A FACE RECOGNITION FRAMEWORK USING SELF-ADAPTIVE DIFFERENTIAL EVOLUTION

It is well known that the development of face recognition (FR) systems is challenging under uncontrolled conditions often related to the variation of pose, illumination, expression, and occlusion. Also, to collect the necessary amount of images is hard to guarantee in many situations, e.g. ID cards, drivers licenses or visas, leading to the one sample per person (OSPP) problem. This work addresses the OSPP problem along with illumination and pose variation using an FR framework composed of a self-adaptive Differential Evolution, named FRjDE. The main feature of the framework stands on the use of the optimization algorithm for choosing which preprocessing and feature extraction strategies to use, as well as tunning their parameters. Also, by using the jDE algorithm, F and CR control parameters are self-adapted. Experiments are made using two well-known databases, named CMU-PIE and FERET. Results obtained from the FRjDE approach are compared against the FR framework using the standard DE algorithm and against results found in the literature. Results suggest that the proposed approach is highly competitive and well suited for face recognition.

INTRODUCTION
Over the past decades, Face Recognition (FR) topic has brought the attention of the research community since traditional biometrics approaches became insecure with the evolution of technology. Also, FR systems have a distinct feature compared to other biometric systems since it does not require direct interaction with the user, allowing its application on environments with a high flow of people. The wide range of applications for FR, such as law enforcement, subjects identification, video surveillance, access control, social identification and criminal investigation led to several works proposing solutions to problems that arise on image acquisition [1]. Images acquired are often affected by imaging noises such as variation of pose, illumination, expression, and the use of adornments, which might lead to misclassification [2]. Among these, uncontrolled illumination is a critical factor for real-world applications due to the non-ideal imaging environments frequently encountered in practical situations [3]. In addition, pose variation affects classification in a way that the image loses spatial information, becoming necessary the development of approaches that deal with this condition. Despite these problems, to collect the necessary amount of data is hard to guarantee in many situations e.g. ID cards, drivers licenses or visas leading to the one sample per person (OSPP) problem [4]. Hence, to extract discriminative and robust features becomes a real challenge even to state-of-art approaches.
There are some recent works which attempt to solve the OSPP problem along with issues from image acquisition. Among them, there are methods employing sparse representation classifier [1] [4] [5], two-layer neural local-to-global feature learning framework [6], supervised locality preserving multimanifold (SLPMM) [7], single hidden layer analytic Gabor feedforward neural network (AGFN) [2] and multiple feature subspaces analysis (MFSA) [8]. Despite these, an increasing number of bioinspired FR systems had emerged due to their intelligent problem-solving ability, scalability, flexibility, and adaptive nature [9].
In [10], an FR framework is presented and features the ability to self-adapt to conditions inherent in the database's images. The intent of the framework is to provide techniques for preprocessing and for feature extraction in which the optimization process, carried out by the optimization algorithm, gives as output the best set of techniques and parameters for the task. In this work, the authors compared the performance of a standard Particle Swarm Optimization algorithm and a standard Differential Evolution (DE) algorithm, recommending the use of DE algorithm in the framework.
However, it is well known that fixed parameters are not robust to all optimization problems and to tune these parameters is not trivial [11]. Hence, this paper is an extension of the work presented in BRACIS 2018 [10] and differs from previous work 4 in two points: i) we employ the FR framework using a self-adaptive version of DE [12], called FRjDE, in order to control the parameters of mutation factor (F ) and crossover probability (CR). The goal is to minimize the number of parameters to adjust and analyze the performance of the framework; and ii) we used two well-known databases i.e. CMU-PIE [13] and FERET [14] considering the OSPP problem along with illumination and pose variation. The remaining sections of this work are organized as follows: Section 2 presents the theoretical foundation and related work; Section 3 presents the FR framework; Section 4 shows the experimental methodology and datasets; Section V shows the results and analysis; and Section 6 presents the conclusions and some future directions.

BACKGROUND
In this section, we present the techniques employed for preprocessing, feature extraction and classification. These techniques serves as input for the proposed framework. It is worth to point out that they were chosen based on their performance in previous works and its popularity in literature specially along with bio-inspired algorithm [9].

PREPROCESSING TECHNIQUES
Some preprocessing techniques are available in the framework which are described next. The first technique available is called wavelet-based illumination normalization (WBIN) that is based on the discrete wavelet transform (DWT) [15]. In DWT the image is represented in terms of translations and dilatation of a scaling function and a wavelet function using a 2D filter bank consisting of low-pass and high-pass filters [15]. The different wavelet families make different trade-offs between how compact the basis functions are localized in space and how smooth they are. They can be biorthogonal (bior), Coiflets (coif), Daubechies (db), Haar, reversed biorthogonal (rbio), and Symlets (sym). Each family contains several variations according to its smoothness. The 2D-DWT produces four components, which are approximation (LL), horizontal (HL), vertical (LH), and diagonal (HH).
For the illumination normalization procedure, histogram equalization is performed in the approximation coefficients (LL) to achieve contrast enhancement. The fine details in the image can be controlled multiplying each element of the detail coefficient matrices (HL, LH and HH) with a scale factor (Sf ). Then, the enhanced image is reconstructed using the inverse wavelet transform. The considered parameters within this technique are: the wavelet family (wf ) that can assume 105 possible configurations and the scaling factor (sf ) that can assume any value greater than 0.
The GIC [16], also known as power-law transformation, can control the overall brightness of an image by changing the parameter γ of its formula [16]. The only parameter to adjust within this technique is the parameter γ. If it assumes values lower than 1 will shift the image towards the darker end of the spectrum while γ values greater than 1 will make the image brighter.
The Gaussian Blur uses a 2D convolution operator with a Gaussian distribution to blur and remove details and noises from the image [17]. The parameters within this technique are: Gaussian kernel size, which must assume positive and odd values, and Gaussian kernel standard deviation in X (sdX) and Y (sdY ) directions 1 .
An edge is a set of pixels in the image where intensity abrupt changes, representing the shape of the face, eyes, nose and other discriminant features. In [18], a review of edge detection techniques was performed which featured the Laplacian with better results for visual perception and edge quantity. The parameters that have been considered in this technique are: the aperture size used to compute the second-derivative filters which must be positive and odd, a scale factor (sf ) for the computed Laplacian values and a delta value that is added to the results prior to storing them in the resulting image 1 .

FEATURE EXTRACTION TECHNIQUES
In this section, some feature extraction techniques are described. The first feature extraction technique included in the FR framework is the 2D-DWT, which was previously introduced. According to [16], the information in the approximation component has the most discriminant features. Hence, only this sub-band was used. The considered parameters within this technique are: the wavelet family (wf ) and the number of levels of decomposition (n).
The discrete cosine transform (DCT) was also added to the framework. The DCT technique is popular for image processing because of its energy compaction property. It transforms the image from spatial to frequency domain using cosine functions. In frequency domain, the relevant features tend to be concentrated in low-frequency components or at the corner of the spectrum [19].
According to [20], the local binary patterns (LBP) texture descriptor has some advantages that are: easy to implement, invariant to monotonic illumination changes, and low computational complexity. Its canonical version is used in this work from which the features are extracted directly from the input image using a 3x3 neighborhood. The neighborhood structure is a set of pixels taken from a square neighborhood which are compared against the value of the central pixel (thresholded) resulting in an 8 bits vector converted to decimal. Then, the resultant value is used to represent the pixel.

