Mathematical Morphology Research Articles

A New Insight on the Upwelling along the Atlantic Iberian Coasts and Warm Water Outflow in the Gulf of Cadiz from Multiscale Ultrahigh Resolution Sea Surface Temperature Imagery

The ATLAZUL project is an Interreg effort among 18 partners from Spain and Portugal along the Atlantic Iberian coasts. One of its objectives is the development of new methods and data processing for oceanic information to produce useful products for private and public stakeholders. This study proposes a new insight on the sea surface dynamic of the ATLAZUL area based on almost two years of multiscale high resolution sea surface temperature imagery. The use of techniques such as the Karhunen–Loève transform (Empirical Orthogonal Function) and the Maximum Entropy Spectral Analysis were applied to study long- and short-term features in the sea surface temperature imagery. Mathematical Morphology and the Geometrical Theory of Measure are utilized to compute the Medial Axis Transform and the Hausdorff dimension. The results can be summarized as follows: (i) the tow upwelling areas are identified along the Galician–Portugal coast as indicated in the second and third modes of KLT/EOF analysis, and they are partially affected by wind; (ii) the tow warm water outflows from the Bay of Cádiz to the Gulf of Cádiz are identified as the second and third modes of KLT/EOF analysis, which are also influenced by wind; (iii) the skeletons of the surface signature of the upwelling and of the warmer water outflow, along with their fractal dimensions, indicate a chaotic pattern of spatial distribution and (iv) the harmonic prediction model should be combined with the wind prediction.

Mathematical Morphology on Directional Data

AbstractWe define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.

Morphology for hexagonal image processing: a comprehensive simulation analysis

<p>Morphological operators for binary and grayscale images are commonly used to eliminate noise, recognize contours or specific structures, and arrange shapes in image processing for physiological modeling and biomechanics applications. Even though morphology has been substantially developed in square-pixelbased-image-processing (SIP), no effort has been made to construct morphological operators in hexagonal-pixel-based-image-processing (HIP) yet. In this paper, we transform basic SIP-domain-morphological operators such as dilation, erosion, closing, and opening into HIP-domain and compare their performance with their SIP counterparts. It is the first time to give the fundamental morphological operators in the HIP domain. The operators developed in this paper initiate the research about morphology in the HIP domain by successfully filling a significant gap by eliminating HIP’s lack of basic operators, thus capable of producing enhanced images for better analysis in anatomical models related to biology and medicine research fields.</p>

An efficient nano-design of image processor circuits for morphology operations based on quantum dots

Quantum-dot cellular automata (QCA) are one of the most promising alternatives to traditional VLSI technology despite significant current obstacles. The QCA has the advantages of very low power dissipation, faster switching speed, and extremely low circuit area, which can be used in designing nano-scale image processing circuits. Morphological operations and processing of digital image processing is a significant topic for researchers because it is widely used for analyzing, enhancing, and modifying images to extract meaningful information or improve their visual quality. Image processing is also used for image retrieval and enhancement, image compression, object recognition, machine vision, and medical applications. QCA technology, as a new and leading technology with great potential, can play a fundamental role in morphological operations, processing digital images, image editing, medical imaging, facial recognition, and autonomous vehicles. In recent years, researchers in this field have presented many circuits, but they have many flaws in terms of speed, accuracy, and area consumption, and the need to create more efficient circuits is felt more than ever. Therefore, in this article, a new design for morphological operations and processing digital images is presented using QCA technology. This paper presents a new efficient QCA-based implementation of image processing based on the direct interactions between the QCA cells. This circuit uses two majority gates of five new inputs to produce the output and produces the desired output. In addition, a comparison and analysis of the area and clocking complexity, design cost, and energy dissipation through simulation using QCADesigner and QCADesigner-E are done. The results show that the presented circuit produces the expected and correct output results in 0.75 clock phases, and the obtained results show the high speed and low consumption space of the presented circuit. In addition, the presented circuit performs better than the previous best circuits in terms of quantum cost and delay, and according to the mentioned advantages, it can be used to improve and expand other circuits in image processing.

Retinal Image Quality Assessment Using Morphological Operations

Retinal Image Quality Assessment Using Morphological Operations

Image Enhancement Using Bidimensional Empirical Mode Decomposition and Morphological Operations for Brain Tumor Detection and Classification.

