Journal of Digital Imaging https://doi.org/10.1007/s10278-020-00391-5 ORIGINAL PAPER A Novel Fusion‑Based Texture Descriptor to Improve the Detection of Architectural Distortion in Digital Mammography Osmando Pereira Junior1 · Helder Cesar Rodrigues Oliveira2 Marcelo Andrade da Costa Vieira2 · Adilson Gonzaga2 · Carolina Toledo Ferraz3 · José Hiroki Saito3 · Received: 30 July 2019 / Revised: 12 August 2020 / Accepted: 22 September 2020 © Society for Imaging Informatics in Medicine 2020 Abstract Architectural distortion (AD) is the earliest sign of breast cancer that can be detected on a mammogram, and it is usually associated with malignant tumors. Breast cancer is one of the major causes of death among women, and the chance of cure can increase significantly when detected early. Computer-aided detection (CAD) systems have been used in clinical practice to assist radiologists with the task of detecting breast lesions. However, due to the complexity and subtlety of AD, its detection is still a challenge, even with the assistance of CAD. Recently, the fusion of descriptors has become a trend for improving the performance of computer vision algorithms. In this work, we evaluated some local texture descriptors and their possible combinations, considering different fusion approaches, for application in CAD systems to improve AD detection. In addition, we present a novel fusion-based texture descriptor, the Completed Mean Local Mapped Pattern (CMLMP), which is based on complementary information between three LMP operators (signal, magnitude and center) and the local differences between pixel values and the mean value of a neighborhood. We compared the performance of the proposed descriptor with two other well-known descriptors: the Completed Local Binary Pattern (CLBP) and the Completed Local Mapped Pattern (CLMP), for the task of detecting AD in 350 digital mammography clinical images. The results showed that the descriptor proposed in this work outperforms the others, for both individual and fused approaches. Moreover, the choice of the fusion operator is crucial because it results in different detection performances. Keywords Architectural distortion · Fusion-based texture descriptor · Digital mammography · Fusion operators · Local texture descriptor * Osmando Pereira Junior osmando@iftm.edu.br Helder Cesar Rodrigues Oliveira heldercro@usp.br Carolina Toledo Ferraz caroltoledoferraz@gmail.com José Hiroki Saito saito@cc.faccamp.br Marcelo Andrade da Costa Vieira mvieira@sc.usp.br Adilson Gonzaga agonzaga@sc.usp.br 1 Federal Institute of Education Science and Technology of Triângulo Mineiro (IFTM), Patrocínio, Minas Gerais, Brazil 2 São Carlos School of Engineering, University of São Paulo (EESC/USP), São Carlos, São Paulo, Brazil 3 University Center Campo Limpo Paulista (UNIFACCAMP), Campo Limpo Paulista (SP), São Paulo, Brazil Introduction Breast cancer is one of the leading causes of death among women [1]. Early detection leads to better treatment options, increasing the chances of curing the disease [2, 3]. X-ray mammography is the most commonly used screening tool for the early detection of breast cancer [4, 5]. Among breast lesions, architectural distortion (AD) is the earliest sign of breast cancer that can be detected on a mammogram [6, 7] and there is a considerable risk of malignant tumors associated with it. However, AD is difficult to detect by the radiologist, as it is a subtle contraction of the breast parenchyma with no defined mass or visible border [8, 9]. AD detection is highly associated with the experience of radiologists, and several cases are unnoticed by them [7, 10]. Thus, it is the most common finding of retrospective reviews of false-negative mammograms, where approximately 75% of the malignancy cases were associated with AD [7, 11]. Therefore, 13 Vol.:(0123456789) Journal of Digital Imaging accurate detection of AD in mammography screening is essential for early diagnosis of breast cancer and may significantly increase the chances of cure [2, 3]. Computer-aided detection (CAD) systems have been used in clinical practice to assist radiologists with the task of detecting breast lesions in mammography [12, 13]. Given the complexity and subtlety of AD, even with the support of CAD systems, its detection is still a challenge [9, 14]. CAD uses several techniques of computer vision and artificial intelligence to automatically detect suspicious lesions in mammographic images, where the use of texture descriptors is essential, mainly for the detection of architectural distortion [15, 16]. A texture descriptor aims to capture the general characteristics of patterns in a local context. In recent decades, several methods of texture analysis have appeared. Among them, the Local Binary Pattern (LBP) has been shown to be an efficient solution for the description of textures and has been used successfully in many computer vision tasks [16, 17]. To provide new effective information to LBP code for texture classification, Guo et al. [18] proposed a completed modeling of the local binary pattern operator, called the Completed Local Binary Pattern (CLBP). In addition to the conventional LBP descriptor, represented by the signal operator (CLBP_S), two other operators were defined: the magnitude (CLBP_M) and the center (CLBP_C). The first two operators, CLBP_S and CLBP_M, are complementary components and perform local feature extraction. The last one, CLBP_C, applies a global threshold over the image. The three components are then combined using two different fusion rules: concatenation and joint combination. The final CLBP descriptor obtained better accuracy than others based on the LBP [18]. Another texture descriptor, the Local Mapped Pattern (LMP) [19], was presented as a generalization of the LBP. A smooth approximation to the step function by a sigmoidal function was implemented in the feature extraction rule, which allowed the LMP descriptor to better capture subtle differences between the pixel values of a texture. The LMPbased descriptors achieved promising results in computer vision applications and outperformed LBP-based descriptors in several applications, such as object classification [20], color texture classification