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This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced visualizations of the dataset as well as very distinct clusterizations. It is also faster than similar clusterization methods that are sensitive to density and shapes such as Mitosis and TRICLUST. In addition, k-MS is deterministic and has an intrinsic sense of maximal clusters that can be created for a given input sample and input parameters, differing from k-Means and other clusterization algorithms. In other words, given a constant k , a structuring element and a dataset, k-MS produces k or less clusters without using random/pseudo-random functions. Finally, the proposed algorithm also provides a straightforward means for removing noise from images or datasets in general.

Diffraction imaging is an important technique for high-resolution imaging because of the close relationship between diffractions and small-scale discontinuities. Therefore, we we have developed a diffraction imaging method using a mathematical morphological filter (MMF). In a common image gather, reflections have an evident energy band associated with the Fresnel zone and stationary point, whereas diffractions can be observed in a wide illumination direction and therefore have no energy band. Based on these phenomena, we analyze the amplitude distributions of the diffractions and reflections and develop a time-varying structuring element (SE) in the MMF. Based on the time-varying SE, our method can effectively suppress reflections and has the advantage of automatically preserving the diffractions energy near the stationary point. Numerical and field experiments demonstrate the efficient performance of the proposed method in imaging diffractions and obtaining high-resolution information.

Islanding detection is imperative for the protection of distribution system supported by distributed generation. The accuracy of islanding detection technique mainly depends on the selection of suitable parameter. In this work, the 6 different power system parameters are classified based on sensitivity and performance ability. This is the basic step in the selection of suitable parameter for islanding detection technique. The behavior of different power system parameters is examined using mathematical morphology by considering all possible islanding and non-islanding situations. It has been found, from data interpretation, that dilated reactive power parameter using inclined line structuring element indicates the best competence, among the other parameters, to detect the minute disturbances in power supply. Further, the selection of dilated reactive power parameter is justified mathematically to validate its significance. Moreover, islanding detection technique is proposed consisting of dilated reactive power parameter to distinguish the islanding from other events of similar signatures.

This paper reports investigations led on the combination of the refractive index and morphological dilation to enhance performances towards breast tumour margin delineation during conserving surgeries. The refractive index map of invasive ductal and lobular carcinomas were constructed from an inverse electromagnetic problem. Morphological dilation combined with refractive index thresholding was conducted to classify the tissue regions as malignant or benign. A histology routine was conducted to evaluate the performances of various dilation geometries associated with different thresholds. It was found that the combination of a wide structuring element and high refractive index was improving the correctness of tissue classification in comparison to other configurations or without dilation. The method reports a sensitivity of around 80% and a specificity of 82% for the best case. These results indicate that combining the fundamental optical properties of tissues denoted by their refractive index with morphological dilation may open routes to define supporting procedures during breast-conserving surgeries.

A356 aluminum alloy is a material widely used in the production of automobile wheels. Internal defects such as gas holes and shrinkage cavities are likely to develop in the process of low pressure casting. X-ray images of the hub are able to provide some information on such defects. This paper proposes a defect extraction method which is built on mathematical morphology. It involves three operations, i.e., the top-hat transform, the top-hat reconstruction transform and the dilation reconstruction. A larger square structuring element and a small threshold are used firstly to obtain all potential defect areas of the hub. A structuring element of a suitable size are applied to different defect areas in subsequent extraction. A new threshold is then decided to get the final defect extraction results. The experimental results show that the above defect extraction method not only works on X-ray hub images, but is robust against the interference caused by noises and hub geometry, and hence can potentially be extensively applied to X-ray detection of hubs.

