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.

Skeleton extraction of boiler flame images based on mathematical morphology

In this paper, a method and algorithm of skeleton extraction based on binary mathematical morphology is presented. Sequential structuring elements (SEs) is also studied, which is the key problem of skeleton extraction. The examples of boiler flame image processing show that the detected skeletons can present the geometric shape of flame images well.

Void defect detection in BGA solder joints using mathematical morphology

Voids are one of the major defects in ball grid array （BGA） solder joints due to a large amount of outgassing flux that gets entrapped during reflow. X-ray nondestructive machines are used to make voids visible as lighter areas inside the solder joints in X-ray images for detection However, it has always been difficult to analyze this problem automatically because of some challenges such as noise, inconsistent lighting and void-like artifacts. This study realized accurate extraction and automatic a-nalysis of void defects in solder joints by adopting a technical proposal, in which Otsu algorithm was used to segment solder balls and void defects were extracted through opening and closing operations and top-hat transformation in mathematical mor-phology. Experimental results show that the technical proposal mentioned here has good robustness and can be applied in the detection of voids in BGA solder joints.

Image edge detection based on nonsubsampled contourlet transform and mathematical morphology

A novel algorithm for image edge detection is presented. This algorithm combines the nonsubsampled contourlet transform and the mathematical morphology. First, the source image is decomposed by the nonsubsampled contourlet transform into multi-scale and multi-directional subbands. Then the edges in the high-frequency and low-frequency sub-bands are respectively extracted by the dualthreshold modulus maxima method and the mathematical morphology operator. Finally, the edges from the high- frequency and low-frequency sub-bands are integrated to the edges of the source image, which are refined, and isolated points are excluded to achieve the edges of the source image. The simulation results show that the proposed algorithm can effectively suppress noise, eliminate pseudo-edges and overcome the adverse effects caused by uneven illumination to a certain extent. Compared with the traditional methods such as LoG, Sobel, and Carmy operators and the modulus maxima algorithm, the proposed method can maintain sufficient positioning accuracy and edge details, and it can also make an improvement in the completeness, smoothness and clearness of the outline.

EDGE DETECTION METHOD OF REMOTE SENSING IMAGES BASED ON MATHEMATICAL MORPHOLOGY OF MULTI-STRUCTURE ELEMENTS

This paper puts forward an effective, specific algorithm for edge detection. Based on multi-structure elements of gray mathematics morphology, in the light of difference between noise and edge shape of RS images, the paper establishes multi-structure elements to detect edge by utilizing the grey form transformation principle. Compared with some classical edge detection operators, such as Sobel Edge Detection Operator, LOG Edge Detection Operator, and Canny Edge Detection Operator, the experiment indicates that this new algorithm possesses very good edge detection ability, which can detect edges more effectively, but its noise-resisting ability is relatively low. Because of the bigger noise & remote sensing image, the authors probe into putting forward other edge detection method based on combination of wavelet directivity checkout technology and small-scale Mathematical Morphology finally. So, position at the edge can be accurately located, the noise can be inhibited to a certain extent and the effect of edge detection is obvious.

Quantitative Study on Polymer Flocculation Mechanism Based on Mathematical Morphology

Until now, understanding of polymer flocculation has remained restricted within the qualitative explanations of the bridge unite theory and the electricity neutralization theory, because people not only lacked the systemic knowl- edge of the polymer flocculation mechanism, the flocculation dynamic process study and the flocculation effect esti- mate, but also could not penetrate within the flocculation process microscopic field to obtain the structural character parameters such as floccule structure, the frame bridge models and so on. In this paper, not only coal slurry flocculation images were photographed by using the transmission electron microscope, but also the basic theory of the mathematical morphology was applied to the coal slurry flocculation image processing. The steps and methods of the mathematical morphology were expounded in detail. The micro-structural parameters such as the flocculate size and the bridge length were obtained, which combined the microscopic flocculation grain configuration observations with the macroscopic flocculation effect, so as to get the maximum amount of veracious information to describe and explain the whole floc- culation course by rule and line. On this basis, not only the flocculation models of polymers in the coal slurry are sug- gested, but the quantitative study on flocculation mechanism has been achieved.

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.

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.