CLASSIFICATION
For the classification task, each image to be classified is compared to each image in the database in terms of similarity returning the most similar one. Then, a match occurs if both images are from the same person. This classification is carried out by the well known k-Nearest Neighbors (k-NN) classifier, where k = 1 [21]. As k-NN is a common classifier in the literature, it suggests a reliable choice for this case study. In this work, four different distance measures are available in the framework. The first distance measurement implemented is the Manhattan distance (L 1 -norm), that is the distance between two points alongside the axis at right angles. Similarly, the well-known Euclidean distance (L 2 -norm) measures the distance between two points directly and was also employed. In addition to these, the L 2SQR -norm (the square of the L 2 -norm) and L ∞ -norm were also implemented.

DIFFERENTIAL EVOLUTION AND SELF-ADAPTIVE DIFFERENTIAL EVOLUTION (JDE)
The Differential Evolution (DE) algorithm is a metaheuristic proposed by Storn and Price in 1996 for continuous optimization problems [22]. It consists of a population of size N P of solution vectors of size D, where new individuals are generated by recombination of individuals of the previous generation. Each individual has a fitness value proportional to how good it is and this value is responsible for guiding the DE in the search space. A newer individual compete with the previous one and must have a better fitness in order to replace the competing individual.
The input parameters that enable to control the search are the population size, the crossover probability (CR) and the mutation factor (F ). DE has a nomenclature that describes the adopted configuration. This takes the form of DE/a/b/c, where a represents the solution vector to be perturbed. The most commonly used strategies are selecting at random (rand) and selecting the best solution (best). The b identifies the number of difference vectors used in the perturbation of a. Last, c is the recombination operator performed such as bin for binomial and exp for exponential [23]. The most popular configuration is demonstrated in the referenced pseudo-codes i.e. DE/rand/1/bin.
The standard DE keeps the control parameters fixed during the whole optimization process and are defined by the user. On the other hand, the jDE [12] uses a self-adaptive strategy to control F and CR parameters. Each individual i in the population is extended with two new dimensions representing F i and CR i control parameters which are adjusted on-the-fly. Better values of these control parameters lead to better individuals which, in turn, are more likely to survive and produce offspring and, hence, propagate these parameter values [12].
The parameters F G+1 i and CR G+1 i are calculated as shown in Equation 1 and Equation 2 where rand {1,··· ,4} are uniform random values within the range [0, 1], τ 1 and τ 2 represent fixed probabilities to adjust control parameters F and CR, respectively, and F lower and F upper are the fixed lower and upper bounds that the parameter F can assume.
To the new (2)

RELATED WORK
The works described in this section were chosen based on the FR problem being tackled (illumination and pose variation) and the experimental methodology employed using the CMU-PIE and FERET databases. Also, the OSPP problem is a real-world condition and is considered in the related work.
In [1], a customized dictionary-based face recognition approach is proposed using the extended joint sparse representation. The proposed approach learn a customized variation dictionary from the on-location probing face images and then utilizes the information of both the customized dictionary and the gallery samples to classify the probe samples. [4] presents a model called Local Robust Sparse Representation (LRSR) to tackle the problem of query images with various intra-class variations. The idea is to combine the local sparse representation model with a patch-based generic variation dictionary learning model to predict the possible facial intra-class variation of the query images. The authors stated that their methodology outperforms the state-of-art approaches. In [5] is proposed an additive strategy to the Extended Sparse Representation Classifier (ESRC) aiming to solve the mutual influences of the reflectance and illumination in intra-class variant bases of the ESRC and remove the redundant identity information of the generic face. Two additive models were introduced: the Reflectance and Illumination (RandL) and the High-and Low-frequency (HandL). The final classification is determined by the sum of two weighting residuals.
In their experiments, the Wavelet Denoising Model (WDM) and the Logarithmic Total Variation (LTV) are employed to extract facial features in R&L ESRC and H&L ESRC, respectively. [6] proposed a two-layer neural local-to-global feature learning framework to address OSPP face recognition. In the first layer, the objective-oriented local features are learned by a patch-based fuzzy rough set feature selection strategy and in the second layer, global structural information is extracted from local features by a sparse auto-encoder. The authors claimed that their framework can achieve superior performance than other state-of-theart feature learning algorithms for OSPP face recognition. In [7] the authors presented a supervised learning method called supervised locality preserving multimanifold (SLPMM). In their approach, two graphs are made to represent the information inside every manifold and among different manifolds, with this it simultaneously maximizes the between-manifold scatter and minimizes the within-manifold scatter. [2] proposed a single hidden layer analytic Gabor feedforward neural network (AGFN).
The input layer receives raw images and propagates geometrically localized sub-image patches to the hidden layer, then vertically and horizontally accumulated Gabor magnitude features are extracted over several orientation and scale settings. Moreover, a whitening process with dimension reduction is employed and the extracted features are fused or classification decision. Finally, [8] present a multiple feature subspaces analysis (MFSA) approach, which takes advantage of facial symmetry. They divide each enrolled face into two halves about the bilateral symmetry axis and further partition every half into several local face patches. Then, they cluster all the patches into multiple groups according to their locations at the half face and learn a feature subspace for each group. The classification is performed employing the k-NN classifier.
Most methods present in literature are limited because they are designed to solve a specific set of image conditions, lacking the ability to adapt themselves to different conditions. Real-world applications require robustness, since new challenges arises regarding images conditions. Following, we present the proposed framework which aims to fill that gap in existing methods.

THE FR FRAMEWORK
The FR framework provides techniques for preprocessing and feature extraction in which the optimization process, carried out by the bio-inspired algorithm, gives as output the best set of techniques for the classification task [10]. Besides that, the parameters of selected techniques are also optimized by the framework as well as the distance metric employed by the classifier. Figure 1 represents the FR system flowchart. The dataset should be split into three subsets: training, validation and test. In the training stage, the validation subset is used to evaluate the candidate solutions generated by the optimization algorithm based on the training subset. In the test stage, the test subset is used to evaluate the optimized model generated after training. In both the training and test stages, the fitness evaluation is done based on the recognition rate. The techniques introduced in Section 2.1 and 2.2 are available in the framework, as well as the distance measures presented in Section 2.3. For preprocessing, the first technique employed was WBIN to adjust contrast and enhance face structure. After, the GIC for brightness adjustment and Gaussian Blur to remove noise from the image were added to the pool. Last, a technique for edge detection, the Laplacian was included in our framework. It is worth to point out that the sequence in which these techniques are applied are in the same order as presented here. Hence, in this implementation, the optimization algorithm can choose if the techniques will be applied and its parameters but not the order they will be applied. Considering feature extraction, the order of the techniques employed does not affect the results since the features are concatenated. Despite the techniques implemented in this instance of the framework, any preprocessing or feature extraction technique may be implemented in the pool of techniques. Figure 2 illustrates the employed techniques and their respective parameters.
The optimization algorithm acts in the training stage and the techniques, as well as their parameters, are encoded in the solution vector as real-coded variables. Figures 3 shows how the solution vector is encoded, consisting of WBIN, GIC, Gaussian Blur, Laplacian Edge Detection, DWT, DCT, LBP, and the distance metric of k-NN, respectively. The parameter f lag represents if the technique will be used or not. As the optimization algorithms operate in the continuous domain, the parameter f lag is discretized to 0 or 1. Also, due to the stochastic nature of the optimization process, if a parameter assumes a value that is out of its bounds, the value is set to the closest bound. Any real-coded algorithm for continuous optimization may be used in the FR framework. 7  The optimization algorithm starts by initializing the population with random solution vectors and, as the iterations cycle begins, the solutions are modified accordingly to the algorithm strategy. A predefined number of iterations is established as a stopping criterion. When the stop criterion is reached, the setting that achieved the best recognition rate is selected as the optimized solution. To test the classification model, the test set is transformed using the optimized set of techniques and thus, generating the processed test images dataset. Finally, the processed test images are classified by the optimized k-NN classifier using the processed training dataset as reference.