The three steps of brain image processing – preprocessing, segmentation, and classification are becoming increasingly important in patient care. The aim of this article is to present a proposed method in the mentioned three-steps, with emphasis on the preprocessing step, which includes noise removal and contrast enhancement. The fast and adaptive bidimensional empirical mode decomposition and the anisotropic diffusion equation as well as the modified combination of top-hat and bottom-hat transforms are used for noise reduction and contrast enhancement. Fast C-means clustering with enhanced image is used to detect tumors and the tumor cluster corresponds to the maximum centroid. Finally, Ensemble learning is used for classification. The Figshare brain tumor dataset contains magnetic resonance images used for data selection. The optimal parameters for both noise reduction and contrast enhancement are investigated using a tumor contaminated with Gaussian noise. The results are evaluated against state-of-the-art results and qualitative performance metrics to demonstrate the dominance of the proposed approach. The fast C-means algorithm is applied to detect tumors using twelve enhanced images. The detected tumors were compared to the ground truth and showed an accuracy and specificity of 99% each, and a sensitivity and precision of 90% each. Six statistical features are retrieved from 150 enhanced images using wavelet packet coefficients at level 4 of the Daubechies 4 wavelet function. These features are used to develop the classifier model using ensemble learning to create a model with training and testing accuracy of 96.7% and 76.7%, respectively. When this model is applied to classify twelve detected tumor images, the accuracy is 75%; there are three misclassified images, all of which belong to the pituitary disease group. Based on the research, it appears that the proposed approach could lead to the development of computer-aided diagnosis (CADx) software that physicians can use as a reference for the treatment of rain tumor.

Training Artificial Neural Networks to Detect Multiple Sclerosis Lesions Using Granulometric Data from Preprocessed Magnetic Resonance Images with Morphological Transformations

The symptoms of multiple sclerosis (MS) are determined by the location of demyelinating lesions in the white matter of the brain and spinal cord. Currently, magnetic resonance imaging (MRI) is the most common tool used for diagnosing MS, understanding the course of the disease, and analyzing the effects of treatments. However, undesirable components may appear during the generation of MRI scans, such as noise or intensity variations. Mathematical morphology (MM) is a powerful image analysis technique that helps to filter the image and extract relevant structures. Granulometry is an image measurement tool for measuring MM that determines the size distribution of objects in an image without explicitly segmenting each object. While several methods have been proposed for the automatic segmentation of MS lesions in MRI scans, in some cases, only simple data preprocessing, such as image resizing to standardize the input dimensions, has been performed before the algorithm training. Therefore, this paper proposes an MRI preprocessing algorithm capable of performing elementary morphological transformations in brain images of MS patients and healthy individuals in order to delete undesirable components and extract the relevant structures such as MS lesions. Also, the algorithm computes the granulometry in MRI scans to describe the size qualities of lesions. Using this algorithm, we trained two artificial neural networks (ANNs) to predict MS diagnoses. By computing the differences in granulometry measurements between an image with MS lesions and a reference image (without lesions), we determined the size characterization of the lesions. Then, the ANNs were evaluated with the validation set, and the performance results (test accuracy = 0.9753; cross-entropy loss = 0.0247) show that the proposed algorithm can support specialists in making decisions to diagnose MS and estimating the disease progress based on granulometry values.

Concrete Crack Detection and Segregation: A Feature Fusion, Crack Isolation, and Explainable AI-Based Approach.

