28–30]. Moreover, we have proposed to use an optical system with converging spherical wave illumination for bacteria identification based on recorded Fresnel patterns [31], which according to our knowledge were not analyzed. Obtained results have shown that colonies of a different bacterial species generate specific Fresnel diffraction signatures with unique features, which can be exploited for species classification [31].
The potential use of diffraction patterns in microbiological diagnosis is limited by the features that can be used by bacterial species classifiers. Previously performed by other authors examinations were based on the analysis of pseudo-Zernike moments and Haralick’s texture features of forward light scattering patterns of bacterial colonies [25,32]. Feature vector composed of pseudo-Zernike and Haralick-based features was extracted and used for the classification process. Performed analysis, in contrast to the existing work assumes spectrum partitioning into regions of interest and calculation of the feature values of different regions of the spectrum, so that for one spectrum and one feature we have several values. In addition, we do not rely on the features described in [25]. We also compared other classifiers performance. Obtained identification results were more accurate and less than 20 features was needed to build our models in contrary to those reported in [25]. Comparative analysis of the two methods, both in terms of the optical system and data analysis will be the subject of a future studies.
In this paper, we propose novel application of the image processing and statistical analysis methods to examine Fresnel patterns of bacterial colonies, which enable highly effective determination of bacteria species. The paper covers whole process form optical system configuration, through pattern registration, image analysis and processing finally followed by statistical analysis and presentation of obtained results. Data obtained with optical system were processed, partitioned into 3, 5 and 10 disjoint areas, in order to extract features needed for the classification and then analyzed with use of three classification algorithms, with and without normalization of the data. Results were verified by cross-validation classification error estimation and with use of multi-class sensitivity and specificity measures.
2. Materials and methods
2.1 Bacterial colonies samples preparation
In this work seven bacteria species, were examined: Salmonella Enteritidis (ATCC 13076), Escherichia coli (PCM O119), Staphylococcus aureus (PCM 2267), Staphylococcus intermedius (PCM 2405), Citrobacter freundii (PCM 531), Proteus mirabilis (PCM 547) and Pseudomonas aeruginosa (ATCC 27853). The cultures were obtained from the microbiological laboratory of the Department of Epizootiology and Veterinary Administration with Clinic of Infectious Diseases of the Wroclaw University of Environmental and Life Science. Bacteria suspensions were first incubated for 18 hours at the temperature of 37°C. Respective dilutions were seeded on the surface of the solid nutrient medium in Petri dish, so as to obtain 12-20 colonies per plate, and were again incubated at 37°C for the next 11 hours. The bacteria colonies were grown on Columbia agar (Oxoid).
2.2 Optical system for analysis of light diffraction on bacterial colonies
The configuration of the proposed optical system with converging spherical wave illumination for analysis of light diffraction on bacterial colonies is shown on Fig. 1. Its properties were analyzed widely in [31]. It includes the laser diode module (LS) (635 nm, 1 mW, collimated, Thorlabs), natural density filter F (optical density: 0-4.0, Edmund Optics), linear polarizer P (Thorlabs), beam expander BE (Edmund Optics, 4X), iris diaphragm (D), transforming lens L0 (achromatic doublet, focal distance: 48.6 cm, clear aperture: 6.35cm, Edmund Optics), XYZ sample positioning stage with Petri dish (S), which enables the adjustment of uniform illumination of the single bacteria colony, CMOS camera C (EO-1312, Edmund Optics) and computer (K). In this configuration bacterial colony is illuminated by converging spherical wave generated by transforming lens in order to control lateral scale changes of diffraction patterns. The sample S was located in the distance 8 cm from the back-surface of transforming lens L0 and the CMOS camera in the distance 26 cm.
Fig. 1 The configuration of the optical system for bacteria species classification based on Fresnel diffraction patterns
Recorded patterns are 8 bits, gray scale images with 1280 by 1024 pixels each. The diameter of light beam was approximately equal to the diameter of bacterial colony. Exemplary Fresnel patterns of bacterial colonies are presented on the Fig. 2.
2.3. Classification vs. Identification
It is very important to differentiate between classification and identification concepts. By classification we understand process of building statistical classifiers, basing on diffraction patterns features, and using them for prediction of unknown bacteria species, while identification is only prediction of unknown bacteria species. Therefore identification can be assumed as final part of classification. Therefore terms will be used alternatively when it comes to obtained results.
