Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.

Analysis of quantitative pore features based on mathematical morphology

Wood identification is a basic technique of wood science and industry. Pore features are among the most important identification features for hardwoods. We have used a method based on an analysis of quantitative pore feature, which differs from traditional qualitative methods. We applies mathematical morphology methods such as dilation and erosion, open and close transforma- tion of wood cross-sections, image repairing, noise filtering and edge detection to segment the pores from their background. Then the mean square errors （MSE） of pores were computed to describe the distribution of pores. Our experiment shows that it is easy to classify the pore features into three basic types, just as in traditional qualitative methods, but with the use of MSE of pores. This quantitative method improves wood identification considerably.

Extracting heartrate from optical signal of functional near-infrared spectroscopy based on mathematical morphology

Functional near-infrared spectroscopy(fNIRS),as a new optical functional neuroimaging method,has been widely used in neuroscience research.In some research fields with NIRS,heartrate(HR)(or heartbeat)is needed as useful information to evaluate its influence,or to know the state ofsubject,or to remove its artifact.If HR(or heartbeat)can be detected with high accuracy from theoptical intensity,this will undoubtedly benefit a lot to many NIRS studies.Previous studies haveused the moving time window method or mathematical morphology method(MMM)to detectheartbeats in the optical intensity.However,there are some disadvantages in these methods.In thisstudy,we proposed a method combining the periodic information of heartbeats and the operator ofmathematical morphology to automatically detect heartbeats in the optical intensity.First theoptical intensity is smoothed using a moving average flter.Then,the opening operator of math-ematical morphology extracts peaks in the smoothed optical intensity.Finally,one peak is iden-tified as a heartbeat peak if this peak is the maximum in a predefined point range.Throughvalidation on experimental data,our method can overcome the disadvantages of previous methods,and detet heartbeats in the optical signal of fNIRS with nearly 100%accuracy.

Mathematical Morphology-Based Artificial Technique for Renewable Power Application

This paper suggests a combined novel control strategy for DFIG based wind power systems(WPS)under both nonlinear and unbalanced load conditions.The combined control approach is designed by coordinating the machine side converter(MSC)and the load side converter(LSC)control approaches.The proposed MSC control approach is designed by using a model predictive control(MPC)approach to generate appropriate real and reactive power.The MSC controller selects an appropriate rotor voltage vector by using a minimized optimization cost function for the converter operation.It shows its superiority by eliminating the requirement of transformation,switching table,and the PWM techniques.The proposed MSC reduces the cost,complexity,and computational burden of the WPS.On the other hand,the LSC control approach is designed by using a mathematical morphological technique(MMT)for appropriate DC component extraction.Due to the appropriate DC-component extraction,the WPS can compensate the harmonics during both steady and dynamic states.Further,the LSC controller also provides active power filter operation even under the shutdown of WPS condition.To verify the applicability of coordinated control operation,the WPS-based microgrid system is tested under various test conditions.The proposed WPS is designed by using a MATLAB/Simulink software.

A Hybrid Signal Processing Method Combining Mathematical Morphology and Walsh Theory for Power Quality Disturbance Detection and Classification

In this paper, a novel signal processing method combining mathematical morphology (MM) and Walsh theory is proposed, which uses Walsh functions to control the structuring element (SE) and MM operators. Based on the Walsh-MM method, a scheme for power quality disturbances detection and classification is developed, which involves three steps: denoising, feature extraction and morphological clustering. First, various evolution rules of Walsh function are used to generate groups of SEs for the multiscale Walsh-ordered morphological operation, so the original signal can be denoised. Next, the fundamental wave of the denoised signal is suppressed by Hadamard matrix;thus, disturbances can be extracted. Finally, the Walsh power spectrum of the waveform extracted in the previous step is calculated, and the parameters of which are taken by morphological clustering to classify the disturbances. Simulation results reveal the proposed scheme can effectively detect and classify disturbances, and the Walsh-MM method is less affected by noise and only involves simple calculation, which has a potential to be implemented in hardware and more suitable for real-time application.