Scientific knowledge of image-based crack detection methods is limited in understanding their performance across diverse crack sizes, types, and environmental conditions. Builders and engineers often face difficulties with image resolution, detecting fine cracks, and differentiating between structural and non-structural issues. Enhanced algorithms and analysis techniques are needed for more accurate assessments. Hence, this research aims to generate an intelligent scheme that can recognize the presence of cracks and visualize the percentage of cracks from an image along with an explanation. The proposed method fuses features from concrete surface images through a ResNet-50 convolutional neural network (CNN) and curvelet transform handcrafted (HC) method, optimized by linear discriminant analysis (LDA), and the eXtreme gradient boosting (XGB) classifier then uses these features to recognize cracks. This study evaluates several CNN models, including VGG-16, VGG-19, Inception-V3, and ResNet-50, and various HC techniques, such as wavelet transform, counterlet transform, and curvelet transform for feature extraction. Principal component analysis (PCA) and LDA are assessed for feature optimization. For classification, XGB, random forest (RF), adaptive boosting (AdaBoost), and category boosting (CatBoost) are tested. To isolate and quantify the crack region, this research combines image thresholding, morphological operations, and contour detection with the convex hulls method and forms a novel algorithm. Two explainable AI (XAI) tools, local interpretable model-agnostic explanations (LIMEs) and gradient-weighted class activation mapping++ (Grad-CAM++) are integrated with the proposed method to enhance result clarity. This research introduces a novel feature fusion approach that enhances crack detection accuracy and interpretability. The method demonstrates superior performance by achieving 99.93% and 99.69% accuracy on two existing datasets, outperforming state-of-the-art methods. Additionally, the development of an algorithm for isolating and quantifying crack regions represents a significant advancement in image processing for structural analysis. The proposed approach provides a robust and reliable tool for real-time crack detection and assessment in concrete structures, facilitating timely maintenance and improving structural safety. By offering detailed explanations of the model's decisions, the research addresses the critical need for transparency in AI applications, thus increasing trust and adoption in engineering practice.

Automatic recognition system for concrete cracks with support vector machine based on crack features

Cracks are a common problem in concrete surfaces. With the continuous optimization of machine vision-based inspection systems, effective crack detection and recognition is the core of the entire system. In this study, support vector machine (SVM) was used to distinguish cracks from other regions. To complete the recognition system of the SVM, a framework consisting of an image processing and recognition model was proposed. An algorithm combining the Prewitt operator with the Otsu threshold was proposed for image segmentation. The binary image processed by the new algorithm combined with mathematical morphology can result in a more complete crack zone and fewer interference regions. After the initial parameter extraction, most of the impurity areas were screened by preliminary discrimination, removing 99% of the impurities. This processing step ensured the balance and effectiveness of the samples. To establish an automatic identification model based on SVM with a radial basis function, compactness, occupancy rate, and length–width ratio were selected as input parameters after comparing these three features with all six features of the crack. The recognition accuracy of this system reaches 97.14%, demonstrating that the proposed method is effective and satisfies practical requirements.

EpidermaQuant: Unsupervised Detection and Quantification of Epidermal Differentiation Markers on H-DAB-Stained Images of Reconstructed Human Epidermis.

The integrity of the reconstructed human epidermis generated in vitro can be assessed using histological analyses combined with immunohistochemical staining of keratinocyte differentiation markers. Technical differences during the preparation and capture of stained images may influence the outcome of computational methods. Due to the specific nature of the analyzed material, no annotated datasets or dedicated methods are publicly available. Using a dataset with 598 unannotated images showing cross-sections of in vitro reconstructed human epidermis stained with DAB-based immunohistochemistry reaction to visualize four different keratinocyte differentiation marker proteins (filaggrin, keratin 10, Ki67, HSPA2) and counterstained with hematoxylin, we developed an unsupervised method for the detection and quantification of immunohistochemical staining. The pipeline consists of the following steps: (i) color normalization; (ii) color deconvolution; (iii) morphological operations; (iv) automatic image rotation; and (v) clustering. The most effective combination of methods includes (i) Reinhard's normalization; (ii) Ruifrok and Johnston color-deconvolution method; (iii) proposed image-rotation method based on boundary distribution of image intensity; and (iv) k-means clustering. The results of the work should enhance the performance of quantitative analyses of protein markers in reconstructed human epidermis samples and enable the comparison of their spatial distribution between different experimental conditions.