under varying illumination [21], classification of rotated textures [22], iris recognition under varying pupil size [23] and detection of architectural distortion in digital mammography [24]. Vieira et al. [22] proposed the Completed Local Mapped Pattern descriptor (CLMP) for the classification of textures at different orientations considering that LMP-based descriptors outperformed those based on LBP. As in the case of CLBP, local differences were decomposed into two complementary components, the signal (CLMP_S) and the magnitude (CLMP_M). In addition to these operators, the 13 CLMP_C was proposed with the goal of adding global texture information as for the CLBP_C operator. In the context of texture analysis in different orientations, the descriptor CLMP performed better than CLBP, with less processing time. A variation of the LMP descriptor, the Mean Local Mapped Pattern (M-LMP), was introduced by Ferraz et al. [20] for the classification of objects in images. When extracting the M-LMP features, pixels from a circular neighborhood were compared with the average value of gray levels in that neighborhood. M-LMP performance was compared with two other texture descriptors: the CS-LBP [25] and SIFT [26], and the M-LMP achieved greater accuracy with less processing time for the classification task. In addition to texture descriptors, other approaches have used statistical methods [27, 28] and convolutional neural networks (CNNs) [29, 30] for feature extraction. Recently, the fusion of descriptors has become a trend for improving the performance of computer vision algorithms [31]. Thus, in this paper, we propose a novel fusionbased texture descriptor, the Completed Mean Local Mapped Pattern (CMLMP), for application in mammography CAD systems to improve AD detection. The CMLMP is based on complementary information between three LMP operators (signal, magnitude and center) and local differences between pixel values and the mean value of a neighborhood. Furthermore, we evaluated the performance of the proposed descriptor with two other texture descriptors, CLBP [18] and CLMP [22], and their possible combinations considering different fusion approaches. Related Works One of the most widely used texture descriptors is the Local Binary Pattern (LBP) [17]. Due to its efficiency, simplicity and easy implementation, many variations have been proposed for different tasks [18, 32–36]. Another approach commonly used to describe textures in images is the ”statistical approach”. For the classification task, the aim is to find a probabilistic decision rule that associates the texture with a specific class [37]. Some textural measures normally used are: energy, contrast and angular momentum. Over the last ten years, several methods have been proposed for computerized detection of AD in mammographic images, where a wide range of different approaches have been proposed. Most of them performed the analysis of breast tissue by applying texture descriptors to images of digitized mammograms (screen-film mammography), extracted from the Mini Mammographic Image Analysis Society Digital Mammogram Database (mini-MIAS) [38] and/or Digital Database for Screening Mammography (DDSM) [39]. The most relevant works addressing the Journal of Digital Imaging detection of architectural distortion in mammography are summarized in Table 1, which are briefly described in this section. Nemoto et al. [40] proposed a complete pipeline for the analysis of 25 Fuji computed radiography (FCR) mammograms. After a preprocessing step, they extracted nine features from the suspicious regions: six of them (four contrast measurements, energy and skewness) were calculated over the intensity image; two (skewness and second moment) were calculated over the Laplacian filtered image; and the other one refers to the distance between the suspicious region and the skin. The authors used the Mahalanobis distance for classification and reported a sensitivity of 80.0% for AD classification. Jasionowska et al. [10] proposed an approach based on images in the frequency domain for AD detection, where 13 features were extracted from each suspicious region. Some of them (contrast, correlation, energy, entropy and homogeneity) were based on the Gray-Level Co-occurrence Matrix (GLCM), seven were statistical measures (variance, standard deviation, kurtosis, skewness, energy and entropy), and two (slope and point of intersection with y-axis) were computed using the approximation of angular spectrum. After classification with support vector machine (SVM), they achieved a sensitivity of 68.0%. Minavathi et al. [41] proposed an AD detection pipeline where textural, gradient-based and intensity features were extracted from digitized mammograms. The authors used both SVM and multilayer perceptron (MLP) classifiers. The best achieved sensitivity was 94.7%, and the specificity was 89.6%. Rangayyan et al. [42] proposed 13 features that aim to assess the specularity and angular dispersion of breast lesion patterns. They used MLP for classification and obtained a sensitivity of 80.0% with an area under the receiver operating characteristic curve (AUC) of 75.0%. Mohammadi et al. [43] used the local texture descriptor called Monogenic Binary Coding (MBC) for detecting architectural distortion in Regions of Interest (ROI) of digitized mammograms. They used the DDSM dataset and measured the performance in terms of accuracy (Acc), which best result equals 91.2%. Kamra et al. [28] presented an approach in which 284 textural features were extracted from three datasets of digitized mammograms: DDSM, mini-MIAS and a private dataset. A set of 280 features were obtained from the GLCM with different radii, two features based on fractal analysis, and two features extracted from the Fourier power spectrum. They reduced the feature vector’s size by applying a postprocessing step and followed the classification with an SVM classifier. The results were reported according to the dataset: for the mini-MIAS, it reached an accuracy of 95.3% , sensitivity of 85.7% , specificity of 97.2% and AUC of 98.0% ; for the DDSM, accuracy of 92.9% , sensitivity of 93.3% , specificity of 92.0% and AUC of 95.0% ; and for the private dataset, accuracy of 