Mathematical Morphology Analysis Research Articles

Knowledge-driven based three-dimensional prospectivity modeling of Fe–Cu skarn deposits; a case study of the Fanchang volcanic basin, anhui province, Eastern China

Mineral exploration at depth is becoming increasingly important as a result of the decades of discovery and mining of surficial or near-surface mineralization, leading to targeting of deeper-seated mineralization and mineral systems. The numerous challenges posed by this transition to deeper exploration can be partly overcome by the application of 3D prospectivity modeling. This study provides an outline of this type of prospectivity modeling and focuses on the under-explored Fanchang volcanic basin, an area prospective for skarn-type Fe–Cu mineralization within the Middle–Lower Yangtze River Metallogenic belt (MLYRB) of eastern China. The approach used utilizes a 3D geological model of the Fanchang volcanic basin that enables the identification and extraction of favorable elements for mineralization using 3D spatial and mathematical morphology analysis methods. A 3D distance field method was also used to obtain distance field information for the favorable ore-forming factors delineated during this study. The limited exploration to date in the study area means that there is a lack of specific information (e.g., location, size, grade) for the mineralization in this region. As such, knowledge-driven Index Overlay with Multi-Class (IOMC), Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), and Fuzzy Comprehensive Evaluation (FCE) approaches were used to generate 3D prospectivity models for the Fanchang volcanic basin. The resulting weight coefficients relating to favorable ore-forming factors were quantified using an Analytic Hierarchy Process (AHP) approach, yielding random consistency ratio (CR) values of 0.0125. These are all less than a value of 0.1, which would indicate inconsistencies between the matrix values and values for the entirety of the hierarchy, indicating that our calculated weighting coefficients are precise and accurate. Comparison of the 3D prospectivity modeling results of the three methods using a prediction area (P–A) plot indicates that 88% of the known mineralization and mineralized occurrences within the basin were located within an area of only 12% of the study area considered prospective during modeling using the IOMC method. In comparison, TOPSIS and FCE modeling positively identified 82% (18% of the study area) and 91% (9% of the study area) of the mineralization in the study area, respectively. These results indicate that these approaches are viable tools for exploration targeting in relatively unexplored areas without specific orebody size, location, and grade data, and the FCE method appears more efficient and reliable than the other two methods in predicting locations to explore for Fe–Cu skarn mineralization. The approaches outlined during this study are widely applicable for exploration for other mineralizing systems in under-explored regions elsewhere and the specific high prospectivity targets identified during this study and the links between exploration indicators and high prospectivity regions also provide key areas and insights for both future modeling and mineral exploration within the Fanchang volcanic basin and the wider MLYRB.

Automatic Recognition of Solar Active Regions Based on Real-time SDO/HMI Full-disk Magnetograms

Solar Active Regions (ARs) are the main source regions of solar activities. The morphology, structure, and characteristic of ARs are important factors in determining solar eruptions. Therefore, the recognition of ARs is the precondition to predict solar eruptions. SDO/HMI can continuously provide full-disk photospheric images with high temporal and spatial resolution. Referring to the method of Zhang et al.[1], we performed a study of fast automatic recognition of ARs from full-disk HMI magnetograms, which involves the intensity-based thresholding, mathematical morphological analysis and region growing. Through comparing the automatic recognition ARs with the ARs compiled by NOAA/SWPC from 2010 May to 2018 December, it is found that the number of ARs recognized automatically and the number of SWPC ARs are basically consistent in the trend of variation, and their correlation coefficient is 0.87. The total number of ARs automatically recognized is slightly less than the number of SWPC ARs. Most of the unidentified ARs are small areas, weak magnetic fields and simple magnetic structures, which are highly impossible to produce powerful eruptions to affect the space environment. This method of the automatic AR recognition from real-time HMI full-disk magnetograms can directly provide the real-time AR data for forecasting solar eruptions, and accelerate the operational application of solar eruption prediction models.