Foreign object detection in urban rail transit based on deep differentiation segmentation neural network

With the increasing scale of urban rail transit, foreign object intrusion has become a significant operational safety hazard in urban rail transit. Although the laser-based automatic foreign object detection system has advantages such as long-distance detection and insensitivity to light changes, it has drawbacks such as large blind spots and low visualization. In response to the problems existing in laser detection systems, we proposed a novel video-based deep differentiation segmentation neural network for foreign object detection. Firstly, the foreign object detection is transformed into a binary classification problem, and the foreign object is determined as the image's foreground using image segmentation principles. Secondly, build a deep segmentation network based on deep convolution. Finally, perform morphological operations and threshold judgment on the foreground segmentation image to filter out the final detection results. To improve the detection effect, we reduced the impact of airflow disturbance by sampling and calculating the average background image. At the same time, the channel attention model and spatial attention model are added to the deep differentiation neural network. Collecting real data on subway platforms for experiments shows that the proposed method has a detection accuracy of 95.8 %, which is superior to traditional detection methods and recent image segmentation neural networks.

Citrus recognition in orchard scene based on modified HSV-morphology method

The orchard has always been an important scene for citrus pickers, and the existence of factors such as leaf occlusion and color similarity always lead to the difficulty of robot recognition. Based on a citrus image dataset collected from actual orchard scenes, we extract image features and build a mathematical model to identify and count the number of oranges in each image, and show the distribution of apples in the entire dataset. Firstly, this paper establishes a model based on HSV method, focusing on recognizing yellow citrus. Secondly, with the further analysis of the data set, it is found that the cyan citrus exists. Therefore, this paper defines the empirical HSV range of two kinds of citrus at the same time and introduces contour processing to optimize the model. In order to accurately distinguish the immature citrus from the leaves with similar colors and the citrus occluded by leaves, this paper uses more detailed color threshold setting and morphological operation, and makes the eccentricity of the contour less than 0.85. At the same time, considering the size and overlap of citrus, morphological operations such as dilation and erosion and contour detection techniques are applied to further improve the recognition ability of the model. Finally, the experimental results show that the average accuracy of the established model reaches 92.1%, which has a good recognition effect on citrus.

Improved YOLOv5 Network for High-Precision Three-Dimensional Positioning and Attitude Measurement of Container Spreaders in Automated Quayside Cranes.

For automated quayside container cranes, accurate measurement of the three-dimensional positioning and attitude of the container spreader is crucial for the safe and efficient transfer of containers. This paper proposes a high-precision measurement method for the spreader's three-dimensional position and rotational angles based on a single vertically mounted fixed-focus visual camera. Firstly, an image preprocessing method is proposed for complex port environments. The improved YOLOv5 network, enhanced with an attention mechanism, increases the detection accuracy of the spreader's keypoints and the container lock holes. Combined with image morphological processing methods, the three-dimensional position and rotational angle changes of the spreader are measured. Compared to traditional detection methods, the single-camera-based method for three-dimensional positioning and attitude measurement of the spreader employed in this paper achieves higher detection accuracy for spreader keypoints and lock holes in experiments and improves the operational speed of single operations in actual tests, making it a feasible measurement approach.

Rs-net: Residual Sharp U-Net architecture for pavement crack segmentation and severity assessment

U-net, a fully convolutional network-based image segmentation method, has demonstrated widespread adaptability in the crack segmentation task. The combination of the semantically dissimilar features of the encoder (shallow layers) and the decoder (deep layers) in the skip connections leads to blurry features map and leads to undesirable over- or under-segmentation of target regions. Additionally, the shallow architecture of the U-Net model prevents the extraction of more discriminatory information from input images. This paper proposes a Residual Sharp U-Net (RS-Net) architecture for crack segmentation and severity assessment in pavement surfaces to address these limitations. The proposed architecture uses residual block in the U-Net model to extract a more insightful representation of features. In addition to that, a sharpening kernel filter is used instead of plain skip connections to generate a fine-tuned encoder features map before combining it with decoder features maps to reduce the dissimilarity between them and smoothes artifacts in the network layers during early training. The proposed architecture is also integrated with various morphological operations to assess the severity of cracks and categorize them into hairline, medium, and severe labels. Experiments results demonstrated that the RS-Net model has promising segmentation performance, outperforming earlier U-Net variations on testing data for crack segmentation and severity assessment, with a promising accuracy (>0.97)

A Magnetic Flux Leakage Detector for Ferromagnetic Pipeline Welds with a Magnetization Direction Perpendicular to the Direction of Travel.