88.0%, sensitivity of 87.5%, specificity of 88.2% and AUC of 93.0%. Table 1  Relevant works addressing the detection of architectural distortion in mammography Author Dataset #Images with AD #Images without AD Classification Performance* Nemoto et al. (2009) [40] Jasionowska et al. (2010) [10] private FCR dataset DDSM 25 33 - S = 80% S = 68% Minavathi et al. (2011) [41] Minavathi et al. (2011) [41] Rangayyan et al. (2013) [42] Mohammadi et al. [43] mini-MIAS DDSM private digitized dataset DDSM 19 23 106 Kamra et al. (2015) [28] DDSM Kamra et al. (2015) [28] Kamra et al. (2015) [28] mini-MIAS private digitized dataset 60 13 Casti et al. (2016) [44] Oliveira et al. (2017) [24] Liu et al. (2018) [27] Liu et al. (2018) [27] Oliveira et al. (2019) [30] Akhtar et al. (2020) [55] Costa et al. (2020) [54] DDSM private FFDM dataset DDSM mini-MIAS private FFDM dataset DDSM & mini-MIAS private FFDM dataset 150∗∗ ∗∗ 23∗∗ 122 100 63 19 175 64 140 258∗∗ 152 97 52 150∗∗ 25 36 50∗∗ 785 175 69 140 S = 94.7%, Sp = 89.6% S = 94.7%, Sp = 89.6% S = 80%, AUC = 75.0% Acc = 91.2% Acc = 92.9%, S = 93.3%, Sp = 92.0%, AUC = 95% Acc = 95.3%, S = 85.7%, Sp = 97.2%, AUC = 98% Acc = 88.0%, S = 87.5%, Sp = 88.2%, AUC = 93.0% S = 81.0% Acc = 90%, AUC = 97.3% S = 90% S = 90% Acc = 75.3%, AUC = 82.9% S = 85.0% Acc = 80.9%, AUC = 89.0% *Accuracy (Acc), sensitivity (S), specificity (Sp) and area under receiver operating characteristic curve (AUC) **These values refer to the number of ROIs, not to the number of mammograms 13 Journal of Digital Imaging Casti et al. [44] proposed a complete pipeline to detect suspicious lesions in digitized mammograms, where a set of 7 differential features (area, compactness, elongation, distance, directionality, weighted directionality and dispersion) were calculated for classification of suspicious spots. They used a classifier based on Fisher’s linear discriminant analysis and reported a sensitivity of 81.0% for the detection of AD in the DDSM dataset. Using a modified version of the Twin Bounded Support Vector Machine (TBSVM) for the detection of regions with AD on the DDSM and MIAS dataset, Liu et al. [27] proposed a method where 241 features were extracted: 228 features from the GLCM; 11 related to the measurement of spiculated patterns; and the entropies of Renyi and Tsallis. After the feature selection and classification steps, they reported a sensitivity of 90.0% for AD detection. Oliveira et al. [24] proposed the use of texture descriptors developed to map local micropatterns (LBP and LMP) in the task of detecting AD. They used a dataset composed of 100 digital mamography images, from which they extracted, per image, one ROI with AD and another one with normal tissue. The efficiency of the proposed MLP classifier was compared to four GLCM measurements: contrast, correlation, energy and homogeneity. The best two results were obtained with the LMP and energy of GLCM, where the classifier reached AUCs of 97.3% and 94.6%, respectively. In addition to the handcrafted descriptors, another methodology that has been recently reported in the literature for AD detection was the use of convolutional neural networks (CNNs). CNNs have been the winning card in computer vision achieving good performance in many tasks [45]. Recently, many network architectures have been developed, including Resnet [46], XNOR-Net [47], Mobilenet [48], PPFNet [49] and DEP [29]. Some researchers have used CNNs to extract features from images [50, 51] and then have applied these features as descriptors for classification tasks. Beyond these methods, there is a popular unsupervised learning neural network called autoencoders [52]. Autoencoders are a representation learning method that can learn data and represent them in lower dimensions [53]. Oliveira et al. [30] used an autoencoder to improve the detection of AD in digital mammography. The authors used two different datasets, one to train the autoencoder and the other to test the proposed model. They reported an accuracy of 75.3% and an AUC of 82.9%. Costa et al. [54] evaluated the detection of AD in digital mammography using well-known deep learning models, such as VGG-16, using transfer learning approaches. The proposal is to map the region containing AD by aggregating the regions of interest recovered by the sliding window. Among the several ways to train the VGG-16 layers, the best result reached an accuracy of 80.9% and AUC of 89.0%. 13 Even today, in the digital era, new methods for AD detection have been proposed based on digitized mammograms [9]. The study performed by Akhtar et al. [55] proposed a new approach using an ensemble composed of AdaBoost and Random Forest classifiers. They used 133 images with and without AD from the DDSM and mini-MIAS databases. The results, reported by means of sensitivity in an FROC curve with thresholds of 90% and 85%, indicate over 16 false-positive ROIs per image. Despite the popularity of deep learning methods, there are some issues related to the use of such an approach, including the need for computers with high-performance GPUs, the large number of images required for network training, the loss of information in pooling layers and the overfitting of the model [45, 56]. Furthermore, Liu et al. [57] presented a large-scale study in which they evaluated the performance of 32 LBP-based descriptors and compared them to those of eight deep convolutional networks applied over 30 texture datasets for different classification tasks. The authors showed that some LBP-based descriptors overcame CNN approaches, achieving the best overall performance. The CLMP descriptor [22] and CLBP [18] present different information among their three operators, which allows more discriminating features when combining them. The M-LMP descriptor [20] presented better performance than other LMP and LBP variations. Material and Method Although full-field digital mammography (FFDM) is the preferred tool for breast cancer screening, most of the solutions proposed in the literature for the detection of architectural distortion use datasets of digitized mammograms. To assess our proposed descriptor for the AD detection task, we created a dataset composed exclusively of FFDM images. Digital Mammography