EXPERIMENTS
As DE and jDE are stochastic algorithms, multiple runs are required. The measurements needed for each algorithm in each dataset was established using a confidence interval of 95% with a standard deviation of 2.5% [24]. Based on this criterion, 10 runs were performed for each algorithm in each dataset. The recognition rate, which is the ratio between the number of reference face images assigned to the correct class and the total amount of reference face images, and processing time are used as performance metrics. Table 1 shows the parameters for DE and the common parameters for both De and jDE algorithms. All parameters were set using literature recommendations [23].  [25] and, once verified, the Wilcoxon signed-rank paired test [26] is applied. Both tests were performed under a 95% confidence interval.
To better understand the behavior of the optimization algorithms, convergence and diversity charts are generated. The convergence chart represents the recognition rate of the best solution at each iteration. The population's diversity chart is obtained using Equation 6 from Corriveu et al. [27]. This chart represents how spread the solutions are in the search space, this way, it is possible to draw whether the algorithm is performing a more local or global search at each iteration.
All experiments were run in an Intel Core i7-4770 computer with 16 GB RAM memory using Python programming language with multiprocessing library for parallelism. Parallelism is achieved distributing the fitness evaluation of optimization algorithms population in 7 out of 8 available processing cores. Following, we describe the datasets used in this work.

CMU-PIE DATABASE
The CMU-PIE [13] database consists of 41,368 images of 68 subjects. Each subject has several images under 13 different poses and 43 illumination conditions, and with 4 expressions. For experimentation, it was selected five subsets based on the camera used (i.e. C05, C07, C09, C27 and C29). Each camera is set in different angles, this way presenting five different poses: 1) looking right; 2) up; 3) down; 4) front; and 5) left, respectively. Figure 4 illustrates the five subsets. For a fair comparison with literature, we have selected about 24 images per subject with different illumination conditions according to database documentation. Each one of the five subsets is evaluated independently and grouped together (named C All ). When using the subsets individually, we aim to analyze the OSPP problem, in which only one single image per person is available in the training set. That being said, the first image of every subject from each subset is used. The remaining images are randomly split in half representing the validation and test sets. In the experiment using C All , the validation, test and training sets from each subset are grouped together, respectively. This experiment makes possible to evaluate the proposed approach in a set containing intra-pose variation. It is worth to point out that this last experiment does not characterize the OSPP problem.

FERET DATABASE
The b-series subset from FERET database [14] was employed, which consists of 1,800 images from 200 subjects with facial pose angles ranging from +60 o to -60 o and size of 256x384. Table 2 presents the description of subsets used in this experiment and Figure 5 shows some face images samples. For comparison purposes with the literature, the frontal subset ba is used as training set, and all the remaining subsets are grouped together as validation and test sets (b All ). Here we consider the OSPP problem as well.

RESULTS AND ANALYSIS
This section shows and analyses the results obtained by the FR framework using the self-adaptive version of DE, namely FRjDE. Results are compared with its standard version FR-DE and with results found in the literature. Table 3 presents the results obtained using FRjDE and FR-DE algorithms on each CMU-PIE subset. The last line shows the average recognition rate. Regarding the test stage, it is possible to realize that a gain in accuracy is achieved when jDE is employed for each subset except for C All . Considering the statistical tests, only the subsets C09 (p − value = 0.0113) and C27 (p − value = 0.0047) presented significant differences. Despite that, it is possible to observe an average gain in accuracy in favor of jDE of roughly 1%. In the training stage, no statistical difference was verified. Table 4 shows the recognition rates for FRjDE and FR-DE on FERET database. For this dataset, statistical difference in favor of jDE (p − value = 0.0069) was verified in the test stage of 3.24% better on average.
In a general analysis, it is possible to conclude that adjusting the control parameters during the optimization process with jDE leads to a more precise and accurate search for an optimized solution.  Regarding processing time, Table 5 presents the average running times for each CMU-PIE subset and for the FERET database, respectively. From Table 5, no significant difference can be verified comparing FRjDE and FR-DE. However, comparing the absolute values obtained, it is possible to observe that FRjDE was faster to train and test in general. This is possibly a reflection of a better search in the problem space due to the self-adjustment of the control parameters in FRjDE. 00h 02m 7s ± 00h 00m 23s 0.0724s ± 0.0362s 0h 1m 43s ± 0h 0m 17s 0.0760s ± 0.0234s C07 0h 4m 11s ± 00h 03m 58s 0.0310s ± 0.0440s 0h 34m 46s ± 0h 41m 15s 0.0416s ± 0.0399s C09 0h 03m 15s ± 0h 2m 0s 0.0653s ± 0.0424s 0h 3m 20s ± 0h 3m 2s 0.0588s ± 0.0375s C27 2h 4m 47s ± 0h 42m 27s 0.0097s ± 0.0024s 2h 23m 3s ± 1h 5m 42s 0.0571s ± 0.0775s C29 0h 2m 18s ± 0h 01m 8s 0.0898s ± 0.0008s 0h 2m 14s ± 0h 0m 27s 0.0735s ± 0.0245s C All 6h 3m 25s ± 5h 45m 54s 0.1132s ± 0.0125s 8h 11m 46s ± 6h 16m 45s 0.1043s ± 0.0059s FERET 2h 13m 37s ± 0h 42m 11s 0.0093s ± 0.0025s 3h 25m 15s ± 1h 17m 29s 0.0152s ± 0.0069s Tables 6 and 7 show the settings found by FRjDE in training step for C All CMU-PIE subset and FERET database, respectively. Each one of the ten executions is shown in rows, while the techniques chosen are in columns. A dash symbol means that the technique was not employed in the related execution. Since similar conclusions can be drawn from the CMU-PIE subsets, we only present the settings for C All subset. Considering C All subset, it is possible to realize that WBIN was chosen in every execution except one, and the LBP technique was always chosen. This demonstrates the importance of these techniques to deal with the conditions on CMU-PIE database. Also, the preferred distance measure was the Manhattan distance (L 1 ). On the other hand, the Gaussian Blur, Laplacian and DWT were never chosen. Differently from CMU-PIE database, the Gaussian Blur and DWT was chosen in every execution for FERET database. Also, we can observe that the Manhattan distance was once more the preferred distance measure.
The best results achieved by the FR framework using jDE in the two databases are compared with the results obtained by related work found in the literature (Section 2.5). The best average result obtained by FRjDE in training and test stages was  --------Yes  Yes  L1  2  db11  0.2381  ----------Yes  L2sqr  3  rbio3.5 0.2715  ----------Yes  L1  4  coif14 0.0000  ----------Yes  L2  5  db6  0.2487 1.0566  ---------Yes  L2  6  sym20 0.8519 2.2367  ---------Yes  L1  7 db27  chosen for comparison. Table 8 shows the recognition rates achieved by FRjDE and related works on CMU-PIE database. The last line shows the results obtained by using the most common parameters found in the literature accomplished with the set of techniques defined by our approach. It is worth to remember that all these works consider the OSPP problem. As one can see, the proposed approach presents outstanding accuracy when compared to the related work considering these subsets. Also, the experiment considering pose variation within all subsets (C All ) shows that the proposed approach achieves high recognition rates even when slightly pose variation occurs. Overall, considering illumination compensation properties, the presented method proved to be competitive with related works for this dataset. From Table 8, regarding the results achieved using literature settings, as different techniques reached the same highest recognition rate, the criterion used to selected the experiment to try out with literature settings was less processing time. For the C05 subset, experiment 4 was chosen where DWT, DCT, GIC and Laplacian techniques were employed with Manhattan distance. So, we set scale factor to 3 and the haar wavelet for DWT, the γ parameter from GIC to 2 and the kernel size to 3x3 with no scale or delta value for Laplacian using the Euclidean distance. As one can see, it reached also 100% recognition rate showing that the parameters are insensitive for this case, this way once more proving the easiness of this subset. On the other hand, the parameters for experiment 7 using C07 dataset showed to be sensitive dropping 10.52% recognition rate when using literature settings. In this experiment, the GIC and Laplacian technique were employed with Manhattan distance. We set the same values used in subset C05 with Euclidean distance. In experiment 5 from C09, the techniques chosen by jDE algorithm were DWT, GIC and Laplacian with Manhattan distance. Employing literature parameters, a slightly drop was observed (≈4.09%). Considering experiment 9 from subset C27, a higher drop in accuracy was verified (≈19.48%). In this, Gaussian Blur and WBIN were employed besides GIC and DCT using the Manhattan distance. For Gaussian Blur, the kernel size was set to 3x3 and the standard deviations were computed from kernel size, and for WBIN, the haar wavelet was employed with scale factor 3. Experiment 2 using jDE was chosen to comparison using C29 subset. A considerable accuracy drop of ≈23.78% was verified. The techniques employed in this experiment were DCT and WBIN with Manhattan distance. Finally, experiment 9 from C All revealed an accuracy drop of ≈17.28%, once more proving the importance of parameters adjustment. The techniques employed were WBIN and LBP.  Table 9 presents the results obtained by the related work and by the FR framework using jDE on FERET database. Partial results of each subset and the average (b All ) are shown in columns, while the algorithms are shown in rows. The last row shows results achieved using the techniques found by the framework but with parameter values commonly used in literature. For comparison, the setup obtained by experiment 3 was chosen. Through this, one may realize that even though our approach is not specific to handle pose variation, competitive results were achieved considering the works presented. Also, when analyzing results obtained by the SLPMM and the MFSA+ approaches, the superiority of the results obtained by the proposed approach are evident. Furthermore, our approach achieved overall best average using b All subset compared to all algorithms highlighting the robustness of the proposed method, since b All considers all different conditions contained in FERET b-series dataset. On the other hand, for most subsets (bd, be, bf, bg, and bh) the method from [2] achieved better results. This was expected since their work is focused on a pose-invariant approach. From this dataset, the greater the variation of pose angle, the more difficult it is to solve by an FR system. Hence, our approach achieved the best performance in the subsets with greater pose variation, i.e. bb, bc and bi, and also was very competitive in the bh subset. Once again, it is possible to draw from the results using literature settings the importance of tuning the parameters of the employed techniques.  Figure 6 shows the convergence and diversity charts for FERET database using FRjDE. Only the charts of FERET dataset are presented because the same behavior of convergence and diversity is obtained from CMU-PIE subsets. In the convergence chart, it is possible to observe that close to the 40th iteration the best solution improves at a slow rate but continuously improving when the stop criterion is reached. Due to the multimodal search space nature of the problem, the diversity in our experiments remained high during all optimization step.