In this paper, morphological operations on hexagonal lattices and regular hexagonal regions are applied to 2D parallel beam computerized tomography (CT) image denoising. To show some denoising effects of the morphological operations, for an input image, we add certain amount of noise to get the noised image; and perform Radon transform and inverse Radon transform on the noised image to obtain a CT image. To compare hexagonal lattices with square lattices fairly, the CT image is resampled to an image defined on a certain randomized grid, which is in turn resampled to an image defined on a hexagonal lattice and an image defined on the corresponding square lattice (with the same sampling rate), respectively. For the morphological operations, we use a structuring element defined on a hexagonal lattice and a structuring element defined on a square lattice such that those two structuring elements have the same number of ones. Each of those two images performs an erosion with the corresponding structuring element. Then use those two images as masks and use the two corresponding eroded images as makers to perform morphological image reconstructions to obtain the two reconstructed images. Finally, both usual and Phantom images are used as test images. For many different tested noise levels, the output data show that the image reconstructed on the hexagonal lattice is usually more similar to the input image than the one reconstructed on the square lattice.

Structuring elements of fixed shape and size are used in most conventional mathematical morphology operations, which makes the border of image targets shift, produces new image artifacts and loses small image objects due to the diversity and complexity of the image targets. In this paper, a new construction algorithm for adaptive structuring elements is proposed based on the neighborhood gray difference changing vector field and relative density. The proposed structuring element is able to adaptively change shape according to the gray and edge characteristics of an image. This algorithm involves first incorporating the gray difference changing vector field to smooth the local image region and make the gray level within the image target more uniform and then defining a border degree function based on relative density to determine whether the center pixel of the local image region is a border pixel. The adaptive structuring element is composed of all the strong border pixels found in a local image region. Dilation and erosion operations and other derivative operations are proposed with this new adaptive structuring element based on conventional morphology operation principles. The experimental results show that this proposed algorithm is able to effectively suppress the shifting effect of the image target borders while accurately locating the border of the image target region. Additionally, other effective image information is retained and image distortion is reduced while weakening the image details.

Although automatic fuzzy clustering framework (AFCF) based on improved density peak clustering is able to achieve automatic and efficient image segmentation, the framework suffers from two problems. The first one is that the adaptive morphological reconstruction (AMR) employed by the AFCF is easily influenced by the initial structuring element. The second one is that the improved density peak clustering using a density balance strategy is complex for finding potential clustering centers. To address these two problems, we propose a fast and automatic image segmentation algorithm using superpixel-based graph clustering (FAS-SGC). The proposed algorithm has two major contributions. First, the AMR based on regional minimum removal (AMR-RMR) is presented to improve the superpixel result generated by the AMR. The binary morphological reconstruction is performed on a regional minimum image, which overcomes the problem that the initial structuring element of the AMR is chosen empirically, since the geometrical information of images is effectively explored and utilized. Second, we use an eigenvalue gradient clustering (EGC) instead of improved density peak (DP) algorithms to obtain potential clustering centers, since the EGC is faster and requires fewer parameters than the DP algorithm. Experiments show that the proposed algorithm is able to achieve automatic image segmentation, providing better segmentation results while requiring less execution time than other state-of-the-art algorithms.

Channels are one exploratory object in the oil and gas industry, and detailed channel studies can help identify the sedimentation processes in an area. In addition, channels are a drilling hazard i...

The extraction of the vibration impulse signal plays a crucial role in the fault diagnosis of rolling element bearing. However, the detection of weak fault signals generally suffers the strong background noise. To solve this problem, a new adaptive multiscale enhanced combination gradient morphological filter (MECGMF) is proposed for the fault diagnosis of rolling element bearing. In this method, according to the filtering ability of four basic morphological filter operators, an enhanced combination gradient morphological operation (ECGMF) is first proposed. This design enhances the ability of MECGMF to extract impulse signals from strong background noise. And accordingly, a new adaptive selection strategy named kurtosis fault feature ratio (KFFR) is proposed to select an optimal structuring element (SE) scale. Subsequently, the optimal SE scale is the largest measure of multiscale morphological filtering for extracting bearing fault information. In the meanwhile, the effectiveness of the proposed method is verified by simulation and experiment. Finally, the experimental results demonstrate that MECGMF can effectively restrain the noise interference and extract fault characteristic signals of rolling element bearing from strong background noise. Moreover, comparative tests show that the proposed method is more effective in detecting wind turbine bearing failures.