Dataset The dataset used in this study consists of 350 clinical images. These data were acquired at the Institute of Radiology of São Paulo (InRAD) of the University of São Paulo Medical School (FMUSP) in a Hologic Selenia DimensionsTM system in the FFDM mode. This work was approved under the Institutional Review Board (IRB #1.581.220 ). The dataset is composed of 175 examinations with AD and 175 without any type of lesion, i.e., healthy mammograms. All AD cases were confirmed and marked by a radiologist. ROIs with a size of 256 × 256 were extracted from the central point of each region previously marked by the radiologist. Figure 1 shows an example of a clinical image from our dataset and a magnified region containing the architectural distortion. Journal of Digital Imaging Fig. 1  Example of a mammography with architectural distortion marked by a red box. The region containing the architectural distortion has been magnified for better visualization AD is not associated with masses and is well characterized based on its neighborhood. Therefore, to increase the number of samples in the dataset, we extracted 50 ROIs around the center of the lesion. During the ROI extraction, one criterion was considered: the central point of the AD must be inside the selected ROI. For mammograms without anomalies, 50 ROIs were randomly extracted from the breast tissue. Figure 2 shows examples of ROIs extracted from mammograms with and without AD, where each ROI belongs to a different mammogram. The final dataset was composed of 17,500 samples. Each ROI was processed for contrast enhancement, and the pixel values were rescaled to the range [0, 255]. Fig. 2  Examples of ROIs (a) with AD and (b) without AD. Each ROI was extracted from different clinical images Feature Extraction and Classification Figure 3 shows the framework of our method for architectural distortion recognition. We applied the texture descriptors CLBP [18], CLMP [22] and the CMLMP (Completed Mean Local Mapped Pattern), proposed in this paper, over the entire dataset. We considered each pixel surrounded by a symmetrical circular neighborhood of unitary radius and with eight neighbors. Three coded images [58] are generated for each descriptor, one per component, signal (S), magnitude (M) and center(C). The 1-D histograms of the coded images are used to build the feature vectors DESC_S, DESC_M and DESC_C, where DESC = {CLBP, CLMP, CMLMP}. To take advantage of the complementary information [18, 22] among these different descriptor components, we used the same methods presented in [18] (concatenation, joint and hybrid combination) to fuse either the 13 Journal of Digital Imaging Fig. 3  Framework of the proposed AD detection method individual feature vectors or the individual coded images, taken two by two or all three components. We applied the concatenation fusion operator (⊕) [59], as shown in Fig. 4, over the individual feature vectors DESC_S, DESC_M and DESC_C, and generated four concatenated feature vectors for each texture descriptor, which were denoted DESC_S⊕DESC_M, DESC_S⊕DESC_C, DESC_M⊕DESC_C and DESC_S⊕DESC_M⊕DESC_C. The concatenation operator can be described as follows. Given two feature vectors, v1 with B1 bins, and v2 with B2 13 bins, we considered the concatenation of feature vectors given by Eq. 1: v3 = v1 ⊕ v2 , (1) where v3 is the fused vector resulting from the concatenation of v1 and v2 , whose size is B3 = B1 + B2. The length of the concatenated feature vector is equal to the sum of lengths of respective individual feature vectors. The use of the operator ⊕, instead of the notation ‘ _ ’ Journal of Digital Imaging Fig. 4  The concatenation fusion operation Fig. 5  The joint fusion operation presented in [18], allows a clear representation of the concatenated components, even for the concatenation between different descriptors. To combine the coded images, we applied the joint fusion operator (│) over them, as shown in Fig. 5. A joint 2-D histogram of the coded images taken two by two was generated. The jointly fused feature vectors DESC_S│DESC_M, DESC_S│DESC_C and DESC_M│DESC_C were obtained by vectorizing these joint 2-D histograms. The length of the resulting fused feature vector is equal to the product between the maximum feature values B of the respective individual coded images. The jointly 3-D histogram of the three coded images was built and then converted into a 1-D histogram to generate the jointly fused feature vector DESC_ S│DESC_M│DESC_C, with length B = BS ⋅ BM ⋅ BC . As discussed before for the concatenation operator, the use of the operator│to represent the Joint fusion, instead of the notation ‘/’, also presented in [18], allows a clear representation for the joint fusion applied over different descriptors. Concerning the hybrid combination, we concatenated the individual feature vectors with the jointly fused ones. Three fused vectors were generated, which we denoted as DESC_S⊕(DESC_M│DESC_C), DESC_M⊕(DESC_ S│DESC_C) and DESC_C⊕(DESC_S│DESC_M). To classify an image as AD or non-AD, we used the K-nearest neighbors (KNN) classifier with the leave-oneout cross-validation method. Two different experiments were performed (see Fig. 6). In experiment #1, the target dataset consists of all images in dataset with the exception of the current image to be predicted, whereas in experiment #2, the target dataset consists of all images, with the exception of the N samples of the same mammogram as the current image to be predicted. The query sample, i.e., the sample to be predicted, is compared to all samples in the target dataset. We measured their similarity by calculating the Euclidean distance, defined by Eq. (2), between the feature vector of the query 13 Journal of Digital Imaging Fig. 6  Leave-one-out cross-validation method. Experiment #1 the target dataset consists of all images, with the exception of the current ROI to be predicted. Experiment #2 the target dataset consists of all sample ( 𝐐 ) and the feature vector of the ith target sample ( 𝐓i ), where B stands for the length of the feature vectors. √ √ B √∑ (2) d(𝐐, 𝐓i ) = √ (Qb − Tib )2 b=1 The query sample is considered of the same class as the majority number of neighbors among the K nearest targets. In