CONCLUSION AND FUTURE WORK
To the best of our knowledge, from early studies to the most recent ones, it can be said that there is no generic technique for FR that is immune to the challenges that arise when a face is captured in uncontrolled conditions. Hence, we employed an FR framework with the aid of a self-adaptive DE, namely FRjDE. The main aspect is the definition of which set of techniques and its ideal parameters values should be used for the FR using jDE. In this work, we implemented several illumination compensation techniques to handle the problem of illumination variation, as it is a critical factor. The well known CMU-PIE and FERET face datasets were used to evaluate the proposed approach since it permits to compare the results with relevant works found in the literature.
Considering CMU-PIE database, both algorithms showed to be suitable in compensation illumination variation achieving more than 99% of recognition rate in most subsets. Also, 100% was reached on subsets C05, C09 and C29. Besides that, in the experiment with C All subset, it was possible to verify the capability of the proposed approach in dealing with slight changes of pose. For the FERET database, the recognition rates do not reach real-world levels of accuracy, however, the results achieved are outstanding since the dataset contains pose variation. Regarding the usage of self-adaptive control parameters, it proved to improve recognition rate significantly in most cases. Hence, we can state that employing jDE instead of standard DE lead to higher accuracy considering the dataset conditions. It is worth to point out that the OSPP problem was considered for both datasets. Besides these conclusions, it can be observed that the present FR problem is highly multimodal since different sets of techniques can achieve similar (or the same) results.
In this work, we only consider a specific sequence of the employed preprocessing techniques. We suggest to include the possibility of interchange these techniques in the optimization step. Despite the fact that high recognition rates were achieved, it seems that there is still room for improvement. With this, one could use some strategy such as meta-learning to fine tune the previously achieved solution. To achieve robustness in relation to the problems that arise on image acquisition, different kinds of problems need to be tackled. For this, other techniques must be added to the framework and other datasets should be tested. Also, a physical interpretation analysis of the images could be performed considering the parameters found for the preprocessing techniques. Finally, the testing phase is performed in the range of milliseconds, however, the training phase still lasts hours for some datasets. This does not invalidate our approach for real-world application, but some parallel programming strategies or massively parallel hardware architectures, such as GPGPUs, could be used.


Low-rank representations with incoherent dictionary for face recognition

Face recognition remains a hot topic in computer vision, and it is challenging to tackle the problem that both the training and testing images are corrupted. In this paper, we propose a novel semi-supervised method based on the theory of the low-rank matrix recovery for face recognition, which can simultaneously learn discriminative low-rank and sparse representations for both training and testing images. To this end, a correlation penalty term is introduced into the formulation of our proposed method to learn an incoherent dictionary. Experimental results on several face image databases demonstrate the effectiveness of our method, i.e., the proposed method is robust to the illumination, expression and pose variations, as well as images with noises such as block occlusion or uniform noises.