For the sake of realizing the safety detection of natural gas and petroleum pipeline welds, this paper designs a ferromagnetic pipeline weld magnetic flux leakage detector based on the calculation of the magnetic circuit of the detection probe, with the magnetization direction perpendicular to the traveling direction. The traditional pipeline magnetic flux leakage detection device uses a detection system mode in which the magnetization direction is parallel to the direction of travel. However, due to the structural characteristics of the weld, the traditional detection system mode is not applicable. Since the weld magnetic flux leakage detector needs to travel along the direction of the weld, the detector designed in this paper rotates the magnetizer 90 degrees along the direction of the weld seam so that the magnetization direction is perpendicular to the direction of travel, breaking through the technical barrier that make traditional magnetic flux leakage detection devices unsuitable for weld detection. The detection device includes a magnetizing structure, a data sampling device, and a driving and traveling device. The magnetic flux leakage signal collected by the detector is converted into a digital image in the form of a grayscale matrix. Using mathematical morphology and chain code algorithms in image processing technology, a pipeline weld defect inversion software system is developed, and a preliminary quantitative analysis of pipeline weld defects is achieved. The application of this technology enables the inspection and protection of oil and gas pipeline welds throughout their life cycle, broadens the scope of existing inspection objects, and is of great safety significance for ensuring national public security.

WATER BODIES EXTRACTION USING MATHEMATICAL MORPHOLOGY

The management of water resources is vital for maintaining the world’s ecosystems. Conventional methods of extracting water bodies remain very limited due to the complexity of the implementation. This leads to a reduction in the extraction precision. Our main objec- tive is to improve the detection of water bodies. We tested the accuracy of our method on the Sentinel-2 Dataset that contains images with different complexity levels and heterogeneous structures like shadows, roads, buildings, etc. This article presents an original method that implements the idea of separating the three-component RGB image matrices and then processing only the green matrix because it contains all water bodies with high precision. Our method is based mainly on the mathematical morphology. Firstly, we propose a simple and fast binary algorithm to detect the maximum of water bodies existing in the images. This step was carried out using the Hit-or-Miss Transform. The second step exploits applying the Top-Hat Transform to refine the segmentation result. By comparing our method with several currently used methods, we notice that our method improves the quality of segmentation and gives excellent results, which exceed 95% for all the metrics used to calculate the classification quality in the purview of remote sensing. The error obtained with our method remains less than 1 %. We can affirm that our method is very suitable for detecting bodies of water compared to all current methods.

Evolution stage identification and spatial pattern analysis of Nitraria tangutorum nebkhas based on Gaofen-2 satellite data

The quantitative extraction and evolution stage identification of the Nitraria tangutorum nebkhas are the basis for the restoration of regional plants and the reconstruction of degraded ecosystems. In this paper, the Nitraria tangutorum nebkha in Dengkou County of China was taken as the research object. Through the spectral and texture information of Gaofen-2 satellite image, the quantitative extraction of Nitraria tangutorum nebkha area and coverage information was completed using methods of gray threshold method, mathematical morphology, FCLSU mixed pixel decomposition, kernel density spatial analysis; the current evolution stage of the Nitraria tangutorum nebkha was identified, and their spatial distribution characteristics were analyzed. The results showed that: (1) The user accuracy and mapping accuracy of Nitraria tangutorum nebkha extracted from Random Forest combined with object-oriented classification method were up to 90.32%. (2) The method proposed can achieve an accuracy of 93.76% in extracting the spatial position of Nitraria tangutorum nebkhas. (3) The evolution of Nitraria tangutorum nebkhas can be divided into three stages: embryonic or developmental stage, stable stage, and declining stage, with a proportion of 60.70%, 20.97%, and 18.33%, respectively; The Nitraria tangutorum nebkhas in the study area is mainly in their embryonic or developmental stage, and the proportion of Nitraria tangutorum nebkhas in the declining stage is also large. It can provide technical and theoretical support for the precise extraction of nebkhas in arid and semi-arid desert areas, the identification of their current evolutionary stages, and the study of their spatial distribution patterns.