2.4 Image analysis
The presented analysis workflow consists of image processing with normalization, followed by an analysis of the extracted diffraction patterns features (see Fig. 3). Performed studies were based on differences between Fresnel patterns of different species. The proposed image processing enables future extraction from the recorded Fresnel diffraction patterns and uses it in the classification process. Previously, we have demonstrated that statistical analysis consist of classification, feature selection and classifier performance assessment methods in case of 4 various bacteria species gave 5.47% the classification error [33].
Fig. 3 Workflow of the performed studies of the bacteria species Fresnel diffraction patterns, with split into two statistical analysis workflows. Workflow contain normalization as an optional step.
To obtain more accurate results we applied two independent enhancements into previously proposed analysis workflow [19,20]. The first one is normalization of the recorded Fresnel patterns of bacterial colonies as a preprocessing stage of the analysis, while the second is an addition to the previously proposed statistical apparatus. The new ones are Quadratic Discriminant Analysis (QDA), Support Vector Machine (SVM) and Analysis of Variance (ANOVA), sensitivity and specificity measures. The complete workflow of the performed studies is depicted in the Fig. 3.
To examine influence of the normalization on the classification results, the workflow from Fig. 3 was performed twice: with and without normalization step. The diagram will be explained in details further in the text.
2.5 Image processing
The recorded Fresnel patterns of bacterial colonies have been processed by the dedicated macro written in ImageJ free software (http://rsb.info.nih.gov/ij/) [34,35].
2.5.1. Preprocessing
The macro was written to distinguish the center and edges of the diffraction patterns. The Fresnel patterns contain set of the diffraction rings, where the number, size and spatial structure of these rings depend on the bacteria species. The set of diffraction rings is correlated with the morphology of colony and with its amplitude and phase properties, which are unique for each species (see Fig. 4). Previously, we have demonstrated that it is necessary to analyze the concentric annulus-shaped zones of the patterns which further will be called rings to extract the unique features of the diffraction patterns of a different bacteria colonies expressed by a discrete pixel intensities of Fresnel patterns [33]. We have compared partitioning of the Fresnel patterns into 3, 5 and 10 equal thickness rings. Data consist of mean value and standard deviation for each of analyzed rings, named mean.n and sd.n for ring number n. That makes 2n features for n ring partitioning. 3, 5 and 10 rings partitioning was chosen, as visual inspection showed that there are no less than 3 rings and no more than 10 rings in intrinsic structure split of the Fresnel patterns under study. All diffraction patterns were recorded in the same optical system configuration under the same strictly controlled conditions. Examples of 10 rings partitioning of various Fresnel patterns are shown on the Fig. 4. The examples of split patterns show differences in the location and size of each pattern. A special ImageJ macro with human interaction to mark center, edges and perform partitioning of each pattern, was written [35]. The Fresnel patterns were stored as RGB images with the information about the center, edges and partitioning in a green channel, while red and blue channels contained the original patterns.
2.5.2 Normalization
In order to avoid errors related to human and laboratory factors (e.g. recording Fresnel patterns by multiple laboratory workers or in slightly different conditions) the normalization as a preliminary step, is performed. Some small differences in background intensity can be observed on Fig. 2 and Fig. 4. Normalization process was carried out under the assumption of a black (of 0 intensity value) background of each pattern. The mean values of the intensities of pixels belonging to the background (beyond the pattern edges) were calculated separately for each pattern and the value was set as the left edge of the stretched histograms. The histogram stretching was performed accordingly to the standard algorithm that transforms pixel intensities values according to the formula:
where original and new denote original and new pattern pixel values respectively [36,37]. Figure 5 demonstrates the obtained results of this step.2.5.3 Feature extraction
The following features were analyzed: mean called mean.n and standard deviation called sd.n values of pixel intensities within each of the rings, where n denotes ring number starting from the center of the colony diffraction pattern. In other words mean.5 is a set of the values calculated as the means of the pixel intensities-in the fifth ring of each pattern, while sd.7 is a set of the values calculated as the standard deviations of the pixel intensities in the seventh ring of each pattern. In this way, 20 classification features for each image were obtained. For each bacteria species about 50 Fresnel patterns were analyzed (see Table 1).
Table 1. Number of patterns analyzed for various bacteria species.