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

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

Application of an information fusion scheme for rolling element bearing fault diagnosis

This study addresses the high level of misdiagnoses and low reliability of individual rolling element bearing fault diagnosis methods by proposing a fault diagnosis scheme with enhanced diagnosis accuracy that combines the results of two individual diagnosis methods based on an improved information fusion method. The proposed scheme applies variational mode decomposition in conjunction with a support vector machine for conducting fault diagnosis in the frequency domain, which achieves high fault diagnosis precision for learned fault conditions. Meanwhile, good generalization ability is achieved for identifying the operational conditions of bearings in the time domain by integrated mathematical morphology and correlation analysis. Subsequently, conflicts arising between evidences derived from the individual detection results are measured comprehensively using a novel strategy, and the evidences are then combined based on the Dempster–Shafer theory (DST) to enhance the information fusion effect. The effectiveness of the proposed information fusion method is verified by means of a numerical example in comparison with other fusion methods based on DST. The experimental application of the proposed information fusion fault diagnosis scheme demonstrates the complementary advantages of the two individual methods for significantly improving the diagnosis accuracy relative to the accuracies of the individual methods alone.

Classifying tree species in the plantations of southern China based on wavelet analysis and mathematical morphology

It is essential to classify tree species accurately for the sustainable management of forest resources and effective monitoring of species diversity. Airborne hyperspectral images have high spatial and spectral resolution, and consequently, the large quantity of information on spectral and spatial structures is effective for tree species classification. In this research, Gaofeng Forest Farm in Nanning, Guangxi Province, China, was used as the study site, and the airborne hyperspectral images were used as the data source. The spectral and textural information extracted by wavelet analysis and edge information extracted by mathematical morphological analysis composed a feature set. The feature set was filtered through a random forest, and object-oriented methods were used to classify tree species through a support vector classifier. The results showed that spectral features extracted by wavelet analysis were highly effective in classifying tree species that had the greatest spectral separability. Horizontal and vertical textures had no positive effect on the classification accuracy, while diagonal textures improved the classification accuracy of tree species. Texture features were not sensitive to stands with small areas and broken distributions, while the edge structure features extracted from mathematical morphology were sensitive to the complex forests. The overall accuracy of tree species classification by combining spectral, textural, and edge structural features was 96.54%, with a Kappa coefficient of 0.96. In the comparative test, the first-derivative and second-derivative of the hyperspectral image and texture features composed a feature set. Using the same classification methods, the OA was 80.91% and Kappa was 0.7711. Therefore, the wavelet analysis and mathematical morphology can significantly improve the tree species classification accuracy of hyperspectral images. Accurate tree species classification can provide basic scientific data for forest resource monitoring and management measures.

Methods for the Structural Analysis of Highly Elastic Materials

The object of the research is highly elastic knitted fabrics, and the subject is the method of their structural analysis. The aim of the work is to develop a new method for the analysis of the structure of elastomeric materials, which makes it possible to study the parameters of highly elastic knitted fabrics’ structure in an equilibrium and stress-strain state, taking into account the assessment of the nature of its changes during various types of influences on the material. The prospects and the possibility of applying the methods of direct observation of the material’s microstructure by means of optoelectronic microscopy and the existing technical solution for their implementation in analyzing the structure of highly elastic knitted fabrics are shown in the work. A method for determining the structural characteristics of knitted fabrics, including highly elastic ones, has been developed. The proposed technique provides a quantitative assessment of the parameters of an elastomeric knitted fabric’s structure, taking into account the actual material’s state, and its changes after external influence using the methods of mathematical morphology, morphological analysis and spectral analysis of the fabric’s microstructure images. The results of practical approbation of the proposed method suggest that its application is possible and sufficiently effective.

Almost Regular Metrics on Groups and Lipschitz-Continuity of Distance Transforms

In this article, the almost inner (resp. lower, upper) regularity of metrics on a group is proposed. In terms of these regularities, a sufficient and necessary condition for distance transforms to be Lipschitz-1 continuous is given, and relations between balls with different centres and radii are discussed. It turns out that the three almost regularities of metrics introduced and the results obtained here might provide useful tools in discrete analysis, mathematical morphology and image analysis, etc.

The application of the tasseled cap transformation and feature knowledge for the extraction of coastline information from remote sensing images

The coastline is the dividing line between the ocean and land. Monitoring coastline dynamics is of crucial importance because it provides essential information for understanding the coastal response to contemporary climate change and human impacts. Real-time monitoring of coastlines has increasingly depended on remote sensing images at high temporal and spatial resolutions. In this study, a method combining the tasseled cap transformation (TCT) and feature knowledge is proposed to extract coastline information. Because traditional remote sensing methods cannot be used where total suspended sediment content is high, land and ocean separation was carried out using the wetness component of the Otsu method. A mathematical morphology analysis was used to remove the influence of lakes, rivers, and ships. Coastlines with shorter length were eliminated, and intermittent coastlines were connected based on a coordinate geometry description (such as length, distance, and direction). For the period of 2000–2018, Landsat-5 TM (Thematic Mapper) and Landsat-8 OLI (Operational Land Imager) images of the Zhoushan Islands, China, were used to extract coastline information using a method combining TCT and feature knowledge. A comparison of the results with reference data obtained by visual interpretation shows that the average of producer accuracy and user accuracy are 93.62% and 96.15%, respectively, and the average of length error was 2.45%. Therefore, the proposed method was effective in delineating the boundary between land and ocean and more effective than traditional methods in areas with high suspended sediment concentrations.

