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.

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.

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.

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.

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.

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.

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.

An infrared and visible image fusion method based upon multi-scale and top-hat transforms

The high-frequency components in the traditional multi-scale transform method are approximately sparse, which can represent different information of the details. But in the low-frequency component, the coefficients around the zero value are very few, so we cannot sparsely represent low-frequency image information. The low-frequency component contains the main energy of the image and depicts the profile of the image. Direct fusion of the low-frequency component will not be conducive to obtain highly accurate fusion result. Therefore, this paper presents an infrared and visible image fusion method combining the multi-scale and top-hat transforms. On one hand, the new top-hat-transform can effectively extract the salient features of the low-frequency component. On the other hand, the multi-scale transform can extract highfrequency detailed information in multiple scales and from diverse directions. The combination of the two methods is conducive to the acquisition of more characteristics and more accurate fusion results. Among them, for the low-frequency component, a new type of top-hat transform is used to extract low-frequency features, and then different fusion rules are applied to fuse the low-frequency features and low-frequency background; for high-frequency components, the product of characteristics method is used to integrate the detailed information in high-frequency. Experimental results show that the proposed algorithm can obtain more detailed information and clearer infrared target fusion results than the traditional multiscale transform methods. Compared with the state-of-the-art fusion methods based on sparse representation, the proposed algorithm is simple and efficacious, and the time consumption is significantly reduced.

A Sort of Gray-scale Morphological Dilations and Erosions

We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as the commuting property with translation and homothety, of these operators are discussed as well.

Using SPOT 5 fusion-ready imagery to detect Chinese tamarisk(saltcedar)with mathematical morphological method

Chinese tamarisk(saltcedar)is a deciduous shrub that occurs widely across the Yellow River Delta in China.The spatial structure of Chinese tamarisk is believed to have an influence on the landscape and habitats of rare birds.In this study,first,Chinese tamarisk is detected using Canny edge detector and mathematical morphological operators based on SPOT 5 fusion-ready imagery.Then the numbers,areas,locations,and patch spacing of Chinese tamarisk patches are calculated.The experiments show that the detection accuracy of Chinese tamarisk patches is about 93.4%after the disconnection of connected patches.The distribution orientation of about 70%of the patches is approximately south-north.About 91%of the minimum distances among the patches are between 12.5 and 57.5 m.The rose graph indicates that the main azimuth between patches is north--northwest,and the second is northeast and southeast.The present study indicates that the integrating Canny edge detector with the algorithms for extracting circular and elliptical objects based on mathematical morphology is simple and effective for detecting Chinese tamarisk patches and is easy to identify the spatial structure of Chinese tamarisk patches,which reduces the time and labor for the visual interpretation of Chinese tamarisk patches.

Application of Morphological Max-Lifting Scheme for Identification of Induction Motor Stator Inter-turn Short Circuit

The harmonic components of stator winding current in induction motor will change under the condition of stator inter-turn short circuit.According to these characteristics,in this paper,a novel technique based on morphological maxlifting scheme is proposed for identification of induction motor stator inter-turn short circuit.A max-lifting scheme is applied to process stator winding currents to extract these characteristics.An indicator,r,is computed to identify the short circuit.The transient model of induction motor is employed to simulate oneturn to six-turn stator inter-turn short circuits in an induction motor.Extensive simulation work has been conducted under normal conditions,abnormal conditions(voltage imbalance and varying load),stator inter-turn short circuit conditions,and conditions of any combinations of the above.The results have shown that the scheme proposed in this paper has a high identification rate for induction motor stator inter-turn short circuit.

Monitoring changes in the Menik Farm IDP camps in Sri Lanka using multi-temporal very high-resolution satellite data

This paper presents the results of the application of mathematical morphology for the automatic quantification of the number of tents and the detection of changes in the Menik Farm IDP camp in Sri Lanka.The tents were retrieved using an area-constraint top-hat opening applied to WorldView-1 data.The counting of tents was based on the centroids of the automatically detected structures indicating an overall number of 25,150 tents on the 26 June 2009.The comparison with a visual interpretation produced an R2 of 0.97 with an error of 1.25%.In addition,an automated detection of changes inside a camp area was conducted.The comparison of the satellite image of 26 June 2009(WorldView-1)and an image of 28 February 2010(GeoEye-1)is based on mutual(mixed)information metric,after using morphological image processing techniques and previously specified criterion.Changes are observed on a terrain of around 15.2%of the total camp area and 3813 of previously detected structures disappeared in a period of 8 months.

Time-frequency multiresolution of fault-generated transient signals in transmission lines using a morphological filter

The ongoing transformation of electrical power systems highlights the weaknesses of the protection schemes of traditional devices because they are designed and configured according to traditional characteristics of the system.Therefore,this work proposes a new methodology to study the fault-generated high frequency transient signals in transmission lines through multiresolution analysis.The high frequency components are determined by a new digital filtering technique based on mathematical morphology theory and a spectral energy index.Consequently,wide spectra of signals in the time–frequency domain are obtained.The performance of this method is verified on an electrical power system modeled in ATP-Draw,where simulation and test signals are developed for different locations,fault resistances,inception angles,high frequency noises,sampling frequencies,types of faults,and shapes of the structuring element.The results show the characteristics of the fault such as the traveling wave frequency,location,and starting time.