other words, if K2 + 1 of samples from the K nearest neighbors were of class AD, then the query sample is classified as AD; otherwise, it is classified as non-AD. In the first moment, we used K = 1 and performed the first nearest neighbor classifier (1-NN). In the second moment, we determined a value K that increases the number of hits achieved in the classification. The performance of the AD detection method is evaluated in terms of sensitivity (S) and accuracy (Acc). The sensitivity, defined by Eq. (3), is the ratio of AD samples correctly classified as AD; and the accuracy, defined by Eq. (4), is the ratio of all samples correctly classified (AD and non-AD), where true positive (TP) is the number of AD samples correctly classified as AD, false negative (FN) is the number of AD samples wrongly classified as non-AD, true negative (TN) is the number of non-AD samples correctly classified as non-AD, and false positive (FP) is the number of non-AD samples wrongly classified as AD. S= TP TP + FN 13 (3) images, with the exception of the N ROIs of the same mammogram as the current ROI to be predicted Acc = TP + TN TP + FN + TN + FP (4) From the treatment point of view, the occurrence of FN is worse than FP, since in FN cases, the cancer has time to grow, hindering the treatment [2, 3]. Then, a given descriptor could be considered more appropriate than others to be used in the task of detecting architectural distortion when it reaches the highest sensitivity with high accuracy. Completed Mean Local Mapped Pattern (CMLMP) The proposed descriptor Completed Mean Local Mapped Pattern (CMLMP) is based on CLMP [22] complementary information and on the M-LMP [20] extraction feature method. It is composed of three components: signal (CMLMP_S), magnitude (CMLMP_M) and center (CMLMP_C). The signal component considers local grayscale differences in a circular neighborhood for each pixel in the image; the magnitude component relates local grayscale differences with global information; and the center component takes into account only global texture information. Each one of them is characterized by a specific feature extraction rule and generates an individual coded image, with one feature (code) for each pixel in the image, with the exception of the pixels on the edge of the image. The MATLAB code implementation for CMLMP is available for download at https​://githu​b.com/LAVI-USP/CMLMP​. Let p be a pixel in the (x, y) coordinates of an X × Y image, with gray value g(x, y), surrounded by a symmetrical circular neighborhood of radius R ( R > 0) and with N equally spaced neighbors, as shown in Fig. 7. If the coordinates of Journal of Digital Imaging 1 f(gdiff ) a b 0.5 Fig. 7  The circular neighborhood for R = 1 and N = 8 b p are (0,0), then the coordinates of each neighbor pi |Ni=1 are (−R ⋅ sin(2𝜋(i − 1)∕N), R ⋅ cos(2𝜋(i − 1)∕N)) , with gray value gi. The gray value of neighbors that are not located in the center of each pixel can be estimated by bilinear interpolation [22, 60]. The feature extraction rules for CMLMP_S, CMLMP_M and CMLMP_C applied over p(x, y) are presented in Eq. (5), where h = {S, M, C}; W is a weight vector for which Wi = 2(i−1); BS, BM and BC , with B ∈ ℤ+, are the maximum feature values in the respective coded image; and fh is the specific sigmoidal mapping function, defined in Eq. (6). � ∑N � f W i=1 hi i CMLMP_h(x, y) = ∑N (Bh − 1) + 0.5 (5) W i=1 i 1 gdiff _h fh = − 1+e 𝛽h (6) The grayscale differences for the signal, magnitude and center components, gdiff _S , gdiff _M and gdiff _C , are defined in Eqs. (7), (8) and (9), respectively. gdiff _S =gi − gmean (7) gdiff _M =|gi − gmean | − G (8) gdiff _C =g(x, y) − G (9) where gmean is the average gray value for the N neighbors, given by Eq. (10), and G is the average gray value among all pixels of the X × Y image, defined by Eq. (11). gmean = G= N 1∑ g N i=1 i X Y 1 ∑∑ g X ⋅ Y x=1 y=1 (x,y) (10) (11) 0 -255 0 >> a 255 gdiff Fig. 8  The mapping function behavior for a range of 𝛽 values (modified from [21]) The sigmoidal function f maps the grayscale difference gdiff to a correspondent pattern in the respective coded image. Its curve behavior is defined by the curve slope parameter (𝛽 ), where 𝛽 is a positive real number. Similar to other LMP-based descriptors, the performance of the proposed descriptor is affected by 𝛽 , which changes the sensitivity of the method to the nuances in the neighborhood [21]. As shown in Fig. 8, small values of 𝛽 saturate the mapping function to zero, for negative gdiff , or to one, for positive gdiff . As 𝛽 increases, the number of different values returned by the mapping function f (gdiff ) increases. Large values of 𝛽 make the sigmoidal mapping curve flatter, closer to a straight line parallel to the gdiff axis, for which the mapping function maps the grayscale differences to values closer to 0.5. The curve slope parameter for each sigmoidal mapping function, 𝛽S , 𝛽M and 𝛽C , and the maximum feature values BS , BM and BC , must be tuned to achieve a high performance in the desired application. We simultaneously tuned the parameters 𝛽 and B for each component by using a genetic algorithm, with accuracy as the objective function [21]. After coded image generation, we can build different feature vectors by considering the three CMLMP coded images as individual or as fused approaches. For the individual approach, we use each component as an individual descriptor, where the histogram of the coded image generates the respective feature vector with length BS , BM or BC. In the fused approach, by combining the individual feature vectors, we generate the concatenated feature vectors CMLMP_S⊕CMLMP_M, CMLMP_S⊕CMLMP_C, CMLMP_M⊕CMLMP_C and CMLMP_S⊕CMLMP_M⊕ CMLMP_C. The length of the concatenated feature vector is equal to the sum of the length of the individual feature vectors. 