Introduction
Face recognition (FR) is an interesting and popular issue in the communities of computer vision and pattern recognition, which plays an important role in $ Fully documented templates are available in the elsarticle package on CTAN.
practical applications, e.g., security monitoring and access control. Reducing the dimensionality of the face images is a simple yet effective idea for FR, classical methods like Eigenfaces [1], Fisherfaces [2], Laplacianfaces [3] and their extensions [4,5,6]. With the efforts of the researchers, local discriminant embedding (LDE) [7] and many other methods have been successfully applied in FR. On controlled datasets many face recognition algorithms can achieve superb performance. Unfortunately, they cannot perform well in some real-world situations. According to [8] and [9], the key point to solve the problem is to handle variations in illumination, images misalignment, and occlusion in the testing images simultaneously.
In recent years, the sparse-representation-based classification (SRC) [10] has become very popular in FR. The key idea of SRC is to represent an input sample as a sparse linear combination over all the training samples, in which the 1 -norm is usually used as a sparsity constraint. The results in [10] on FR are promising, and SRC is also robust to face occlusion and corruption in the test images. Nevertheless, the training images should be well aligned in SRC.
To deal with face misalignment, an improved method is presented in [8]. To counteract outliers such as noises in FR, Yang proposed a modified SRC-based framework [11,12]. Unfortunately, the above methods cannot handle well the situation when both training and testing samples are corrupted. To further assess the robustness of sparse representation based recognition algorithms, this problem should be addressed.
According to traditional subspace theory, face images of the same class are often lie in the same low-rank subspace [13,14,15], but due to illumination changes, expression or pose variations and other issues, the actual face images often do not maintain the low-rank structure, which will affect the recognition performance. Recently, low-rank matrix recovery (LRMR), has been successfully applied to FR [13], LRMR can obtain the low-rank data even from the corrupted data. It can efficiently remove sparse noises like illumination changes and occlusions in corrupted face images. Yin et al. [16] presented a new method called low rank matrix recovery with structural incoherence and low rank pro-jection (LRSI LRP) which can correct the corrupted test images with a low rank projection matrix. Zhao et al. [17] developed a discriminative low-rank representation method for collaborative representation-based (DLRR-CR) robust face recognition. Chen et al. [18] proposed a robust low-rank recovery algorithm (RLRR) with a distance-measure structure for face recognition. For the recognition problem, label information should be incorporated to learn discriminative dictionary. Chen et al. [19] adopts the low-rank recovery technique to recover the clean low-rank data matrix from the training data class by class and a structural incoherence term is introduced to enforce the resulting lowrank dictionary for each class to be independent, then the clean data matrix is employed as dictionary for SRC to classify test data. Ma et al. [20] proposed a discriminative low-rank dictionary learning method for FR. The proposed algorithm tries to optimize the sub-dictionaries for each class to be low-rank. In order to learn a dictionary which is not only low-rank but also discriminative, Li et al. [21] applied the constraint on the coding coefficients to make the ratio of the within-class scatter to the between-class scatter be small. However, all of them explore structural information class by class, which cannot capture the global structure. To explore the global structure information among all the training images, Zhang et al. [22] proposed a discriminative, structured lowrank method. It incorporates a code regularization term with block-diagonal structure which can regularize images from the same class to have the same representation to learn discriminative dictionary. However, it is not usually the case. The fact is that face images which are from the same class usually lie in the same subspace and have relevant representation, but the representation is not necessarily the same. To overcome the defect, Li et al. [23,24] proposed a semi-supervised framework to learn robust face representations with classwise block-diagonal structure. It can learn robust representations of training and testing images simultaneously and capture classwise block-diagonal structure with a classwise regularization term at the same time. It can achieve significant performance gains even when both the training and testing samples are corrupted.
Prior work demonstrated that high-quality dictionary can greatly improve the performance of sparse representation approaches [11,12,13,19]. The researchers have made many efforts to learn a good dictionary [19,20,21]. The dictionary learning techniques always focus on the reconstruction accuracy and discriminative power of the dictionary. For example, in [20] and [21] the relationship between two dictionaries for different classes was addressed. Lin et al. [25] proposed an incoherent dictionary learning model that maximizes the incoherence of basis atoms in one single output dictionary, and the experimental results demonstrated the advantages of incoherence constraint.
In this paper, a novel semi-supervised method based on the theory of lowrank matrix recovery is proposed for FR, which focuses on handling the situation that both the training and testing samples are corrupted. Meanwhile, inspired by [25] we explicitly incorporate a correlation penalty in the dictionary learning model to make the dictionary more discerning. The representation learning process is shown in Fig. 1. Our method has several advantages which are summarized as follows.
• We adopt a semi-supervised framework to learn face representation with incoherent dictionary, which can simultaneously learn low-rank and sparse representations of both training and testing images.
• Furthermore, our proposed method is robust to the case that both training and testing images are badly corrupted. We conducted some experiments under the scenarios where samples are corrupted like in Fig. 2.
• In addition, incoherent dictionary with desirable reconstruction and discrimination capability can be learned by the proposed approach.
The rest of this paper is outlined as follows. First, we briefly review related work 0n the low-rank matrix recovery and incoherent dictionary learning in Section 2. Section 3 presents our method. The optimization process based on the inexact Augmented Lagrange Multiplier method for our model is given in Section 4. Section 5 illustrates the classification technique. Computational complexity of our proposed method is presented in Section 6. Experimental results on several face image databases and corresponding discussions are given in Section 7. Finally, Section 8 concludes this paper.

Related Work
First, we summarize some notations. Throughout this paper, notations with a bar denote symbols of training images, while notations with a hat denote symbols of testing images. LetȲ = Ȳ 1 ,Ȳ 2 , . . . ,Ȳ C ∈ R d×n be the feature matrix which is composed of training images of C classes, and the feature matrix Ŷ = ŷ 1 ,ŷ 2 , . . . ,ŷ ns ∈ R d×ns is composed of n s testing images. Thus Y = Ȳ ,Ŷ is the feature matrix of the whole database, where each column of Y denotes the feature of an image. Each image of Y can be coded as a linear combination of the base elements of dictionary D ∈ R d×m , i.e.
where X = X ,X , andX corresponds to the representation matrix of training images, whileX corresponds to the representation matrix of testing images.

Low-Rank and Sparse Representation
Suppose we are given a set of corrupted images from multiple classes, now the problem is to learn robust representations of training and testing images simultaneously. Low-rankness is an appropriate criterion to capture the low dimensional structure from the high-dimensional data [13]. To obtain the clean database Y, learning low-rank representations can be solved as follows, Effectiveness of low-rank and sparse representation for the classification problem has been demonstrated in [19] and [26].
As we know from [13] and [27], low-rank model can reveal the subspace structure of data, sparse representation has been shown to achieve promising performance in FR [10,28,29]. Taking advantage of low-rank and sparse representation is very meaningful, and low-rank and sparse representation for the classification problem is very effective [22,30]. Li et al. [24] imposed both low-rank and sparse constraints on the representation matrix, the method is called learning low-rank and sparse representation (LRRS) for FR, this model is formulated as follows, As the above problem is non-convex, the common way is to substitute the 1norm for 0 -norm and the nuclear norm for the rank function. Therefore, the optimization problem (3) is relaxed into the following problem, The nuclear norm X * (i.e., the sum of singular values), · 1 is defined as the sum of the absolute values of entries in the given matrix, λ and β control the sparsity of sparse noise term E and sparse representation term X, and D is the dictionary that linearly spans the data space.

Incoherent Dictionary Learning (IDL) model
The quality of dictionary is critical for FR, especially when training and testing samples are corrupted, high-quality dictionary can greatly improve the performance of sparse representation approaches [11,12,13,19]. Lin et al. [25] proposed an incoherent dictionary learning model, which maximizes the incoherence of basis atoms in one single output dictionary to learn a discriminative dictionary. The correlation measure of a dictionary D can be defined as, where I ∈ R m×m is an identity matrix, we can see from the formula (5) that the correlation measure is zero when the columns of dictionary D are orthogonal, in which case the dictionary D is the most irrelevant.

Low-Rank Representations with Incoherent Dictionary
The experimental results in [23] and [24] verified that the semi-supervised learning method can effectively deal with the case that both the training and testing samples are corrupted. Inspired by the work of [23] and [24], we also exploit the semi-supervised learning framework. We propose a new method of low-rank representations with incoherent dictionary (LRRID) for FR. Finally, the objective function is proposed to learn the sparse and low-rank representation with the incoherent dictionary by explicitly incorporating a correlation penalty into the dictionary learning model, There are three regularization parameters (λ > 0, β > 0 and γ > 0) that reflect relative contributions of each term.

Optimization
By introducing two auxiliary variables J and L, we convert problem (6) into the following equivalent optimization problem, The optimization problem (7) can be solved based on the Augmented Lagrange Multiplier (ALM) method [31], so we adopt the inexact ALM method for efficiency in this paper. The augmented Lagrangian function of problem (7) is as follows, where T 1 , T 2 , and T 3 are Lagrangian multipliers and µ > 0 is the penalty parameter, and A, B = trace A T B . We solve problem (8) iteratively by updating J, X, L, E and D once at a time, and the detailed procedures are as follows.
Updating J: Fix the other variables and solve the following problem, where U, Σ, V T = SVD X k + T k 2 µ k and S [·] is the soft-thresholding (shrinkage) operator defined as follows, Updating X: Fix the other variables and solve the following problem, The optimal solution to (11) is given by Updating L: Fix the other variables and solve the following problem, Updating E: Fix the other variables and solve the following problem, Updating D: Fix the other variables and solve the following problem, The optimization problem (15) can be solved via the first-order gradient descent method [26,32]: where and F (D q ) is the gradient of F (D q ) with respect to D q , parameter η is the step size, and Π D is the projection function which maps each column to the 2 -norm unit ball. More specifically, the dictionary is learned iteratively by finding the local minimum along the gradient direction based on the small step size and normalizing each column vector until convergence. The optimization process of (8) is summarized in Algorithm 1.

