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.

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 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.

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.

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.

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.

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.

Yield estimation of metallic layers in integrated circuits

In the existing models of estimating the yield and critical area, the defect outline is usually assumed to be circular, but the observed real defect outlines are irregular in shape. In this paper, estimation of the yield and critical area is made using the Monte Carlo technique and the relationship between the errors of yield estimated by circular defect and the rectangle degree of the defect is analysed. The rectangular model of a real defect is presented, and the yield model is provided correspondingly. The models take into account an outline similar to that of an original defect, the characteristics of two-dimensional distribution of defects, the feature of a layout routing, and the character of yield estimation. In order to make the models practicable, the critical area computations related to rectangular defect and regular （vertical or horizontal） routing are discussed. The critical areas associated with rectangular defect and non- regular routing are developed also, based on the mathematical morphology. The experimental results show that the new yield model may predict the yield caused by real defects more accurately than the circular model. It is significant that the yield is accurately estimated using the proposed model for IC metals.

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.

Segmentation of Vessels by Morphological Filters and Dynamic Thresholding

A method of segmenting vessels by morphological filters and dynamic thresholding for digital subtraction angiography （DSA） images is presented. The first step is to reduce the noise and enhance the details of image by using morpholngical operators. The second is to segment vessels by dynamic thresholding combined with global thresholding based on the properties of DSA images. Artificial images and actual images have been tested. Experiment results show that the proposed method is efficient and is of great potential for the segmentation of vessels in medical images.

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.

Gravel Image Segmentation in Noisy Background Based on Partial Entropy Method

Because of wide variation in gray levels and particle dimensions and the presence of many small gravel objects in the background, as well as corrupting the image by noise, it is difficult to segment gravel objects. In this paper, we develop a partial entropy method and succeed to realize gravel objects segmentation. We give entropy principles and fast calculation methods. Moreover, we use minimum entropy error automaticly to select a threshold to segment image. We introduce the filter method using mathematical morphology. The segment experiments are performed by using different window dimensions for a group of gravel image and demonstrates that this method has high segmentation rate and low noise sensitivity.

AUV Local Path Planning Based on Acoustic Image Processing

The forward-looking image sonar is a necessary vision device for Autonomous Underwater Vehicles （AUV）. Based on the acoustic image received from forward-looking image sonar, AUV local path is planned. When the environment model is made to adapt to local path planning, an iterative algorithm of binary conversion is used for image segmentation. Raw data of the acoustic image, which were received from serial port, are processed. By the use of ＂Mathematic Morphology＂ to filter noise, a mathematic model of environment for local path planning is established after coordinate transformation. The optimal path is searched by the distant transmission （Dt） algorithm. Simulation is conducted for the analysis of the algorithm. Experiment on the sea proves it reliable.

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.