Mathematical morphology-based imaging of gastrointestinal cancer cell motility and 5-aminolevulinic acid-induced fluorescence.

The aim of this study was the quantitative evaluation of gastrointestinal cancer cell motility and 5-aminolevulinic acid (5-ALA)-induced fluorescence in vitro using mathematical morphology and structural analysis methods. The results of our study showed that MKN28 cells derived from the lymph node have the highest motility compared with AGS or HCT116 cells derived from primary tumors. Regions of single cells were characterized as most moving, and "tightly packed" cell colonies as nearly immobile. We determined the reduction of cell motility in late passage compared to early passage. Application of 5-ALA caused fluorescence in all investigated cells, and the fluorescence was different with regard to the cell type and application time. We observed higher fluorescence in MKN28 cells. Comprehensive image analysis did not reveal any statistically significant difference in fluorescence intensity between "tightly packed" cell regions, where nearly no motility was registered and loosely distributed cells, where the highest cell motility was registered. In conclusions, our study revealed that MKN28 cells derived from the lymph node have higher motility and 5-ALA-induced fluorescence than AGS or HCT116 derived from primary tumors. Moreover, image analysis based on a large amount of processed data is an important tool to study these tumor cell properties.

Plant Leaf Image Reconstruction Based on Point Cloud Characteristics

We present a method of leaf image reconstruction for plants whose midribs are close to straight. First, tangerine leaves are used as an example to illustrate the geometric and leaf-shape features of such leaves and suggest an extraction method using principal component analysis. Hence, this method was used to extract the geometric features, and additional methods such as coordinate conversion, mathematical morphology, and scan line analysis were applied to extract the leaf shape features. Then, based on these leaf shape features, a Bezier deformation function of the tangerine leaf edges and their curved Bezier deformation function in the normal vector direction were employed to obtain a parametric equation of the leaves according to their rectangular deformation. Finally, a simple illumination model for the leaves is presented. The reconstruction results show that the method is highly efficient and geometrically realistic. These results will be useful for the further study of plant leaf image reconstruction.

Tailoring cream by modifying the composition of the fat and interfacial proteins to modulate stirred milk gel texture

The formulation-structure-texture relationship in stirred emulsion-filled food gels has rarely been analysed, let alone in realistic conditions. By studying thermal (calorimetry), structural (laser diffraction, confocal microscopy and mathematical morphology analysis) and textural (rheology and tribology) properties, this work advanced the understanding of this relationship in stirred gels made entirely from milk ingredients. Indeed, tailoring the fat composition (AMF, olein or stearin fractions) and interfacial proteins (native or heat-aggregated WPI) in cream resulted in different properties. Crystallisation of the fat droplets and probably their interactions (aggregation or partial coalescence), pore size, microgel size and the coarseness of the protein network in stirred milk gels were all modified by the cream formulation. The changes in properties led to different textures and lubrication behaviours of the stirred milk gels. The highlighted relationships between formulation, structure and texture are recapitulated in a concluding diagram.

Tissue Intrinsic Fluorescence Spectra-Based Digital Pathology of Liver Fibrosis by Marker-Controlled Segmentation.

Tissue intrinsic emission fluorescence provides useful diagnostic information for various diseases. Because of its unique feature of spectral profiles depending on tissue types, spectroscopic imaging is a promising tool for accurate evaluation of endogenous fluorophores. However, due to difficulties in discriminating those sources, quantitative analysis remains challenging. In this study, we quantitatively investigated spectral-spatial features of multi-photon excitation fluorescence in normal and diseased livers. For morphometrics of multi-photon excitation spectra, we examined a marker-controlled segmentation approach and its application to liver fibrosis assessment by employing a mouse model of carbon tetrachloride (CCl4)-induced liver fibrosis. We formulated a procedure of internal marker selection where markers were chosen to reflect typical biochemical species in the liver, followed by image segmentation and local morphological feature extraction. Image segmentation enabled us to apply mathematical morphology analysis, and the local feature was applied to the automated classification test based on a machine learning framework, both demonstrating highly accurate classifications. Through the analyses, we showed that spectral imaging of native fluorescence from liver tissues have the capability of differentiating not only between normal and diseased, but also between progressive disease states. The proposed approach provides the basics of spectroscopy-based digital histopathology of chronic liver diseases, and can be applied to a range of diseases associated with autofluorescence alterations.