An Implementation of Multiscale Line Detection and Mathematical Morphology for Efficient and Precise Blood Vessel Segmentation in Fundus Images

Diagnosing various diseases such as glaucoma,age-related macular degeneration,cardiovascular conditions,and diabetic retinopathy involves segmenting retinal blood vessels.The task is particularly challenging when dealing with color fundus images due to issues like non-uniformillumination,low contrast,and variations in vessel appearance,especially in the presence of different pathologies.Furthermore,the speed of the retinal vessel segmentation system is of utmost importance.With the surge of now available big data,the speed of the algorithm becomes increasingly important,carrying almost equivalent weightage to the accuracy of the algorithm.To address these challenges,we present a novel approach for retinal vessel segmentation,leveraging efficient and robust techniques based on multiscale line detection and mathematical morphology.Our algorithm’s performance is evaluated on two publicly available datasets,namely the Digital Retinal Images for Vessel Extraction dataset(DRIVE)and the Structure Analysis of Retina(STARE)dataset.The experimental results demonstrate the effectiveness of our method,withmean accuracy values of 0.9467 forDRIVE and 0.9535 for STARE datasets,aswell as sensitivity values of 0.6952 forDRIVE and 0.6809 for STARE datasets.Notably,our algorithmexhibits competitive performance with state-of-the-art methods.Importantly,it operates at an average speed of 3.73 s per image for DRIVE and 3.75 s for STARE datasets.It is worth noting that these results were achieved using Matlab scripts containing multiple loops.This suggests that the processing time can be further reduced by replacing loops with vectorization.Thus the proposed algorithm can be deployed in real time applications.In summary,our proposed system strikes a fine balance between swift computation and accuracy that is on par with the best available methods in the field.

Ultra-short Term Wind Speed Prediction Using Mathematical Morphology Decomposition and Long Short-term Memory

This paper proposes a new model,which consists of a mathematical morphology(MM)decomposer and two long short term memory(LSTM)networks,to perform ultra-short term wind speed forecast.The MM decomposer is developed in order to improve the forecast accuracy,which separates the wind speed into two parts:a stationary long-term baseline and a nonstationary short-term residue.Afterwards,two LSTM networks are implemented to forecast the baseline and residue,respectively.Besides,this paper makes an integrated forecast that takes into account multiple climate factors,such as temperature and air pressure.The baseline,temperature and air pressure are used as the inputs of baseline network for training and prediction,and the baseline,residue,temperature and air pressure are used as the inputs of residue network for training and prediction.The performance of the proposed model has been validated using data collected from the Australian Meteorological Station,which is compared with least squares-support vector machine(LS-SVM),back-propagation artificial neural network(BPNN),LSTM,MM-LS-SVM,and MM-BPNN.The results demonstrate that the proposed model is more suitable to solve non-stationary time-series forecast,and achieves higher accuracy than the other models under various conditions.

A Signal Based “W” Structural Elements for Multi-scale Mathematical Morphology Analysis and Application to Fault Diagnosis of Rolling Bearings of Wind Turbines

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.

3-D Storm Automatic Identification Based on Mathematical Morphology

The strom identification, tracking, and forecasting method is one of the important nowcasting techniques. Accurate storm identification is a prerequisite for successful storm tracking and forecasting. Storm identification faces two difficulties： one is false merger and the other is failure to isolate adjacent storms within a cluster of storms. The TITAN （Thunderstorm Identification, Tracking, Analysis, and Nowcasting） algorithm is apt to identify adjacent storm cells as one storm because it uses a single reflectivity threshold. The SCIT （Storm Cell Identification and Tracking） algorithm uses seven reflectivity thresholds and therefore is capable of isolating adjacent storm cells, but it discards the results identified by the lower threshold, leading to the loss of the internal structure information of storms. Both TITAN and SCIT have the problem of failing to satisfactorily identify false merger. To overcome these shortcomings, this paper proposes a novel approach based on mathematical morphology. The approach first applies the single threshold identification followed by implementing an erosion process to mitigate the false merger problem. During multi-threshold identification stages, dilation operation is performed against the storm cells which are just obtained by the higher threshold identification, until the storm edges touch each other or touch the edges of the previous storms identified by the lower threshold. The results of experiment show that by combining the strengths of the dilation and erosion operations, this approach is able to mitigate the false merger problem as well as maintain the internal structure of sub-storms when isolating storms within a cluster of storms.