Classification
To classify the test data, we employ a linear classifier in the testing phase as in [24]. The coefficientsX for training samples andX for testing samples can be derived through Algorithm 1. We can learn a linear classifier W based on the coefficients of training samples and their labels like [33], where H is the label matrix of training samples, η is the weight of regularization term. Clearly, the formulation (19) is a convex problem, which is solved directly by setting the partial derivatives with respect to W to zero, and the solution is given by Then label for test sample j is given by: where i * is corresponding to the classifier with the largest output.

Computational Complexity
The overall computational complexity of our method is O md (n t + n s ) + m 3 , where m is the number of the bases, d is the feature dimension, n t represents the number of training samples, and n s represents the number of testing samples. The computational complexity of our method is linear with the sample number. In comparison, the sparse representation based recognition methods in [10] and [20] have computational complexity of O m 2 dn s [30], which are slower than our method when n t < (m − 1) n s and m < dn s . Generally, the overall computational complexity of [24] is similar to that of ours.

Experiments and Analysis
We evaluate our approach on three public databases: the ORL database [34], the Extended Yale B database [35,36], and the AR database [37]. Some sample images from these databases are shown in Fig. 3. We test the robustness of LRRID when both training and testing images are corrupted, including block occlusion, illumination change, pose variation, expression change, pixel corruptions and uniform noises, respectively. We compare our method LRRID with some state-of-the-art methods including its special case (LRRS), which are enumerated as follows, (1) LRRID: It is to learn discriminative low-rank and sparse representations for both training and testing images simultaneously in a semi-supervised framework with the incoherent dictionary. The objective function is shown in formulation (6).
(2) LRRS [24]: It is to learn low-rank and sparse representations. The dictionary is composed by the training samples. The objective function is shown in formulation (4).
(3) RCBD [24]: It is to learn representation of training images, testing images and discriminative dictionary simultaneously in a semi-supervised framework with classwise block-diagonal structure regularization to the training images.
(4) DLRD SR [20]: It is to learn discriminative low-rank dictionary class by class, and sparse representation based classification method is employed with respect to the learned dictionary.
(5) SRC [10]: It is to learn sparse representation with the dictionary which is composed of the training samples. Specially, SRC indicates the case that the whole training samples are used as the dictionary. SRC* indicates the case that the dictionary size is the same as ours.
It is worth noting that our method and the work of [24] both adopt the semi-supervised framework, so the experimental results of RCBD have reference value.

ORL Face Database
The ORL database [34] contains 400 face images of 40 people in total, 10 images for each subject. The face images are taken under different lighting conditions, varying facial expressions and facial details, some example images are shown in Fig. 3 (a). Following the protocol in [24], for each class, we randomly  Table 1.   accuracy all the time, our method shows high robustness to the severe corruption like block occlusion, and achieves significant improvement. We can find that our method has stronger identification capability than LRRS by utilizing the incoherent dictionary. The recognition accuracy shows that the performance of our method is better when both training and testing face images are badly corrupted. To some extent, it validates that the incoherent dictionary contains more discriminating information. It also demonstrates that high quality dictionary is demanded for learning discriminative representation when both training and testing face images are badly corrupted.
We present some examples of decomposition results in Fig. 4 with 20% block occlusion. As shown in Fig. 4, the top five images are original images with 20% block corruption, while the second row is the learned incoherent dictionary (D) corresponding to the testing images, the third row denotes the low-rank recovery images (DX) and the bottom five images are the corresponding sparse noise (E) including block corruption, facial expression, and pose changes.

Extended Yale B
The Extended Yale B [35,36] dataset contains 38 subjects with 2414 face images, they are taken under different lighting conditions, Fig. 3  database. We perform 10 times for each experiment and the average recognition accuracy is shown in Table 2. We can see that our approach achieves the best results and outperforms the state-of-the-art method RCBD significantly. The method of RCBD does not have a superb performance when the dimensionality is low, it may lose some structure information. The recognition accuracy of DLRD SR is not very high when the dimension is low, while our method has better performance. After dictionary learning, our method outperforms LRRS by 1.83% on average. The experimental results validate the effectiveness and robustness of our method when face images are corrupted by illumination variations.

AR Face Database
The AR face database [37] includes over 4000 face images for 126 individuals. Following the protocol in [24], a compact dictionary with 5 items for each class is preferred under different scenarios. And the parameters are set as fol-lows, λ = 0.1, β = 0.1 and γ = 0.0001 on the AR database. We perform 10 times for each experiment and the average recognition accuracy is listed in Table 3.   to the other classes. Fig. 7 demonstrates that the face images can be properly represented, and it also validates the effectiveness of the learned dictionary by our method.

Conclusion
In this paper, we proposed a new face recognition method based on the semisupervised framework, in which the incoherent dictionary is introduced to simultaneously learn the discriminative low-rank and sparse representations for both training and testing images. The research indicates that the proposed method can learn robust representations of training and testing images simultaneously even when both training and testing images are badly corrupted. Furthermore, the new method integrates the correlation penalty into the dictionary learning model which can make the dictionary more discerning. All the updating formulas are derived by using the inexact ALM algorithm. The experimental results confirm that our proposed method is effective and robust, achieving state-ofthe-art performance especially when both the training and testing samples are contaminated, including illumination changes, occlusion and pixel corruption.
Parameter selection is a nontrivial task in pattern classification, and there are some parameters in our proposed method, how to choose the best setting parameters in our method is a problem to be further investigated in our future work.  Update J by (9).


extfieldsofstudy:
Physics
Computer Science

text:
A Research on MBES data classification denoising algorithm based on Octree index

For the Multi-Beam Echo Sounder (MBES) data denoising problem, the noise is divided into near-ground noise and outlier noise away from the seabed. The algorithm in this paper considers the spatial distribution characteristics of noise and removes two kinds of noise by initial denoising and precise denoising. The algorithm first uses the octree index to organize the point cloud and removes the outlier noise. Then combined with Bayesian estimation theory and statistical methods to remove near-ground noise. This paper designs experiments to process MBES data and compare it with the statistical filter of PCL point cloud library. The experimental results show that compared with the PCL statistical filter, the algorithm used in this paper has good denoising effect and can better preserve the information such as regional boundaries.

with the residual of the seabed trend surface. However, the sensitivity of the method to noise and the efficiency of data processing are related to the size of the detection window, and the window size needs to be manually and repeatedly adjusted. Zhang Zhiwei et al proposed an algorithm based on the estimation of the weighted iteration to fit the trend surface [11]. The algorithm is highly sensitive to noise, but it is difficult to guarantee the computational efficiency when iteratively processing the massive point cloud. Zhang Zhiheng introduced the natural point influence domain and improved the trend surface filtering method [12]. The method is sensitive to noise, but this method needs to search for the natural neighbors of each sounding point. The algorithm is complex and it is not efficient to process massive data.
Through the analysis of a large number of MBES data noise, this paper divides the MBES data noise into two categories: 1. Near-ground noise. This kind of noise is close to the surface of the seabed topography; 2. Obvious outlier noise. This noise is far from the terrain and is sparse. Based on the above analysis, this paper designs algorithms to remove two types of noise according to the characteristics of them. The algorithm is divided into two steps: Initial denoising and precise denoising, respectively removing obvious outlier noise and near-ground noise. Firstly, the octree index is built to construct the topological relationship of the scattered point cloud, and use the number of points in the voxel as a standard to receive or reject the point to remove obvious outlier noise. Then bayesian dynamic estimation theory and statistical methods are used to remove near-surface noise close to the terrain. Design experiments to analyze the execution efficiency and denoising effect of the algorithm.