Reconstruction of three-dimensional grain structure in polycrystalline iron via an interactive segmentation method

Using a total of 297 segmented sections, we reconstructed the three-dimensional (3D) structure of pure iron and obtained the largest dataset of 16254 3D complete grains reported to date. The mean values of equivalent sphere radius and face number of pure iron were observed to be consistent with those of Monte Carlo simulated grains, phase-field simulated grains, Ti-alloy grains, and Ni-based super alloy grains. In this work, by finding a balance between automatic methods and manual refinement, we developed an interactive segmentation method to segment serial sections accurately in the reconstruction of the 3D microstructure; this approach can save time as well as substantially eliminate errors. The segmentation process comprises four operations: image preprocessing, breakpoint detection based on mathematical morphology analysis, optimized automatic connection of the breakpoints, and manual refinement by artificial evaluation.

Adaptive Morphological Feature Extraction and Support Vector Regressive Classification for Bearing Fault Diagnosis

Numerous studies on fault diagnosis have been conducted in recent years because the timely and correct detection of machine fault effectively minimizes the damage resulting in the unexpected breakdown of machineries. The mathematical morphological analysis has been performed to denoise raw signal. However, the improper choice of the length of the structure element (SE) will substantially influence the effectiveness of fault feature extraction. Moreover, the classification of fault type is a significant step in intelligent fault diagnosis, and many techniques have already been developed, such as support vector machine (SVM). This study proposes an intelligent fault diagnosis strategy that combines the extraction of morphological feature and support vector regression (SVR) classifier. The vibration signal is first processed using various scales of morphological analysis, where the length of SE is determined adaptively. Thereafter, nine statistical features are extracted from the processed signal. Lastly, an SVR classifier is used to identify the health condition of the machinery. The effectiveness of the proposed scheme is validated using the data set from a bearing test rig. Results show the high accuracy of the proposed method despite the influence of noise.

Some Relationships Between Fuzzy Sets, Mathematical Morphology, Rough Sets, F-Transforms, and Formal Concept Analysis

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.

Three dimensional quantification of anisotropic void evolution in deformed semi-crystalline polyamide 6

The evolution of voids has been used as an efficient indicator of the volume changes occurring during deformation for polymers which undergo high levels of plasticity. This has to be taken into account in determining the constitutive models for these polymers. Void growth during uniaxial stretching of a semi-crystalline polyamide 6 has been studied using 3D image analysis of tomography data. Tests on axi-symmetrical notched round bars have been stopped at: (i) the maximum net stress; (ii) the end of the stress softening stage; (iii) the onset of the final failure. Local synchrotron tomography has been performed so as to observe voids in a predetermined volume of interest around the minimum net section. The shape of the voids was found to be cylindrical. Mathematical morphology analysis was used to identify 3D voids, allowing the void diameter and height histograms to be obtained. An anisotropic shape factor parameter was defined as the ratio between the void diameter and the void height. This shape factor was found to evolve with the degree of deformation. The principal strain components of the voids were calculated and plotted, showing anisotropy and a heterogeneous distribution. The irreversible void growth noted as plastic dilation was also found to be heterogeneous in the deformed net section.

A new approach for performance degradation feature extraction based on generalized pattern spectrum entropy

Performance degradation feature extraction is the basis of degradation condition recognition and remaining service life prediction. In this paper, morphological corrosion operator is introduced into mathematical morphological particle analysis (abbreviated as MMP), proposing a new analytical method named generalized mathematical morphological particle analysis (abbreviated as GMMP). On this basis, a new approach for degradation feature extraction based on generalized pattern spectrum entropy (abbreviated as GPSE) is proposed taking GMMP and information entropy as the theoretical foundation. In this approach, GPSE is calculated as degradation feature parameter in describing performance degradation degree of machinery equipment. Simulation analysis is processed, and the result shows that the value of GPSE will increase correspondingly along with the deepening of the degradation degree and the relevance between GPSE and degradation degree is stable. The effectiveness and practicality of the approach is tested through rolling bearing whole lifetime vibrating data. Rolling bearing fatigue life enhancement testing was carried out in Hangzhou Bearing Test & Research Center, getting the whole lifetime data which is able to cover each degradation condition from normal to invalidation. The approach is applied into analysis of rolling bearing data and the results verify its validity and feasibility.