2.6 Statistical methods
All statistical methods mentioned below were performed with use of the R free software [38].
2.6.1 Analysis workflow
Two statistical analysis workflows were designed and applied (see Fig. 3). The first consisted of a classical split into learning and test sets and cross-validation performance assessment along with sensitivity and specificity. The second one started from ANOVA as a feature selection method followed by cross-validation used as an error estimator along with sensitivity and specificity. Both analysis workflows were applied to normalized and non-normalized pattern data.
Learning set contained 3/4 of the observations (patterns), while the test set contained the rest of the data. The split was made randomly on the whole data set without taking into consideration information about the class (bacteria species), which means that different (random) number of observations was taken from different classes.
Additional analysis, containing part of the workflow, was performed on full data after partitioning patterns into 3, 5 and 10 rings with and without normalization. This part was designed and applied to show which partitioning is best for identification purposes. The analysis consists of cross-validation, sensitivity and specificity measures.
2.6.2 Classification methods
Three classification algorithms were exploited. The obtained results were later verified by a classifier performance assessment method. The following classification methods were performed: Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA) and Support Vector Machine (SVM), while classifier performance assessment was cross-validation (CV) [39,40].
LDA is one of the classical object classification methods based on solid statistical foundations. The method tries to separate two or more classes by linear decision boundaries. These boundaries are constructed with the use of a linear combination of the feature values. Although multidimensional normality assumption is required, LDA is known to be robust to violation of this assumption [39,40].
QDA is based on the same statistical assumptions that LDA, except the one about identical covariance between classes. QDA separates classes with quadratic surface which is calculated with the use of the features [39,40].
SVM is a method in which the optimal hyperplane for linearly separable classes has to be found. Method is extended to classes that are not possible to be linearly separated with the use of kernel function to map the original data into new space, possibly of higher dimensionality. SVM finds the optimal hyperplane between classes by maximizing the margin between the hyperplane and the support vectors, which are the data points that lie closest to the decision surface [39,40].
2.6.3 Feature selection
For each pattern 20 features (20 values) and number of observations (352 patterns) are used for building classification models. Some features differentiate examined patterns better than the other ones. Feature selection methods allow to evaluate, which features differentiate groups better. Therefore, ANOVA (analysis of variance) was used to compare mean values of numerical variables (features) in groups determined by a factor variable (bacteria species). ANOVA is called analysis of variance but its objective is to compare mean values of the particular feature between the groups.
Single factor one way ANOVA was used to find the most discriminative features. The most discriminant features have the most significant differences between their means in classes. For each continuous feature we tested the hypothesis that mean values of this feature are equal for all analyzed groups of bacteria. For each feature the F-value is calculated as F = MSB/MSW, where MSB and MSW are mean squares between and within groups, respectively. The p-value from ANOVA was used to measure significance of F-value: the lower is p-value (Pr(> F)), the better is the separation. Features were then sorted using this separation measure.
To visualize feature selection performance we decided to use boxplot charts. Here, the single box is ranged from top and bottom by hinges that denote quartiles, upper and lower respectively, while the line in the middle is placed on the level of the median value. The whiskers show the largest/smallest observation that falls within a distance of about 1.5 times the box size from the nearest hinge. If any observation falls farther, it is considered as an extreme value (outliers) and it is shown separately [41].
2.6.4 Classifier performance assessment
As it is not possible to use standard performance measures (like sensitivity and stability) for seven classes, cross-validation (CV) was chosen as classifier performance assessment method. CV is a technique for determining how the results of the classification will work for other, independent data sets. In other words – CV estimates the unknown prediction error. CV splits the data set into two complementary subsets (learning and test sets) and performs classification analysis. These two steps are applied given number of times to the whole data set and, as a result the classification error is estimated. In our analysis, 100 repetitions for each classifier and data before and after the normalization were performed.
Sensitivity and specificity are well known statistical measures of the performance of a binary (two class e.g. case and control) classification test. As we are dealing with multi-class case (7 classes) sensitivity and specificity cannot be calculated in the ordinary way. The most widely accepted method of calculating those measures in multi-class case is to treat one of classes as case class and combine the rest of the classes as the control class. In this simple way the binary definition can be applied as many times as we have classes. Averaged values of sensitivity and specificity over all of classes give measures for the whole experiment. We did not calculate accuracy of the classification as it is equal 1-CV error.