Road extraction from very high resolution remotely sensed images is crucial in many urban applications. Acquiring automatically up-to-date and accurate information about roads is significant for various intelligent applications such as smart vehicle navigation, planning urban areas, roads monitoring and traffic management for intelligent transportation systems, and leading proper military operations. All possible knowledge about roads properties must be incorporated in designing intelligent systems that interpret and decide with high precision the existence of roads in remote sensing images. Various extraction techniques rely on mathematical morphology (MM) that detects desired road structures through a sliding standard and empirically chosen structuring element (SE) over the input image. In this paper, we design an intelligent process that not only combines spectral and spatial properties of roads but also impacts significantly the flexibility in retrieving spatial information. Indeed, we propose an adaptive algorithm that supplies tailored and most adequate arbitrary structuring elements for every image at hand. It has the significant impact of providing flexibility since every arbitrary generated SE is exclusively dedicated to the processed image. The processing consists of two major steps: a) we use the particle swarm optimization algorithm to look for the adaptive SEs; b) we introduce a priori knowledge based on human visual interpretation of roads characteristics and define some spatial indices to refine the results. We evaluated our method over many remotely sensed images; accuracy results show that the proposed method outperforms standard approaches which are limited to utilize only empirically chosen and standard SEs.

Background To estimate median liver iron concentration (LIC) calculated from magnetic resonance imaging, excluded vessels of the liver parenchyma region were defined manually. Previous works proposed the automated method for excluding vessels from the liver region. However, only user-defined liver region remained a manual process. Therefore, this work aimed to develop an automated liver region segmentation technique to automate the whole process of median LIC calculation. Methods 553 MR examinations from 471 thalassemia major patients were used in this study. LIC maps (in mg/g dry weight) were calculated and used as the input of segmentation procedures. Anatomical landmark data were detected and used to restrict ROI. After that, the liver region was segmented using fuzzy c-means clustering and reduced segmentation errors by morphological processes. According to the clinical application, erosion with a suitable size of the structuring element was applied to reduce the segmented liver region to avoid uncertainty around the edge of the liver. The segmentation results were evaluated by comparing with manual segmentation performed by a board-certified radiologist. Results The proposed method was able to produce a good grade output in approximately 81% of all data. Approximately 11% of all data required an easy modification step. The rest of the output, approximately 8%, was an unsuccessful grade and required manual intervention by a user. For the evaluation matrices, percent dice similarity coefficient (%DSC) was in the range 86–92, percent Jaccard index (%JC) was 78–86, and Hausdorff distance (H) was 14–28 mm, respectively. In this study, percent false positive (%FP) and percent false negative (%FN) were applied to evaluate under- and over-segmentation that other evaluation matrices could not handle. The average of operation times could be reduced from 10 s per case using traditional method, to 1.5 s per case using our proposed method. Conclusion The experimental results showed that the proposed method provided an effective automated liver segmentation technique, which can be applied clinically for automated median LIC calculation in thalassemia major patients.

Fuzzy image processing involves various fuzzy approaches. These fuzzy approaches help in understanding and processing of images as fuzzy sets. Mathematical morphology is used for analysing the shapes and forms of the objects in images. In morphological methods structuring elements are applied to an input image which creates an output image of the same size. The size and shape of the neighbourhood is chosen in such a way that a morphological operation relating to different shapes in the input image is constructed. In this paper the pixel values of an image are converted to fuzzy near membership values and the corresponding image is found. Using the fuzzy near membership image, gray and binary images are formed using MATLAB. Mathematical morphology operations dilation, erosion, opening and closing for different structuring elements such as line, square, diamond, sphere, disk, cube, neighbourhood, octagon and rectangle are performed for fuzzy membership and binary images. Taking dilation and opening as upper approximations, erosion and closing as lower approximations, the exact measures are calculated for different structuring elements and the corresponding images formed. It is found that the exact measure for the structuring element neighbourhood of fuzzy near membership and binary images are exactly equal. The corresponding images are also exactly similar.