Application of mathematical morphology operation with memristor-based computation-in-memory architecture for detecting manufacturing defects

Mathematical morphology operations are widely used in image processing such as defect analysis in semiconductor manufacturing and medical image analysis.These data-intensive applications have high requirements during hardware implementation that are challenging for conventional hardware platforms such as central processing units(CPUs)and graphics processing units(GPUs).Computation-in-memory(CIM)provides a possible solution for highly efficient morphology operations.In this study,we demonstrate the application of morphology operation with a novel memristor-based auto-detection architecture and demonstrate non-neuromoq)hic computation on a multi-array-based memristor system.Pixel-by-pixel logic computations with low parallelism are converted to parallel operations using memristors.Moreover,hardware-implemented computer-integrated manufacturing was used to experimentally demonstrate typical defect detection tasks in integrated circuit(IC)manufacturing and medical image analysis.In addition,we developed a new implementation scheme employing a four-layer network to realize small-object detection with high parallelism.The system benchmark based on the hardware measurement results showed significant improvement in the energy efficiency by approximately 358 times and 32 times more than when a CPU and GPU were employed,respectively,exhibiting the advantage of the proposed memristor-based morphology operation.

Segmentation of Moving Objects Using Mathematical Morphology

This paper proposes a motion-based region growing segmentation scheme, which incorporatesluminance and motion information simultaneously and uses morphological tools such as open-close byreconstruction and the region-growing version of the watershed algorithm. The main advantage of this scheme is thatthe resultant objects ore characterized by a coherent motion and foe moving object boundaries are precisely located.Simulation results demonstrate the effiency of the Proposed scheme.

Shape Skeletonization via Mathematical Morphology

Skeleton is an important topological descriptor of an image and is widely used in the fields of image analysis. In this paper we present an algorithm based on morphological operations for extracting skeleton from a binary image. Since the original image can be partially or completely reconstructed from the skeleton, this algorithm which works in both analogUe and digital space is useful in image coding and feature description. A fast algorithm for skeletonizing and reconstrUcting digital images and the results of the fast algorithm are also given.

A Smart Mathematic Morphology Method for Recognition and Understanding of Airfield

A method used for recognition and understanding of airfield based on mathematical morphology is proposed in this paper. The new approach can he divided into three steps. First, to extract the typical geometric structure features of airfield, a segmentation method called recursive Otsu algorithm is employed on an airfield image. Second, thinning and shrinking algorithms are utilized to obtain the contour of airfield with single pixel and to remove diffused small particles. Finally, Radon transform is adopted to extract two typical and important components, primary and secondary runways of airfield exactly. At the same time, region growing algorithm is exploited to get the other components such as parking apron and garages. The experimental results demonstrate that the proposed method gives good performance.

A mathematical morphological approach for region of interest coding of microscopy image compression

A novel mathematical morphological approach for region of interest(ROI) automatic determination and JPEG2000-based coding of microscopy image compression is presented.The algorithm is very fast and requires lower computing power,which is particularly suitable for some irregular region-based cell microscopy images with poor qualities.Firstly,an active threshold-based method is discussed to create a rough mask of regions of interest(cells).And then some morphological operations are designed and applied to achieve the segmentation of cells.In addition,an extra morphological operation,dilation,is applied to create the final mask with some redundancies to avoid the"edge effect"after removing false cells.Finally,ROI and region of background(ROB) are obtained and encoded individually in different compression ratio flexibly based on the JPEG2000,which can adjust the quality between ROI and ROB without coding for ROI shape.The experimental results certify the effectiveness of the proposed algorithm,and compared with JPEG2000,the proposed algorithm has better performance in both subjective quality and objective quality at the same compression ratios.