3. Results
3.1 Pattern partitioning
To confirm our previous conclusion that 10 ring partitioning gives best identification results, we performed additional experiments for three classifiers and all of proposed partitioning schemes into 3, 5 and 10 rings. Collected results are sensitivity, specificity and cross-validation error for the full model for each of the partitioning with and without normalization are depicted in Table 2. Additionally we averaged obtained results over classifiers, to show that mean results are best for 10 partitioning.
Table 2. Sensitivity, specificity and cross-validation error for full model for proposed diffraction pattern partitioning into 3, 5 and 10 rings with and without normalization.
For QDA and SVM classifiers cross-validation errors decrease with fixed partition number increase in both non-normalized and normalized case. This is confirmed by averaged results. For LDA the error is comparable for 3 and 10 ring partitioning in both normalized (5,29% and 5,10%) and non-normalized (8,51% and 8,56%) case in contrast to QDA and SVM. The table also shows that LDA error is smallest for normalized, 10 rings partitioning case and that it gave the worst results of all classifiers in all except one case (non-normalized, 3 ring partitioning). This shows that linear classifier is not suitable for the data set under study. The smallest errors and the highest values of sensitivity and specificity measures were obtained in 10 ring partitioning cases with and without normalization (marked as gray background), which suggests that this is the most appropriate fixed partitioning for the proposed bacteria identification method. The table also suggests that QDA will show to be the best of examined classifiers as it gives the smallest errors and highest sensitivity. That conclusion will be verified by the further results.
Further analysis results are obtained for fixed 10 ring partitioning, which according to Table 2 gives the most accurate classification results.
3.2 Classification and cross-validation I
Exemplary run of identification with learning and testing sets split was performed. Data set (352 patterns) was randomly split into learning and test sets containing ¾ (264 patterns) and ¼ (88 patterns) of the data respectively. The identification results are shown in the Table 3. Single run results depend on the split and are presented as an example only. Any conclusion drawn from them will not be reliable because of the randomness of the split. To calculate misclassification errors presented in next parts of the paper we repeated classification multiple times and averaged the errors.
Table 3. Results (accuracy of identification) of exemplary, single run of identification analysis with data split into learning and test sets.
The LDA classification led to comparable results for the cases with and without normalization of the data set, which can be observed in the Table 3. For 88 observations that were included into the test set, the normalized data gave 13 misclassification errors, which gives 85.23% of correctly classified patterns, while non-normalized data gave 11 misclassification errors, which gives 87.50% of correctly classified patterns. LDA classification method gave us worst result, comparing to QDA and SVM. It was expected that for seven classes it is not possible to classify patterns with high accuracy with the use of a simple, linear classification model. Therefore, more complex QDA and SVM classification models were proposed for the task.
QDA classification conducted after the normalization step, resulted in building more accurate classifiers. Obtained results for non-normalized and normalized data are also depicted by Table 3. For non-normalized data QDA analysis gave 16 misclassified patterns (81.82% were correctly classified), while the same analysis for the normalized data set gave only 11 errors (87,50% were correctly classified).
Further, the SVM classification was performed. The SVM classifier can take kernel parameter, which denotes kernel function used in training and predicting. Effectiveness of the classifier depends on kernel function. We used SVM with kernel parameter set to radial value. It was shown that in the case of non-normalized data 16 diffraction patterns were classified wrongly, which gave 81,82% of accurate classification. In the case of the normalized data only 10 misclassified diffraction patterns were noticed, which means 88,64% of accurate classification.
It was demonstrated that normalization process leads to better classification in case of QDA and SVM methods. Those results were confirmed for multiple repetitions of the analysis.
Table 4 depicts the results achieved by exploiting 100-fold cross-validation estimator of misclassification error. The best classification performance of almost 97% accuracy was stated for SVM classifier and normalized data.
Table 4. Cross-validation errors, sensitivity and specificity measures for three classifiers and data set with and without normalization
3.3 Feature selection
ANOVA feature selection results for non-normalized data are shown on the Fig. 6 and for normalized data on the Fig. 7. Results were sorted according to the separation measure mentioned before and in bar charts below they are showed from the best to worse. The best Fresnel pattern features (Table 5 and Table 6) were used to build LDA, QDA and SVM classification models [41].
Fig. 6 ANOVA (F value) feature selection results for non-normalized data. The features are ordered from best to worst.
