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The presence of border noise in Sentinel-1 Ground Range Detected (GRD) products is an undesired processing artifact that limits their full exploitation in a number of applications. All of the Sentinel-1 GRD products generated before March 2018—more than 800,000—are affected by this particular type of noise. In March 2018, an official fix was deployed that solved the problem for a large portion of the newly generated products, but it did not cover the entire range of products, hence the need for an operational tool that is able to effectively and consistently remove border noise in an automated way. Currently, a few solutions have been proposed that try to address the problem, but all of them have limitations. The scope of this paper is therefore to present a new method based on mathematical morphology for the automatic detection and masking of border noise in Sentinel-1 GRD products that is able to overcome the existing limitations. To evaluate the performance of the method, a detailed numerical assessment was carried out, using, as a benchmark, the ‘Remove GRD Border Noise’ module integrated in ESA’s Sentinel Application Platform. The results showed that the proposed method is capable of very accurately removing the undesired noisy pixels from GRD images, regardless of their acquisition mode, polarization, or resolution and can cope with challenging features within the image scenes that typically affect other approaches.

As special aggregation functions, overlap functions have been widely used in the soft computing field. In this work, with the aid of overlap functions, two new groups of fuzzy mathematical morphology (FMM) operators were proposed and applied to image processing, and they obtained better results than existing algorithms. First, based on overlap functions and structuring elements, the first group of new FMM operators (called OSFMM operators) was proposed, and their properties were systematically analyzed. With the implementation of OSFMM operators and the fuzzy C-means (FCM) algorithm, a new image edge extraction algorithm (called the OS-FCM algorithm) was proposed. Then, the second group of new FMM operators (called ORFMM operators) was proposed based on overlap functions and fuzzy relations. Another new image edge extraction algorithm (called OR-FCM algorithm) was proposed by using ORFMM operators and FCM algorithm. Finally, through the edge segmentation experiments of multiple standard images, the actual segmentation effects of the above-mentioned two algorithms and relevant algorithms were compared. The acquired results demonstrate that the image edge extraction algorithms proposed in this work can extract the complete edge of foreground objects on the basis of introducing the least noise.

It is difficult for traditional circuit-fault feature-extraction methods to accurately distinguish between nonlinear analog-circuit faults and analog-circuit faults with high fault rates and high diagnostic costs. To solve this problem, this paper proposes a method of mathematical morphology fractal dimension (VMD-MMFD) based on variational mode decomposition for soft-fault feature extraction in analog circuits. First, the signal is decomposed into variational modes to suppress the influence of environmental noise, and multiple high-dimensional eigenmode functions with different center frequencies are obtained. The fractal dimension of the signal feature information component IMF is calculated, and then, KPCA (Kernel Principal Component Analysis) is used to remove the overlapping and redundant parts of the data. The fault set obtained is used as the basis for judging the working state and the fault type of the circuit. The experimental results of the simulation circuits show that this method can be effectively used for circuit-fault diagnosis.

Mathematical morphology is a framework composed by a set of well-known image processing techniques, widely used for binary and grayscale images, but less commonly used to process color or multivariate images. In this paper, we generalize fuzzy mathematical morphology to process multivariate images in such a way that overcomes the problem of defining an appropriate order among colors. We introduce the soft color erosion and the soft color dilation, which are the foundations of the rest of operators. Besides studying their theoretical properties, we analyze their behavior and compare them with the corresponding morphological operators from other frameworks that deal with color images. The soft color morphology outstands when handling images in the CIEL ∗ a ∗ b ∗ color space, where it guarantees that no colors with different chromatic values to the original ones are created. The soft color morphological operators prove to be easily customizable but also highly interpretable. Besides, they are fast operators and provide smooth outputs, more visually appealing than the crisp color transitions provided by other approaches.

Buzz, squeak and rattle (BSR) noise has become apparent in vehicles due to the significant reductions in engine noise and road noise. The BSR often occurs in driving condition with many interference signals. Thus, the automatic BSR detection remains a challenge for vehicle engineers. In this paper, a rattle signal denoising and enhancing method is proposed to extract the rattle components from in-vehicle background noise. The proposed method combines the advantages of wavelet packet decomposition and mathematical morphology filter. The critical frequency band and the information entropy are introduced to improve the wavelet packet threshold denoising method. A rattle component enhancing method based on multi-scale compound morphological filter is proposed, and the kurtosis values are introduced to determine the best parameters of the filter. To examine the feasibility of the proposed algorithm, synthetic brake caliper rattle signals with various SNR ratios are prepared to verify the algorithm. In the validation analysis, the proposed method can well remove the disturbance background noise in the signal and extract the rattle components with well SNR ratios. It is believed that the algorithm discussed in this paper can be further applied to facilitate the detection of the vehicle rattle noise in industry.