This paper investigates parallel particle swarm optimization (parallel PSO) and mathematical morphology (MM) for classification of very high resolution (VHR) remote sensing images. The proper extraction of spatial features depends on the shape and size of the structuring element (SE) used to probe the image. However, finding the best shape and size of the SE for classification of urban remote sensing imagery is a challenging research topic, because the formats of the features may become more and more complex. For this purpose, this paper proposes a new adaptive algorithm based on the combination of parallel PSO with MM for the construction of adaptive SEs. Such that the shapes and sizes of the constructed SEs change adaptively according to the spatial features of the image and the considered classification task. As a result, the application of parallel PSO reduces the execution time compared to serial PSO, and makes the proposed algorithm can adopt several SEs simultaneously for image classification without complicating the main PSO algorithm. Finally, an experimental example is conducted to show the effectiveness of the proposed algorithms.

Binarization plays an important role in document analysis and recognition (DAR) systems. In this paper, we present our winning algorithm in ICFHR 2018 competition on handwritten document image binarization (H-DIBCO 2018), which is based on background estimation and energy minimization. First, we adopt mathematical morphological operations to estimate and compensate the document background. It uses a disk-shaped structuring element, whose radius is computed by the minimum entropy-based stroke width transform (SWT). Second, we perform Laplacian energy-based segmentation on the compensated document images. Finally, we implement post-processing to preserve text stroke connectivity and eliminate isolated noise. Experimental results indicate that the proposed method outperforms other state-of-the-art techniques on several public available benchmark datasets.

Within computer vision, deep neural networks (DNNs) have gained tremendous popularity in recent years due to their ability to extract and classify visual features. As this technology has become more widespread, some of the shortcomings of the DNNs have become apparent. Recently, researchers have found that DNNs prefer to learn texture from visual signals rather than shape and have observed that more shape extraction correlates to better DNN performance. DNN have been applied to a vast number of problems, with excellent results in many of them, including object detection. The combination of DNN feature extractors with regression and region proposal techniques, like the Faster Region-Proposal Convolutional Neural Network (Faster R-CNN) and Single Shot Detector (SSD), have yielded promising results. Meanwhile, from the field of digital image processing, grayscale morphology extracts shape information using morphological operations. The Differential Morphological Profile (DMP) performs morphological opening and closings with varied structuring element sizes and computes the absolute difference between the resulting steps. The DMP provides a mechanism to improve shape extraction within DNN, and increase model robustness. To that end, a DMP-based neural network, DMPNet, has been created to assist DNN with extracting shape information by adding layers that perform DMP prior to the first convolutional layer. We use the DMPNet as a feature extractor for Faster R-CNN and SSD, and apply it to Maneuverability Hazard Detection in unmanned aerial system (UAS) imagery. The benefits of this approach include better explainability, lower training times, and models more tuned to shape information.

Detection of lesion border from skin image is very essential for developing efficient non-invasive computer-aided diagnosis. For creation of an automatized system, edge detection is an essential step. An improved color space-based edge detection method with linear structure element is introduced in this paper. At first, the input image is converted to red color space and the Sobel operator is applied to detect the border. After this, linear structuring element is introduced, followed by filling up of holes to get appropriate segmented image. The performance of this method is measured by comparing its result with the results obtained by using a standard Sobel edge detection method.

Images segmentation aims to divide an image into several segments. They can be selected according to the composition of the region of interest, the types of tissues, and the functional zones [1]. In this paper, we present a new segmentation method, based on the multi-thresholding method and morphological reconstruction for brain tumor separation from Magnetic Resonance Imaging (MRI). Firstly, we use a pre-processing to enhance image contrast and quality by intensity adjustment. Secondly, the improved image is segmented using the multi-Otsu method and finally, a morphological reconstruction was performed with the appropriate structuring element parameter on the segmented image to determine the tumor. A comparison with some state-of-the-art algorithms demonstrated the efficiency of the proposed method with regard to accuracy.

The basic filters in mathematical morphology are dilation and erosion. They are defined by a flat or non-flat structuring element that is usually shifted pixel-wise over an image and a comparison process that takes place within the corresponding mask. Existing fast algorithms that realise dilation and erosion for grey value images are often limited with respect to size or shape of the structuring element. Usually their algorithmic complexity depends on these aspects. Many fast methods only address flat morphology.