Algorithm principle
The basic idea of the algorithm: First, the octree is used to establish the topological relationship between scattered point clouds, and the number of points in the voxels of all water depth points is counted until the point cloud traversal ends, then remove significant outlier noise outside of given threshold range. Then create a spatial grid, and the depth value of the grid node is estimated based on Bayesian prediction, and the depth difference between each water depth point and the grid node in the node voxel is calculated. According to the statistical characteristics of the point cloud, noise outside the given error range is removed. When the point cloud traverses, the hash table is used to improve the execution efficiency.
The algorithm has the following characteristics: (1) The applicability of the algorithm is wide, and the effect of removing sparse noise is good; (2) The water depth prediction algorithm based on Bayesian estimation is robust and can distinguish between terrain and near-surface noise; (3) The octree tree is simple to build and has a high level of automation, which is suitable for the processing of massive point cloud data. The algorithm principle is described in detail below.

2.1Initial denoising
The basis for removing outlier noise is to establish an octree index. An octree is a tree-like data structure used to describe three-dimensional space. Each node of the octree represents a volume element of a cube, and each node has eight child nodes. The volume elements represented by the eight child nodes are added together to be equal to the volume of the parent node. The topological relationship of point cloud data can be constructed by establishing an octree. By obtaining the neighborhood information of the voxels at each water depth point and setting an appropriate threshold, the apparent outlier noise can be easier removed. The effect of MBES data to establish octree index is shown in Figure 2.

Precise denoising
2.2.1 Node depth estimation. Take the octree tree voxel center point as a node of the grid to establish a spatial grid. The Bayesian dynamic model theory is used to estimate the depth value of the grid nodes, and the dynamic linear model is established to dynamically predict and update grid nodes. Let : ∈ 0 , … , 1 be the predicted sequence of water depth points for the grid nodes, , 0 is the prediction information of the ℎ water depth point to the grid node. The current mesh node's depth estimate is ̂ | , | , and the node update is performed by the following steps: σ n|n 1 σ n 1|n 1 (1) z n|n 1 z n 1|n 1 σ n|n K n σ n (6) According to the above method, the calculation is completed when all neighborhood information participates in the water depth estimation. Finally, get the estimated results of the grid nodes that contain all the neighborhood information.

Statistical denoising.
After all grid nodes have been estimated, the depth difference between the grid nodes and the water depth points in their voxels needs to be calculated and counted. Since the near-ground noise is distributed on both sides of the terrain, the depth difference distribution is symmetrical. The statistical analysis of depth difference is performed on the measured data of 7986215 data points. The resolution of the octree is 0.5m, and the depth difference distribution is shown in Figure 3. The abscissa indicates the depth difference and the ordinate indicates the probability density. It can be found that the depth difference approximates the normal distribution.   Figure 4. algorithm flow.

Program optimization
The thresholds involved in the algorithm are determined as follows: 1) The neighborhood number threshold 1  is to remove the low-density point cloud while avoiding accidental deletion of the surface and edge of the seabed topography, and in the case of the resolution of the octree is 0.5m, 1  takes 2; 2) The denoising threshold 2  determines is typically taken as 2 .

4.1Experimental data and environment
The experimental data is the measured point cloud collected by the R2Sonic2024 multi-beam system, and the measurement area is about 8 square kilometers. The basic configuration of the experimental computer is CPU: 1.8GHz, Intel(R) Core(TM) i7-4500U; RAM: 8GB. The experimental software environment is based on Qt4.8.7+VS2013 compiler +PCL (Ver1.8.0).

Algorithm execution efficiency analysis.
In this experiment, the same experimental data is processed by the algorithm and PCL statistical filter, and the execution time of the two methods is compared. The PCL filter parameters are 100  k and double medium error. The octree resolution of this algorithm is 5m. The experimental results are shown in Table 1 and Figure 5.   Figure 5. Experimental result diagram. It can be obtained from the experimental results that as the number of points clouds increases, the time consumption of the PCL algorithm and the algorithm increase linearly. However, the execution time of the algorithm in this paper grows faster than the PCL algorithm, but eventually the difference between the two tends to be stable. This is because the efficiency of the algorithm in this paper is affected by the number of water depth points involved in the estimation. As the number of point clouds grows, the number of voxels increases, but the number of water depth points in voxels does not change significantly. Therefore, the execution efficiency of this algorithm increases linearly with the increase of point cloud number. The difference between algorithm efficiency and PCL algorithm is controlled at around 8%.

4.2.2
Algorithm denoising effect analysis. The purpose of this experiment was to analyze the denoising quality of the algorithm used in this paper and compare it with the PCL algorithm. In this experiment, a multi-beam point cloud containing 302062 data points with dense noise in the survey area is selected to demonstrate the denoising effect. The following are the experimental results.
(a) Pre-treatment effect (b) Initial denoising effect (c) Precise denoising effect Figure 6. Point cloud overall rendering: before denoising (a) and after denoising (b), (c).   Figure 6 shows the overall effect before and after denoising. Figure6 (a) shows the point cloud effect before denoising, Figure6 (b) shows the point cloud effect after initial denoising, and Figure6 (c) shows the point cloud effect after precise denoising. It can be found that after initial denoising, obvious outlier noise can be removed, and topographic and near-ground noise are preserved. After precise denoising, near-ground noise is removed and topographic features are preserved. Figure 7(d) and Figure 7 (e) shows the denoising details of the algorithm. The algorithm can distinguish terrain and noise better. Figure 7(f) is the denoising effect diagram of PCL algorithm. Denoising using PCL algorithm is difficult to preserve regional boundary information.
In this paper, 1422 noises are removed by initial denoising, 962 noises are removed by precise denoising, 299678 inner points are confirmed, and 298827 inner points are confirmed by PCL algorithm. Calculate the proportion of terrain that is considered to be a noise point. The algorithm error rate is 0.09% and the PCL algorithm error rate is 0.48%. In summary, it can be seen that the algorithm is superior to the PCL algorithm in terms of boundary reservation.

Conclusion
Aiming at the problem of multi-beam point cloud denoising, this paper divides the noise into nearground noise and outlier noise according to the spatial distribution characteristics of noise. After initial denoising and precise denoising, two types of noise are removed respectively. The experimental results show that the algorithm has good denoising effect. Compared with the PCL statistical filter, the algorithm can better preserve the region boundary information. However, it is found that the denoising effect of the algorithm is not good when dealing with strip edges and data staggered layers. These situations will be the focus of subsequent research.


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Partus referral classification using backpropagation neural network

The number of maternal mortalities in Indonesia keeps increasing significantly. The same thing occurs to the number of fetal mortalities which is not less than maternal ones. It is a given knowledge that the condition of expectants is mostly vulnerable to various disorders. Therefore, there is a high possibility of the occurrence of any maternal and fetal mortality. Things most likely to go wrong when the partus occurs and if the disorders are not treated as fast as possible, it will be very dangerous for the expectants. To minimize such occurrences, medical officers have been using a certain method named screening to detect which partus case which potentially has high risk before it is too late. Nevertheless, the results of screening are not always accurate. In this paper, we are going to come up with any other way, which is data mining computation. Data mining has known to be able to help human solving problems as well as a promising region for data classification. Most medical problems have been classified using data mining. Backpropagation Neural Network method will be used in this paper to classify partus referral cases. Thus, Backpropagation Neural Network will be compared to other algorithms to know if it is a better algorithm for this case based on real data of cohort register. The result of the researches confirms that Backpropagation Neural Network is the best of all three methods (Backpropagation Neural Network, C4.5 and Naive Bayes Classifier) used to classify partus referral.