Step feature line extraction from large-scale point clouds of open-pit mine based on structural characteristics

High-precision step feature lines play a crucial role in open-pit mine design, production scheduling, mining volume calculations, road network planning, and slope maintenance. Compared with the feature lines of the geometric model, step feature lines are more irregular, complex, higher in density, and richer in detail. In this study, a novel technique for extracting step feature line from large-scale point clouds of open-pit mine by leveraging structural attributes, that is, SFLE_OPM (Step Feature Line Extraction for Open-Pit Mine), is proposed. First, we adopt the k-dimensional tree (KD-tree) resampling method to reduce the point-cloud density while retaining point-cloud features and utilize bilateral filtering for denoising. Second, we use Point Cloud Properties Network (PCPNET) to estimate the normal, calculate the slope and aspect, and then filter them. We then apply morphological operations to the step surface and obtain more continuous and smoother slope lines. In addition, we construct an Open-Pit Mine Step Feature Line (OPMSFL) dataset and benchmarked SFLE_OPM, achieving an accuracy score of 89.31% and true positive rate score of 80.18%. The results demonstrate that our method yields a higher extraction accuracy and precision than most of the existing methods. Our dataset is available at https://github.com/OPMDataSets/OPMSFL.

VMseg: Using spatial variance to automatically segment retinal non-perfusion on OCT-angiography.

To develop and test VMseg, a new image processing algorithm performing automatic segmentation of retinal non-perfusion in widefield OCT-Angiography images, in order to estimate the non-perfusion index in diabetic patients. We included diabetic patients with severe non-proliferative or proliferative diabetic retinopathy. We acquired images using the PlexElite 9000 OCT-A device with a photomontage of 5 images of size 12 x 12 mm. We then developed VMseg, a Python algorithm for non-perfusion detection, which binarizes a variance map calculated through convolution and morphological operations. We used 70% of our data set (development set) to fine-tune the algorithm parameters (convolution and morphological parameters, binarization thresholds) and evaluated the algorithm performance on the remaining 30% (test set). The obtained automatic segmentations were compared to a ground truth corresponding to manual segmentation from a retina expert and the inference processing time was estimated. We included 51 eyes of 30 patients (27 severe non-proliferative, 24 proliferative diabetic retinopathy). Using the optimal parameters found on the development set to tune the algorithm, the mean dice for the test set was 0.683 (sd = 0.175). We found a higher dice coefficient for images with a higher area of retinal non-perfusion (rs = 0.722, p < 10-4). There was a strong correlation (rs = 0.877, p < 10-4) between VMseg estimated non-perfusion indexes and indexes estimated using the ground truth segmentation. The Bland-Altman plot revealed that 3 eyes (5.9%) were significantly under-segmented by VMseg. We developed VMseg, an automatic algorithm for retinal non-perfusion segmentation on 12 x 12 mm OCT-A widefield photomontages. This simple algorithm was fast at inference time, segmented images in full-resolution and for the OCT-A format, was accurate enough for automatic estimation of retinal non-perfusion index in diabetic patients with diabetic retinopathy.

Brain tumor detection using a MobileNetV2-SSD model with modified feature pyramid network levels

Brain tumors, a subset of these malignancies, demand accurate and efficient diagnosis. Traditional methods use non-invasive medical imaging like magnetic resonance imaging (MRI) and computed tomography (CT). Although necessary for diagnosis, manual brain MRI picture segmentation is tedious and time-consuming. Using deep learning is a promising solution. This study proposes an innovative approach for brain tumor detection, focusing on meningioma tumors. Utilizing threshold-based segmentation, the MobileNetV2 architecture, a modified feature pyramid network (FPN), and single shot MultiBox detector (SSD), our model achieves precise localization and object detection. Pre-processing techniques such as grayscale conversion, histogram equalization, and Gaussian filtering enhance the MRI image quality. Morphological operations and thresholding facilitate tumor segmentation. Data augmentation and a meticulous dataset division aid in model generalization. The architecture combines MobileNetV2 as a feature extractor, SSD for object detection, and FPN for detecting small objects. Modifications, including lowering the minimum FPN level, enhance small object detection accuracy. The proposed model achieved a recall value of around 98% and a precision value of around 89%. Additionally, the proposed model achieved approximately 93% on both the dice similarity coefficient (DSC) value and the index of similarity. Based on the promising results, our research holds significant advancements for the field of medical imaging and tumor detection.