Mathematical Morphological Distributive Concepts over Unions and Intersections

Mathematical Morphological concepts outline techniques for analysing and processing geometric structures based on set theory. In this paper, we present proofs of our theorems on morphological distributive properties over Unions and Intersections with respect to Dilation and Erosion. These results provide new realizations of Dilation, Erosion and conclude that they are distributive over Unions but non-distributive over Intersections.

Experimental and Numerical Research on Water Transport during Adsorption and Desorption in Cement-Based Materials

The durability of cement-based materials is related to water transport and storage in their pore network under different humidity conditions.To understand the mechanism and characteristics of water adsorption and desorption processes from the microscopic scale,this study introduces different points of view for the pore space model generation and numerical simulation of water transport by considering the“ink-bottle”effect.On the basis of the pore structure parameters(i.e.,pore size distribution and porosity)of cement paste and mortar with water-binder ratios of 0.3,0.4 and 0.5 obtained via mercury intrusion porosimetry,randomly formed 3D pore space models are generated using two-phase transformation on Gaussian random fields and verified via image analysis method of mathematical morphology.Considering the Kelvin-Laplace equation and the influence of“ink-bottle”pores,two numerical calculation scenarios based on mathematical morphology are proposed and applied to the generated model to simulate the adsorption-desorption process.The simulated adsorption and desorption curves are close to those of the experiment,verifying the effectiveness of the developed model and methods.The obtained results characterize water transport in cement-based materials during the variation of relative humidity and further explain the hysteresis effect due to“ink-bottle”pores from the microscopic scale.

Method for Morphological Filtering in Seismic Data Processing

A new method is introduced to suppress the noise in seismic data processing. Based on the subtle difference in shape between the noise and the actual signal, we introduce morphologic filtering into seismic data processing. From the shape and the S/N we can see that the effect of morphologic filtering is superior to other methods like id-value filtering, neighbor average filtering, etc. The SNR of the signal after morphological filtering is comparatively great. In addition, the precision of the seismic data after morphological filtering is high. The characteristics of the actual signal, such as frequency and amplitude, are preserved. We give an example of the real seismic data processing using morphological filtering, in which the actual signal is retained, while the random high intensity noise was removed.

Knowledge-based bridge detection from SAR images

Automatic bridge detection is an important application of SAR images. Differed from the classical CFAR method, a new knowledge-based bridge detection approach is proposed. The method not only uses the backscattering intensity difference between targets and background but also applies the contextual information and spatial relationship between objects. According to bridges＇ special characteristics and scattering properties in SAR images, the new knowledge-based method includes three processes： river segmentation, potential bridge areas detection and bridge discrimination. The application to AIRSAR data shows that the new method is not sensitive to rivers＇ shape. Moreover, this method can detect bridges successfully when river segmentation is not very exact and is more robust than the radius projection method.

Visual sensing and morphological image processing of weld pool in laser spot welding

A visual sensing system was established to monitor the weld pool in laser spot welding. The top-hat and bottom-hat transformation algorithms based on mathematical morphology were used to compensate for non-uniform contrast of weld pool edge. Moreover, the canny edge detector was applied to extract the weld paol profile. The edge detected results show that the morphological operation is obviously superior to the traditional contrast enhancement method. In addition, the combination of dilation and erosion was applied to eliminate the irrelevant edge details, and the smooth weld pool edge was acquired. Based on the image processing technology described above, the dynamic process of weld pool diameter during laser spot welding was obtained.

Critical area computation for real defects and arbitrary conductor shapes

In current critical area models, it is generally assumed the defect outlines are circular and the conductors to be rectangle or the merger of rectangles. However, real defects and conductors associated with optimal layout design exhibit a great variety of shapes. Based on mathematical morphology, a new critical area model is presented, which can be used to estimate the critical area of short circuit, open circuit and pinhole. Based on the new model, the efficient validity check algorithms are explored to extract critical areas of short circuit, open circuit and pinhole from layouts. The results of experiment on an approximate layout of 4 × 4 shifts register show that the new model predicts the critical areas accurately. These results suggest that the proposed model and algorithm could provide new approaches for yield prediction.