A Road Extraction Method Based on Region Growing and Mathematical Morphology from Remote Sensing Images

Road traffic is the important driving factor for economic and social development. With the rapid increase of vehicle population, road traffic problems such as traffic jam and traffic accident have become the bottleneck which restricts economic development. In recent years, natural disasters frequently occur in China. Therefore, it is essential to extract road information to compute the degree of road damage for traffic emergency management. A road extraction method based on region growing and mathematical morphology from remote sensing images is proposed in this paper. According to the road features, the remote sensing image is preprocessed to separate road regions from non-road regions preliminarily. After image thresholding, region growing algorithm is used to extract connected regions. Then we sort connected regions by area to exclude the small regions which are probably non-road objects. Finally, the mathematical morphology algorithm is used to fill the holes inside the road regions. The experimental results show that the method proposed can effectively extract roads from remote sensing images. This research also has broad prospects in dealing with traffic emergency management by the government.

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.

Image mathematical morphology and image restoration application in detecting underground bin level

By using image recognition technology, the underground bin level can be detdcted. The bin image is noised by vibration, atomy, backgroun and so on. The image restoration and image mathematical morphology were used based on neural network. A modified Hopfield network was presented for image restoration. The greed algorithm with n-simultaneous updates and apartially asynchronous algorithm were combined, im- proving convergence and avoiding synchronization penalties. Mathematical morphology was widely applicated in digital image processing. The basic idea of mathematical mor- phology is to use construction element measure image morphology for solving under- stand problem. Presented advanced Cellular neural network that forms MMCNN equa- tion to be suit for mathematical morphology filter. It gave the theory of MMCNN dynamic extent and stable state. It was evidenced that arrived mathematical morphology filter through steady of dynamic precess in definite condition. The results of implementation were applied in detecting undergroug bin level.

Enhanced Contrast of Reconstructed Image for Image Secret Sharing Scheme Using Mathematical Morphology

Visual secret sharing (VSS) is one of the cryptographic techniques of Image secret sharing scheme (ISSS) that performs encoding of secret message image (text or picture) into noise like black and white images, which are called as shares. Shares are stacked together and secret message image is decoded using human visual system. One of the major drawbacks of this scheme is its poor contrast of the recovered image, which improves if computational device is available while decoding. In this paper, we propose to improve poor contrast of classical VSS schemes for text or alphanumeric secret messages and low entropy images. Initially, stacked image is binarized using dynamic threshold value. A mathematical morphological operation is applied on the stacked image to enhance contrast of the reconstructed image. Moreover, a method is proposed that allows the size of the structuring element to change according to the contrast and the size of a stacked image. We perform experiments for different types of VSS schemes, different share patterns, different share types (rectangle and circle), and low entropy images. Experimental results demonstrate the efficacy of the proposed scheme.

Gear Vibration Analysis and Gear Fault Diagnosis based on Mathematical Morphology

Gear vibration analysis and gear fault diagnosis are related to the multi-objective decision-making process of machinery equipment production, in which a large amount of data and information should be collected, and the relationship between supply/demand needs and available resources, between production and labor, and between enterprise benefit and social benefit should be balanced generally. Thus, the gear fault diagnosis technologies as well as the professional quality and technical quality are required to be very high. To conform to the forward development of mathematical modeling technology, it is urgent to implement safety product management with computer by using gear vibration analysis and gear fault diagnosis as methods for aiding the research and development of machinery gear fault diagnosis system. 7

Application of PDE and Mathematical Morphology in the Extraction Validation of the Roads

The digital images generated by remote sensors often contain noises that are inherent in the process of imaging and transmission. The application of digital processing techniques greatly enhances the ability to extract information on surface targets from remote sensing data. When digital images are used with high spatial resolution, one of the problems emerging the high variability of targets presents in such images. From the computational point of view, the use of partial differential equations is favored by the large number of numerical methods showed in the literature. Many of the models are considered non-complex both from the mathematical and computational standpoints, due to the characteristics of explicit equations. This work uses techniques of the partial differential equations (PDE) and mathematical morphology to extract cartographic features in digital images of the remote sensing. The selected study area corresponds to an image containing part of the Mário Covas Ring Road, located in the metropolitan region of Sao Paulo (SP), Brazil. The results are promising and show the high potential of using mathematical morphology in the field of cartography.

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.

Revised Mathematical Morphological Concepts

We revise some mathematical morphological operators such as Dilation, Erosion, Opening and Closing. We show proofs of our theorems for the above operators when the structural elements are partitioned. Our results show that structural elements can be partitioned before carrying out morphological operations.

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.