13 Journal of Digital Imaging By combining the coded images, we build the joint 2-D and the joint 3-D histograms of coded images and generate the jointly fused feature vectors CMLMP_S│CMLMP_M, CMLMP_S│CMLMP_C, CMLMP_M│CMLMP_C and CMLMP_S│CMLMP_M│CMLMP_C, with length B equals to BS ⋅ BM , BS ⋅ BC , BM ⋅ BC and BS ⋅ BM ⋅ BC , respectively. We also generate the three hybrid feature vectors CMLMP_S⊕(CMLMP_M│CMLMP_C), CMLMP_ M⊕( C M L M P _ S │ C M L M P _ C ) a n d C M L M P _ C⊕ (CMLMP_S│CMLMP_M). Joint ( ˇ , B) Parameter Tuning Before applying the descriptors over the dataset images, we tuned the pair ( 𝛽 , B) parameters for both CMLMP and CLMP descriptors. We selected 4% of the images (700/17500) and the following constraints were assumed: 𝛽 ∈ [10−2 , 40], B ∈ [2 , 256], 50 individuals as the population size of the genetic algorithm with a maximum of 40 generations. The tuned values are presented in Table 2. To illustrate the joint influence of 𝛽 and B on the performance of the descriptors, we show in Fig. 9 the accuracy behavior for a range of 𝛽 in (0 , 6] and B in (0 , 64] for CMLMP. The range of values used to plot the curves is less than that used to tune the parameters. We noted that small variations in 𝛽S or in BS abruptly change the accuracy value for CMLMP_S, where high accuracy is over the region BS < 20 ∪ 𝛽S < 2. The CMLMP magnitude and center components presented a smoother surface for accuracy. The influence of the optimized parameters on the mapping function for each CMLMP component is shown in Fig. 10. When analyzing a large range of gdiff , the sigmoidal mapping function behavior of CMLMP_S resembles that of the Heaviside step function, which is a consequence of the Results and Discussion In this section we present the acquired results from tuning the 𝛽 and B parameters, the results from two classification experiments and finally the computational complexity for all individual and fused descriptors by means of processing time. (a) 0.85 (b) 0.75 0.8 0.7 Acc Acc 0.75 0.7 0.65 0.6 0.65 0.6 60 6 40 B 0.55 60 20 B 2 0 6 40 4 4 20 2 0 0 (c) 0 0.8 0.75 Acc 0.7 0.65 0.6 0.55 60 6 40 B 4 20 2 0 0 Fig. 9  Classification accuracy achieved with the application of (a) CMLMP_S, (b) CMLMP_M and (c) CMLMP_C, for a range of 𝛽 and B 13 Journal of Digital Imaging Table 2  Tuned parameters Descriptor 𝛽S 𝛽M 𝛽C BS BM BC CMLMP CLMP [22] 0.1516 20.4247 26.2579 41 6 8 3.9095 39.8446 - 31 2 - ∗ *Proposed method f(gdiff ) (a) 1 0.5 CMLMP_S CMLMP_M CMLMP_C 0 -100 0 100 gdiff f( gdiff ) (b) 1 0.5 Fig. 11  Examples of coded images of CMLMP, CLMP and CLBP considering a ROI with AD CMLMP_S CMLMP_M CMLMP_C 0 -2 -1 0 gdiff 1 2 Fig. 10  The sigmoidal mapping function behavior of CMLMP descriptor for optimized 𝛽S , 𝛽M and 𝛽C for gdiff in a range of (a) [-100 , 100] and (b) [-2 , 2] 𝛽S small value (𝛽S = 0.1516). Although it saturates fS (gdiff ) to 0 for gdiff ≤ −1 or to 1 for gdiff ≥ 1, it represents a smooth mapping for gdiff in (−1 , 1). CMLMP_C and CMLMP_M mapping functions have curve behaviors similar to each other, but since 𝛽C > 𝛽M , fC (gdiff ) returns values closer to 0.5 than fM (gdiff ) to the same gdiff value. The descriptors were applied over the images from the digital mammograms dataset considering a symmetrical circular neighborhood with R = 1 and N = 8 . Figure 11 shows the generated coded images for a ROI with architectural distortion. When comparing the S-coded images with the M-coded images, we noted that the former has more detailed texture information, while the latter retained more the spatial patterns. The C-coded images are the result of an intensity transformation in the spatial domain applied over the original ROI. The CLMP_C and the CLBP_C coded images resulted from a binarization of the original ROI with the threshold equal to the average gray value from the whole image. The CMLMP_C coded image resulted from an intensity transformation applied over the original ROI with a sigmoidal mapping function (𝛽C = 26.2579) followed by a quantization with 3 bits (values in [0,7]), since BC = 8. By means of this figure, we might clearly see the complementary information among the different components from the same descriptor. Experiment #1: Test Set Composed of All Mammograms, Excluding the Current ROI to Predict In experiment #1, for each realization of the leave-one-out cross-validation method, only the current query sample 13 Journal of Digital Imaging Table 3  Sensitivity and accuracy (%) for individual descriptors using the methodology of experiment #1 Descriptor B S Acc CMLMP_S∗ 41 99.5 91.5 CMLMP_M∗ 6 CMLMP_C CLMP_S [22] CLMP_M [22] CLMP_C [22],CLBP_C [18] CLBP_Sriu2 [18] CLBP_Mriu2 [18] 8 74.0 72.4 31 2 2 10 10 95.7 91.6 72.4 87.9 76.1 86.0 63.5 54.4 80.2 72.2 ∗ 91.2 83.4 Entries in boldface indicate the best results achieved *Proposed methods was excluded from the target dataset, which means that the query sample was compared with the other N − 1 samples from the same mammogram and with those of the other mammograms during the K-NN classification procedure. Thus, the descriptors are expected to achieve high performance in experiment #1. For classification, we considered K = 1 (1-NN), i.e., the query sample is classified as being of the same class as the nearest neighbor. The performance for the individual descriptors applied over the dataset is presented in Table 3. The highest values for accuracy and sensitivity are shown in boldface. The signal component of the CMLMP descriptor resulted in the best performance. It reached a sensitivity of 99.5%, which means that 8,706 of 8,750 AD samples were correctly classified as AD. Additionally, the accuracy was equal to 91.5%, i.e., 16,013 samples from 17,500 were correctly classified as AD or as non-AD. The classifier returned only 44 FN samples; however, 1,443 FP occurrences were produced. The CLMP_S descriptor achieved the second highest values for sensitivity and accuracy, S = 95.7%, Acc = 86.0% and returned 376 FN and 2,074 FP. The signal components yielded sensitivity values greater than those of magnitude for all descriptors, and the center components resulted in the lowest values. When comparing component by component, the CMLMP descriptor presented better results than the CLMP for all components, and CLMP outperformed the CLBP descriptor. The considered methodology for this experiment modeled the problem as an image retrieval where the individual to be classified is known by the model system, which is not in accordance with the proposed application. In real cases, the new mammogram to be analyzed is unknown by the model system. Experiment #2, presented in the