Working conditions of rolling bearings of wind turbine generators are complicated, and their vibration signals often show non-linear and non-stationary characteristics. In order to improve the efficiency of feature extraction of wind turbine rolling bearings and to strengthen the feature information, a new structural element and an adaptive algorithm based on the peak energy are proposed, which are combined with spectral correlation analysis to form a fault diagnosis algorithm for wind turbine rolling bearings. The proposed method firstly addresses the problem of impulsive signal omissions that are prone to occur in the process of fault feature extraction of traditional structural elements and proposes a “W” structural element to capture more characteristic information. Then, the proposed method selects the scale of multi-scale mathematical morphology, aiming at the problem of multi-scale mathematical morphology scale selection and structural element expansion law. An adaptive algorithm based on peak energy is proposed to carry out morphological scale selection and structural element expansion by improving the computing efficiency and enhancing the feature extraction effect. Finally, the proposed method performs spectral correlation analysis in the frequency domain for an unknown signal of the extracted feature and identifies the fault based on the correlation coefficient. The method is verified by numerical examples using experimental rig bearing data and actual wind field acquisition data and compared with traditional triangular and flat structural elements. The experimental results show that the new structural elements can more effectively extract the pulses in the signal and reduce noise interference, and the fault-diagnosis algorithm can accurately identify the fault category and improve the reliability of the results.

The field of biometrics has become increasingly intriguing due to the significant amount of research being conducted on Iris Recognition (IR) in recent years. It has been observed that alcohol consumption can cause deformation in the iris pattern, resulting from the dilation or constriction of the pupil, which can potentially impact the performance of IR. To address these issues, this paper proposes an efficient iris segmentation model that incorporates a Modified Circle Hough Transform (MCHT) for clustering individuals under the influence of alcohol. The proposed model consists of several steps, namely noise reduction, iris segmentation, pupil segmentation, and clustering of individuals into drinker and non-drinker categories. Initially, input images are obtained from a database. To reduce noise in the images, a Median Filtering (MF) technique is employed. The Canny mathematical morphology (CMM) algorithm is then utilized to segment the iris region from the noise-free image. Subsequently, the MCHT algorithm is applied to perform pupil segmentation based on the segmented iris image. This modification enhances the accuracy and robustness of the system. Finally, the Matrix-Based Clustering (MBC) technique clusters individuals into the drunk and non-drunk categories. The experimental results of the proposed method show that it performs better than other state-of-the-art models, indicating its superior performance. In conclusion, this paper introduces an effective iris segmentation model incorporating the Modified Circle Hough Transform (MCHT) for clustering individuals based on their alcohol consumption. The proposed approach demonstrates enhanced accuracy and robustness compared to existing models, as evidenced by the experimental outcomes.

Enhancement on the edges of the causative source is an indispensable tool in the interpretation of potential-field data. There are a number of methods for recognizing the edges, most of which involve high-pass filters based on derivatives of potential-field data. A new edge-detection method is presented, called the enhanced mathematical morphology (EMM) filter. The EMM filter uses the ratio of the erosion of the total horizontal derivative to the dilation of total horizontal derivative to recognize the edges of the sources, and can display the edges of the shallow and deep bodies simultaneously. The EMM filter does not require the computation of vertical derivatives, which makes this method computationally stable. The EMM filter is tested on synthetic and real potential field data in China. Compared to other edge-detection filters, the new method is able to recognize the source edges more clearly, and the outputs are more insensitive to noise.

In this paper, a new approach to fuzzy mathematical morphology based on discrete t-norms is studied. The discrete t-norms that have to be used in order to preserve the most usual algebraical and morphological properties, such as monotonicity, idempotence, scaling invariance, among others, are fully determined. In addition, the properties related to B-open and B-closed objects and the generalized idempotence are also studied. In fact, all properties satisfied by the approach based on continuous nilpotent t-norms hold in the discrete case. This is quite important since in practice we only work with discrete objects. In addition, it is proved that more discrete t-norms satisfying all the properties are available in this approach than in the continuous case, which reduces to the Łukasiewicz t-norm. This morphology based on discrete t-norms can be considered embedded in more general frameworks, such as L-fuzzy sets or quantale modules, but all these frameworks have been studied only from a theoretical point of view. Our main contribution is the practical application of this discrete approach to image processing. Experimental results on edge detection, noise removal and top-hat transformations for some discrete t-norms and their comparison with the corresponding ones obtained by the umbra approach and the continuous Łukasiewicz t-norm are included showing that this theory can be suitable to be used in a wide range of applications on image processing. In particular, a new edge detector based on the morphological gradient, non-maxima suppression and a hysteresis method is presented.