Pump-probe imaging of pigmented cutaneous melanoma primary lesions gives insight into metastatic potential.

Metastatic melanoma is associated with a poor prognosis, but no method reliably predicts which melanomas of a given stage will ultimately metastasize and which will not. While sentinel lymph node biopsy (SLNB) has emerged as the most powerful predictor of metastatic disease, the majority of people dying from metastatic melanoma still have a negative SLNB. Here we analyze pump-probe microscopy images of thin biopsy slides of primary melanomas to assess their metastatic potential. Pump-probe microscopy reveals detailed chemical information of melanin with subcellular spatial resolution. Quantification of the molecular signatures without reference standards is achieved using a geometrical representation of principal component analysis. Melanin structure is analyzed in unison with the chemical information by applying principles of mathematical morphology. Results show that melanin in metastatic primary lesions has lower chemical diversity than non-metastatic primary lesions, and contains two distinct phenotypes that are indicative of aggressive disease. Further, the mathematical morphology analysis reveals melanin in metastatic primary lesions has a distinct "dusty" quality. Finally, a statistical analysis shows that the combination of the chemical information with spatial structures predicts metastatic potential with much better sensitivity than SLNB and high specificity, suggesting pump-probe microscopy can be an important tool to help predict the metastatic potential of melanomas.

Soot nanostructure evolution in premixed flames by High Resolution Electron Transmission Microscopy (HRTEM)

HRTEM fringe analysis by means of our “Analyse Plan” (AP) tool and a new HRTEM image analysis procedure, based on mathematical morphological analysis (MA), was applied to soot sampled along the axis of sooting premixed benzene and ethylene flames. The layer length obtained by means of MA approach was found to be higher in respect to the layer length derived from AP method, as it better accounts for their local curvature and distortion. The mean layer length obtained by the MA method was then proved to agree well with the data evaluated by Raman spectroscopy. Moreover, the MA method was useful for extracting other soot nanostructural parameters related to the geometry of individual fringes as layer length, tortuosity, and local curvature radii, in turn correlated with the defective nature of soot structure.Some parameters provided by the MA method appeared to be more sensitive and informative about structural changes occurring as soot is formed. In particular, the percentage of fringes with high tortuosity and the percentage of nearly-straight fragments were found to decrease and increase, respectively, throughout the soot formation region. These trends suggested a better stacking of longer and more planar layers testifying the structural order improvement with soot aging. It was also observed that the soot nanostructural ordering occurred faster for benzene with respect to ethylene soot in agreement with H/C and absorption coefficients trends.The distributions of carbon in differently-sized aromatic structures were evaluated on the basis of the fringe length distribution to follow the aromatic growth. The method assigned aromatic sizes to the extracted HRTEM fringes, assuming that the fringes are in the shape of parallelograms. The distributions were found to evolve toward larger size aromatic systems demonstrating the occurrence of aromatic growth during soot formation.

A Signal Based Triangular Structuring Element for Mathematical Morphological Analysis and Its Application in Rolling Element Bearing Fault Diagnosis

Mathematical morphology (MM) is an efficient nonlinear signal processing tool. It can be adopted to extract fault information from bearing signal according to a structuring element (SE). Since the bearing signal features differ for every unique cause of failure, the SEs should be well tailored to extract the fault feature from a particular signal. In the following, a signal based triangular SE according to the statistics of the magnitude of a vibration signal is proposed, together with associated methodology, which processes the bearing signal by MM analysis based on proposed SE to get the morphology spectrum of a signal. A correlation analysis on morphology spectrum is then employed to obtain the final classification of bearing faults. The classification performance of the proposed method is evaluated by a set of bearing vibration signals with inner race, ball, and outer race faults, respectively. Results show that all faults can be detected clearly and correctly. Compared with a commonly used flat SE, the correlation analysis on morphology spectrum with proposed SE gives better performance at fault diagnosis of bearing, especially the identification of the location of outer race fault and the level of fault severity.