next section, addresses this new formulation of the problem. Nevertheless, experiment #1 is still relevant for analyzing the 13 descriptor performance in situations whose objective is to retrieve images of the same individuals. Experiment #2: Test Set Composed of N‑1 Mammograms, Excluding All ROIs of the Current Mammogram to Predict In experiment #2, the query sample was compared only with the samples belonging to the other mammograms. The results for the individual descriptors, considering K = 1, are shown in Table 4. We can see a performance reduction for all descriptors. CMLMP_S reached the best accuracy, Acc = 68.8%, with a small value for sensitivity, S = 57.8%. The CLMP_M achieved the best sensitivity, S = 91.1%, with accuracy equals to 63.2%. To increase the descriptor performance, we optimized the constant K in the KNN algorithm, considered in the classification process. Figure 12 shows the accuracy achieved by the individual descriptor components for a range of K values, K ∈ [1 , 2, 000]. For most descriptors, the highest accuracy was obtained with K equals to 100 nearest neighbors. We combined the different components from the same descriptor by using concatenation and joint fusion operators. The results for individual and fused descriptors are shown in Table 5. For individual descriptors, the CMLMP_C outperformed all others, resulting in the highest sensitivity, S = 81.5%, with accuracy equals to 76.0%. The highest accuracy was reached by the CMLMP_S descriptor, Acc = 77.3%, with sensitivity equals to 78.4%. The CMLMP_M component resulted in sensitivity very similar to that of CMLMP_S, S = 78.3%, but with a smaller accuracy, Acc = 70.8%, and was overcome by CLMP_M. Although the CLMP_M descriptor also outperformed the CMLMP_S in sensitivity, resulting in an increase of 3%, it presented 2.7% lower accuracy. Beyond that, CLMP_M has a very small feature vector size, with Table 4  Sensitivity and accuracy (%) for individual descriptors using the methodology of experiment #2 and K = 1 Descriptor B S Acc CMLMP_S∗ 41 57.8 6 60.6 68.8 8 66.2 68.3 31 2 2 60.9 91.1 72.0 67.3 63.2 54.1 10 10 56.6 63.0 63.7 65.2 CMLMP_M∗ CMLMP_C∗ CLMP_S [22] CLMP_M [22] CLMP_C [22], CLBP_C [18] CLBP_Sriu2 [18] CLBP_Mriu2 [18] Entries in boldface indicate the best results achieved *Proposed methods 66.7 Journal of Digital Imaging 0.8 0.75 Acc 0.7 0.65 CMLMP_S CMLMP_M CMLMP_C CLMP_S CLMP_M CLBP_S CLBP_M CLBP_C 0.6 0.55 0.5 1 10 20 50 100 200 500 800 1000 1200 1500 2000 K nearest neighbours Fig. 12  Accuracy of individual descriptor components for a range of K values only 2 bins (B = 2). The CLMP_C, which is the same as the CLBP_C, presented the smaller performance among all descriptors evaluated, and the CLBP_M resulted in a higher sensitivity and accuracy when compared with CLBP_S, and outperformed CMLMP_M in 2.3% for accuracy, with a reduction in sensitivity of 1.6%. The performance of the fused descriptors is related to the fusion operator and to the descriptors to be combined. Comparing the joint and the concatenation operators, we can see that the former resulted in high accuracy for eleven of twelve combinations. Only in the case of CMLMP_S│CMLMP_C, the classification presented lower accuracy than CMLMP_ S⊕CMLMP_C. Regarding the sensitivity, joint operators achieved higher values for eight of twelve combinations. Only in the cases of CLMP_S⊕CLMP_M, CLMP_M⊕ CLMP_C, CLMP_S⊕CLMP_M⊕CLMP_C and CLBP_M⊕ CLBP_C the concatenation operators outperformed the joint ones. Despite the best results achieved by the joint operator, its feature vector size is larger than the concatenated fused vectors. Consequently, it requires a larger time to determine the distance between the samples, which could be a limiting issue for some applications, and could define the choice by either approach. The high performance for jointly fused descriptors is achieved by combining the three descriptor components. This relationship is not observed for concatenated fusion vectors. We generated the hybrid fused feature vectors by first applying the joint operator over two components of a descriptor and then concatenating the resulting joint feature vector with the third component. Their vector sizes are larger than those of concatenated fused feature descriptors but smaller than those of jointly fused descriptors. For CLBP and CLMP, the hybrid fused descriptors presented higher performance than the two other fusion approaches. For CMLMP, joint combination yields the highest values. Despite the sensitivity values reached by ­CLBP_Mriu2⊕ (CLBP_Sriu2│CLBP_C), S = 79.5%, and by CLMP_M⊕ (CLMP_S│CLMP_C), S = 80.4%, the highest reached sensitivity for the respective descriptors, these values are smaller than that achieved by the CMLMP_C individual descriptor. The best performance was reached by the CMLMP_ S│CMLMP_M│CMLMP_C fused descriptor, whose sensitivity is equal to 85.7% with an accuracy of 77.0%. However, it presents a large feature vector size, B = 1,968, which directly increases the processing time. The CMLMP_ S│CMLMP_M presented the highest accuracy, Acc = 77.8%, but a small sensitivity, S = 80.5%. The jointly fused descriptor CMLMP_S│CMLMP_C, with small size, B = 328, resulted in a performance strictly near to the best one, S = 85.6% and Acc = 76.9%. Computational Complexity All the results were obtained by computer simulations in MATLAB® R2018a, using an operational system Ubuntu 16.04 LTS, with a chipset Intel® CoreTM i7-6700 CPU @ 3.40GHz, 32 GB of RAM memory and a TITAN XP NVIDIA GPU with 12GB of GDDR5X memory. A comparison of the average processing time is presented in Fig. 13, where t feat , measured in milliseconds, refers to the time to generate the feature vectors, and t dist , in microseconds, is the time to determine the Euclidean distance between the query and the target samples. The descriptors are arranged in descending order of sensitivity. Generating the feature vectors is more expensive than determining the distances. The former is related to the complexity of the feature extraction rule and to the fusion operation, and the latter is a consequence of the feature vectors length. Although we cannot relate the performance of the descriptor with its size, the highest t feat