Fig. 7 ANOVA (F value) feature selection results for normalized data. The features are ordered from best to worst.
Table 5. CV error estimation, sensitivity and specificity for best fitted classification models after ANOVA feature selection for non-normalized data
Table 6. CV error estimation, sensitivity and specificity for best fitted classification models after ANOVA feature selection for normalized data.
Two most representative plots illustrating separation of classes are shown in the Fig. 8 and Fig. 9. Figure 8 presents a comparison of basic statistics of the sd.4 feature from the normalized data set for all of bacteria species under study, while Fig. 9 presents the same comparison for the sd.10 feature. The sd.4 feature, which denotes standard deviation of a fourth ring, counting from the center of the patterns, was the one, according to ANOVA analysis, that separated the groups in the best way. The sd.10 feature, which denotes standard deviation of a tenth ring is the worse one for the group differentiation. One can see from the Fig. 9 that sd.10 feature cannot separate bacteria species as six of seven boxes are overlapping and some of them even include one another. That is why it is usually better to build classification model based on a subset of features, since it makes possible to remove data that do not help in class differentiation. Contrary, the Fig. 8 demonstrates clearly that the patterns (bacteria species) are well separated. It can be confusing that lines in the boxes of some species are on similar level but one has to remember that the line denotes median not mean value of the feature and that other features included in the classification model may distinguish these particular classes better while the sd.4 feature is the best for separation of all of the species under study.
3.4 Classification and cross-validation II
Classifier performance assessment of the classification models build after feature selection was the last step in the analysis of the Fresnel diffraction patterns. CV, sensitivity and specificity were calculated as it was above described (for learning and test sets split) but the models were built on the features listed in Table 5 and Table 6. The estimated misclassification errors obtained by CV and averaged for all bacteria species sensitivity and specificity measures are also presented in Tables 5 and 6.
As it was expected, errors were smaller for all classifiers than it was in the case of models built upon all available data (compare Table 4). LDA was again not a sufficient method for the task and gave worst results. Best fitted SVM model for normalized data gave smallest error among all performed SVM classifications. The same situation was observed for QDA model, which gave the best result of all tested classifiers.
Sensitivity measure also point QDA as the best of the models. In every case QDA gave highest sensitivity value. The specificity for non-normalized data is comparable between the models, thus SVM gave best result. The specificity value for normalized data differs on third significant digit, which makes all the models equally effective in correct identification of negative cases. QDA model built for the normalized data was classified with only 1.43% error. Additionally the QDA model build on the normalized data is simplest of all built models, it consist of only 13 features of 20 available. It is a common knowledge that simple models are easier for interpretation. Therefore we suggest that QDA is the best classifier for the task of bacteria species identification.
4. Conclusion
The performed study revealed that well known classification methods like the QDA and SVM are suitable techniques for identification of bacteria species based on their colonies' Fresnel diffraction patterns recorded in the proposed optical system with converging spherical wave illumination. The study demonstrated that the proposed method is not expensive, fast and reliable, and gives 98% identification accuracy in just 36 hours from sample acquiring. This period of time is associated with the process of bacteria sample (bacterial cells solutions and bacterial colonies) preparation and can be limited by decreasing the time of bacterial colonies incubation. Moreover, it should be pointed out that this step of bacteria samples preparation is a standard procedure in all bacteria detection methods, so that proposed technique can be used as first-step method for bacteria species identification. Non-destructive and non-contact character of this investigation enables obtained results verification by other techniques, if it will be necessary. Performed analysis and achieved results demonstrated that it is possible to distinguish the bacteria species even of the same genus (Staphylococcus) with high reliability. It was shown that the normalization process allows achieving better results and the construction of simpler classification models being more accurate as the complex ones. Practical application of the method can be very wide. Therefore, our research will be continued in order to determine final semiauthomatic method that can be offered to microbiologic laboratories. Further analysis research is needed. Other, more interpretable features of the patterns should be examined along with different optical system configurations. Works will also be focused on the limitation of bacterial colonies incubation, which can significantly improve the performance of proposed method.
Acknowledgments
This work was partially supported by the Research Grant from the Polish Ministry of Science and Higher Education (No N N505 557739). The support of the European Union under the European Social Fund (No DG-G/2733/11) is gratefully acknowledged, as well.
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