Introduction
Partus is the outgoing process of conception result from woman's uterus through the way it should've been or not, with help or not [1]. All of the expectants would want a normal process of childbirth after expecting for averagely nine months long. Based on World's Health Organization (WHO), preterm birth complications, birth asphyxia and birth trauma are the 8th and 10th top causes of death consecutively [2]. But the fact is the maternal mortalities have been increased if compared with 20 th century, from 228 to 359 in 10 thousands births [3]. There are about 10-15% of outcomes are having troubles [4] so that the expectants needs to be hurried to the medical place that has higher medical facility.
One of effort that has been made to reduce the risk of partus is improving system of referral. Referral system is one of medical facility that enable responsibilities exchanges of patients both horizontally and vertically to increase the quality, scope and efficiency of medical service [5]. The referral system that currently exists is rather complicated and must go through few steps of administrations before the patient getting the medical service they deserve. Patients that are about to be submitted must meet several predetermined criteria and have a medical examination by medical personnel. While filling the administration, the patient who need the treatments will have to wait. The time spent to wait themselves The problems regarding partus and its referrals have been appointed as a topic on few papers before. It is said that there is a tardiness on recognizing risks, as well as decision making, so that the referral process might as well be too late for the expectants [6]. The parameter of maternal delivery referral has also been evaluated by Zubaidah on her research as the referral processes often face some problems [7]. A good education to expectants is a good way to decrease maternal mortalities [8].
Medical personals use a method which is called screening method. The screening method is a method to predict if expectant has great risk while delivering his baby. To do this method, they are scoring based on the possible risk of deliveries and giving them a score if they meet the criteria. The higher the score, the higher the risk of the delivery so that the process must be conducted on medical place with higher facility, such as hospitals. But sometimes the result of screening method is not always accurate. There are some inexperienced personals giving score of screening so the result is not 100% accurate.
Researches that are related to pregnancy and deliveries have been conducted. One of the topics that has been explored and predicted is preterm birth. C4.5 Algorithm has been used to predict the premature delivery [9] which is optimized using Particle Swarm Optimization to increase its accuracy [10]. There have been conducted some other researches using Neural Network with Particle Swarm Optimization as its optimization to selecting features of premature deliveries prediction [11]. Naïve Bayes also has been used to predict if the delivery will be normal or not [12]. The comparison of few methods of classification has been conducted by several researchers. On a research conducted by Delen, it is said that decision tree (C.5) beat the accuracy of artificial neural networks and logistic regression models on predicting breast cancer survivability [13]. Meanwhile, Bayesian classifiers is said to have an advantage against other algorithms because in medical data sets, attributes are typically independent [14]. While on another research, another famous algorithms, Artificial Neural Network, is proven to outstand other regression models in 28 studies included [15].
Based on the description, we found out that computation methods in data mining are able to be used to predict some cases on medical datasets such as cancers, tumors, pregnancies and deliveries field. But there are barely research conducted regarding partus referral on deliveries cases, which is why on this paper we are going to conduct the research. Back propagation Neural Network will be used to classify paper referral and we will compare other methods which are C4.5 Algorithm and Naive Bayes Classifier as we know that these algorithms are commonly used in previous researches.

Dataset
The collecting process of the dataset that is going to be used is by studying documents. The document used is a secondary documents which is confidential. The collected document from "Register Kohort Ibu" book's validity is trustworthy. "Register Kohort Ibu" is the data source of expectants services as well as their risks written by medical personals. The source itself has been written and reported by midwifes from 2014 to 2016. The amount of record data that has been collected are 321 record data. There are two classes that will be classified based on the label of partus attribute, which is Reffered and Not Reffered. K-fold cross validation is used to divide data training and data test. The information summary of dataset that we used is shown on Table 1.
Because the dataset is not in good shape, was not one for data mining purpose, there is a need to preprocess so that the data is easier to process. The preprocessing consists of changing some records that has missing values with average value of its attribute's values. In Backpropagation Neural Network (BNN) case, we change nominal data (from attribute education) into numerical type of data so it could be processed since BNN can only process numerical data. Right after data is pre-processed, the data will be split using k-cross validation method. The k is determined as 10 for the process as the research conducted by Kohavi recommend us to use stratified ten-fold cross-validation [16]. Finally, the data will be tested using various methods which is described as follows.

Backpropagation Neural Network
Artificial neural network is one of methods in artificial intelligence which is popular and frequently used on medical field [17]. It is said because it's predictive work, although there are some disadvantages like its high sensitivity on parameter from the method. Artificial Neural Network can be used to classify and recognize pattern. Artificial neural network's architecture consists of the amount of neurons in input layer, hidden layers and output layer. For this case, we will use technique of error back propagation to train. Back propagation algorithm is a supervised learning method which can be divided into two phases: propagation and weight update. The two phases are repeated until the performance of the network is good enough. The steps to model Backpropagation Neural Network are described as follows [18]:  Input partus data.  Initialize initial weight (Vi), bias weight (X0), weight (Wi) to y, and bias weight (W0) to y, randomly with range values between -0.5 to 0.5. Determine value of learning rate, hidden layers, maximum epoch and threshold.  Do normalization on inputs using Equation 1; where x' is the new value of xi, xi is the value of x on i-throw, min(x) is the minimum value of x in dataset and max(x) is the maximum value of x.
 Count the output in hidden layer (Zin_i)using Equation 2; where v is initial weight and v .
 Calculates the Yin from the sum the Zi multiply by the weights (Wi and W0) using Equation 3. y = w + w × z + w × z + w × z whereZi is activated with binary sigmoid rules:  If error <= 10 -6 , directly to testing phase, if not then directly to the stage of weighting.  Initialize target which is the testing data which will be compared with predicted results.  Calculate the value of by using Equation 6.

Result and discussion
We have performed the methods discussed above on partus dataset to classify which data will be recommended to have a referral or not. To measure the result, we will depend on accuracy, recall, precision and also Root Mean Squared Error (RMSE). Accuracy, recall and precision are commonly used evaluation measures that can be measured by using confusion matrix methods. While RMSE are evaluation measurement that represents differences between real values and predicted values.The summary of the experiments done is shown on Table 2.  Table 2, although Backpropagation Neural Network needed a longer time to process, Backpropagation Neural Network have the best accuracy, recall, precision and the least RMSE (which means best RMSE since the least error is produced). On the second place is C4.5 Algorithm which is better than Naive Bayes Classifier. And the last place is Naive Bayes Classifier.

Conclusion
It is concluded that the three methods have their own advantages, for example Naïve Bayes Classifier is better for use while data is independent to each other. While for C4.5 Algorithm, the result will be transparent so that humans will be able to use it easily. Although, Backpropagation Neural Network got the highest result of all. In this case, we can conclude the best method to use is Backpropagation Neural Network because it got the best accuracy, recall, precision, and RMSE. Backpropagation Neural Network needs a longer time to train, longer than Decision Tree and Naive Bayes classifier is probably one of the reason that makes the said method got better result.Backpropagation Neural Network is said to have better results on data with large number of features or high dimensionality, like the dataset used. For the further experiment, the use of bigger dataset, different value of k in k-cross validation and more vary methods are recommended to see if Backpropagation Neural Network would still lead the best accuracy. As the result's accuracy is high, it is safe to say that we can use Backpropagation Neural Network to train dataset and as a reference in partus referal classification. For future researches, deep learning of Backpropagation Neural Network is reccomended to be conducted for a better result.