and t dist values are achieved by CMLMP_S│CMLMP_M│CMLMP_C, with the highest sensitivity too, and the smallest t feat and t dist are required for CLMP_C, from which the sensitivity and the accuracy are the smallest. Conclusions In this paper, we evaluated several fusion-based local texture descriptors, considering different fusion approaches, for AD classification in 350 digital mammography clinical images. Moreover, we introduced a new fused-based texture descriptor, the CMLMP, and compared its performance with two 13 M L S C C MP M (C ML _M C LM M M | M P L P LM _M C MP _S CM P_ M (C LM _M | CMLM C C P M M P | LM (C LM _M CM LM _C P_ M P | L P_ M S C LM _S CM P C M P | _ C LM _S CM LM C) M P | L P L _ C M C M S M P _C M P LM _M C LM _C M P_ ) P_ M C LM M) C M P LM C LM _C P_ CM M P M L C LM _C C M M P LM LM _C (C P_ P S C _S C LM | CL P_ LB L P C M C P_ C MP _S ML P_ M LM _M | C MP M L _ C CM (C P_M C MP M LM L LM _C P_ LM BP ) S| P_ _S CL P_C C S | C MP LM LB _ C P_ CM P_ C LM M LM C P_ | C P ) S| LM _M C P C C LM _C LM M P _ P C _S CM LM C LM LM P_S P_ C P C LB S LM _M |C P P_ C L _ S| LB C P C MP M LB _ L _ P_ S| C MP M M L _S C | C BP LM LB _C P C C _ C P L M LM C BP | LB _C L C P_ LM S C BP _S CL P_M _ | M C P_ (C LBP S CL P_ LB C L _ B C P_ ( M M CL P_ BP M C CL P_ C M M C LB (C P_ | C LB _M P_ LB S L P_ S C P | C MP C L _S L _ C C BP | MP C) LB LB _ C _ P_ M L C S L P_M | BP M) C _M M LB (C P_ LB S C P_ ) LB C P_ M CL P_ C | C MP C LB LB _C P_ C S C P_ LM LB C P_ C P_ ) C LB S ,C P LB _C P_ C C S| P_ LM LM P_ M C M C t dist (us) C P_ S P_ S| C M L C MP M (C ML _M C LM M M | M P_ L P LM M C MP _S CM P_ M (C LM _M | CMLM C C P M M P | LM (C LM _M CM LM _C P_ M P | L P_ M S C LM _S CM P C M P | _ C LM _S CM LM C) M P | L P L _ C M C M S M P _C M P LM _M C LM _C M P_ ) P_ M C LM M) C M P LM C LM _C P_ CM M P M L C LM _C C M M P LM LM _C (C P_ P S C _S C LM | CL P_ LB L P C M C P_ C MP _S ML P_ M LM _M | C MP M L _ C CM (C P_M C MP M LM L LM _C P_ LM BP ) S| P_ _S CL P_C C S | C MP LM LB _ C P_ CM P_ C LM M LM C P_ | C P ) S| LM _M C P C C LM _C LM M P _ P C _S CM LM C LM LM P_S P_ C P C LB S LM _M |C P P_ C L _ S| LB C P C MP M LB _ L _ P_ S| C MP M M L _S C | C BP LM LB _C P C C _ C P L M LM C BP | LB _C L C P_ LM S C BP _S CL P_M _ | M C P_ (C LBP S CL P_ LB C L _ B C P_ ( M M CL P_ BP M C CL P_ C M M C LB (C P_ | C LB _M P_ LB S L P_ S C P | C MP C L _S L _ C C BP | MP C) LB LB _ C _ P_ M L C S L P_M | BP M) C _M M LB (C P_ LB S C P_ ) LB C P_ M CL P_ C | C MP C LB LB _C P_ C S C P_ LM LB C P_ C P_ ) C LB S ,C P LB _C P_ C LM LM M C M C t feat (ms) Journal of Digital Imaging (a) 20 15 13 10 5 0 (b)14 12 10 8 6 4 2 0 Fig. 13  Processing time (a) for feature vector generation, in ms, and (b) for Euclidean distance determination, in 𝜇s, for all individual and fused descriptors in descending order of sensitivity other previously published descriptors, CLMP and CLBP, and their possible combinations considering joint and concatenation fusion operators. The center component of the proposed descriptor, CMLMP_C, achieved higher sensitivity than all individual and fused approaches for CLBP and for CLMP descriptors. Despite the smallest size of the concatenated fused feature vectors, the jointly fused descriptors resulted in higher sensitivity and accuracy values for combining the CMLMP components. In conclusion, the proposed descriptor outperforms the others, for both individual and fused approaches, and the fused approach improves the performance of the descriptor. Moreover, the choice of the fusion operator is crucial because it results in different detection performances. In future work, we intend to evaluate the fusion among different descriptors, considering multiscale and multimodal analysis. Journal of Digital Imaging Table 5  Sensitivity (%), accuracy (%) and average processing times for individual and fused descriptors using the methodology of experiment #2 and K = 100 Descriptor CMLMP_S ∗ CMLMP_M CMLMP_C ∗ ∗ CMLMP_S⊕CMLMP_M∗ CMLMP_S⊕CMLMP_C∗ CMLMP_M⊕CMLMP_C∗ CMLMP_S⊕CMLMP_M⊕CMLMP_C ∗ CMLMP_S │ CMLMP_M∗ CMLMP_S │ CMLMP_C∗ CMLMP_M │ CMLMP_C∗ CMLMP_S │ CMLMP_M │ CMLMP_C ∗ CMLMP_S⊕(CMLMP_M │ CMLMP_C) ∗ CMLMP_M⊕(CMLMP_S │ CMLMP_C)∗ CMLMP_C⊕(CMLMP_S │ CMLMP_M)∗ CLMP_S [22] CLMP_M [22] CLMP_C [22] , CLBP_C [18] CLMP_S⊕CLMP_M [22] CLMP_S⊕CLMP_C [22] CLMP_M⊕CLMP_C [22] CLMP_S⊕CLMP_M⊕CLMP_C [22] CLMP_S │ CLMP_M [22] CLMP_S │ CLMP_C [22] CLMP_M │ CLMP_C [22] CLMP_S │ CLMP_M │ CLMP_C [22] CLMP_S⊕(CLMP_M │ CLMP_C) [22] CLMP_M⊕(CLMP_S │ CLMP_C) [22] CLMP_C⊕(CLMP_S │ CLMP_M) [22] CLBP_Sriu2 [18] CLBP_Mriu2 [18] CLBP_Sriu2⊕CLBP_Mriu2 [18] CLBP_Sriu2⊕CLBP_C [18] CLBP_Mriu2⊕CLBP_C [18] CLBP_Sriu2⊕CLBP_Mriu2⊕ CLBP_C [18] CLBP_Sriu2 │ ­CLBP_Mriu2 [18] CLBP_Sriu2 │ CLBP_C [18] CLBP_Mriu2 │ CLBP_C [18] CLBP_Sriu2 │ ­CLBP_Mriu2 │ CLBP_C [18] CLBP_Sriu2⊕(CLBP_Mriu2 │ CLBP_C) [18] CLBP_Mriu2⊕(CLBP_Sriu2 │ CLBP_C) [18] CLBP_C⊕(CLBP_Sriu2 │ ­CLBP_Mriu2) [18] Autoencoder∗∗ [30] AlexNet B S Acc 41 78.4 77.3 8.5 1.0 6 78.3 70.8 7.4 0.6 8 81.5 76.0 1.1 0.6 47 79.3 77.3 15.9 0.8 49 82.9 76.1 9.6 0.9 14 81.6 76.2 8.5 0.6 55 82.4 76.3 17.0 0.9 246 80.5 16.7 2.2 328 85.6 76.9 10.4 2.7 48 83.1 75.6 9.2 0.8 77.0 18.2 13.1 1,968 89 85.7 77.8 t feat(ms) tdist(𝜇s) 85.1 76.1 17.7 1.1 334 83.1 76.8 17.8 2.8 254 83.0 76.1 17.8 2.2 31 2 2 33 33 4 35 62 62 4 124 35 64 64 10 10 20 12 12 22 100 20 20 200 30 30 102 4096 77.2 81.4 57.1 78.1 71.0 80.0 79.5 78.0 79.1 76.3 79.2 73.5 80.4 72.9 67.8 76.7 74.6 65.5 74.3 71.4 75.8 77.0 72.5 77.0 70.7 79.5 72.9 80.0 75.1 74.6 63.6 74.3 71.9 73.6 74.5 74.5 76.4 73.7 76.7 73.9 76.5 72.2 71.2 73.1 72.5 70.2 71.5 71.0 74.4 74.1 73.8 76.0 73.9 75.1 72.2 70.0 8.4 6.5 0.6 14.9 9.0 7.1 15.5 15.6 9.7 7.8 16.6 16.2 16.2 16.2 6.8 6.8 13.6 7.4 7.4 14.2 14.3 8.1 8.1 15.3 14.9 14.9 14.3 - 0.7 0.6 0.6 0.8 0.8 0.6 0.8 0.9 0.9 0.6 1.4 0.8 0.9 0.9 0.6 0.6 0.6 0.6 0.7 1.2 1.2 0.7 0.7 1.8 0.7 0.7 1.2 - - 71.2 77.5 - - Entries in boldface indicate the best results achieved. *Proposed methods **The sensitivity (S) of the autoencoder was calculated exclusively for this paper Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001 and by the São Paulo Research Foundation (FAPESP), grant #2015/20812-5. 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