Pub Date : 2025-01-27DOI: 10.1016/j.spasta.2025.100881
Fabrizio Durante , Sebastian Fuchs , Roberta Pappadà
Driven by the goal of generating risk maps for flood events—characterized by various physical variables such as peak flow and volume, and measured at specific geographic locations—this work proposes several dissimilarity functions for use in unsupervised learning problems and, specifically, in clustering algorithms. These dissimilarities are rank-based, relying on the dependence occurring among the random variables involved, and assign the smallest values to pairs of subsets that are -comonotonic. This concept is less restrictive than classical comonotonicity but, in the multivariate case, can offer a more intuitive understanding of compound phenomena.
An application of these measures is presented through the analysis of flood risks using data from the Po river basin, with results compared to similar studies found in the literature.
{"title":"Clustering of compound events based on multivariate comonotonicity","authors":"Fabrizio Durante , Sebastian Fuchs , Roberta Pappadà","doi":"10.1016/j.spasta.2025.100881","DOIUrl":"10.1016/j.spasta.2025.100881","url":null,"abstract":"<div><div>Driven by the goal of generating risk maps for flood events—characterized by various physical variables such as peak flow and volume, and measured at specific geographic locations—this work proposes several dissimilarity functions for use in unsupervised learning problems and, specifically, in clustering algorithms. These dissimilarities are rank-based, relying on the dependence occurring among the random variables involved, and assign the smallest values to pairs of subsets that are <span><math><mi>π</mi></math></span>-comonotonic. This concept is less restrictive than classical comonotonicity but, in the multivariate case, can offer a more intuitive understanding of compound phenomena.</div><div>An application of these measures is presented through the analysis of flood risks using data from the Po river basin, with results compared to similar studies found in the literature.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"66 ","pages":"Article 100881"},"PeriodicalIF":2.1,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143151696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-13DOI: 10.1016/j.spasta.2025.100880
Roy Cerqueti , Raffaele Mattera
Understanding the significance of individual data points within clustering structures is critical to effective data analysis. Traditional stability methods, while valuable, often overlook the nuanced impact of individual units, particularly in spatial contexts. In this paper, we explore the concept of unit relevance in clustering analysis, emphasizing its importance in capturing the spatio-temporal nature of the clustering problem. We propose a simple measure of unit relevance, the Unit Relevance Index (URI), and define an overall measure of clustering stability based on the aggregation of computed URIs. Considering two experiments on real datasets with geo-referenced time series, we find that the use of spatial constraints in the clustering task yields more stable results. Therefore, the inclusion of the spatial dimension can be seen as a way to stabilize the clustering.
{"title":"Measuring unit relevance and stability in hierarchical spatio-temporal clustering","authors":"Roy Cerqueti , Raffaele Mattera","doi":"10.1016/j.spasta.2025.100880","DOIUrl":"10.1016/j.spasta.2025.100880","url":null,"abstract":"<div><div>Understanding the significance of individual data points within clustering structures is critical to effective data analysis. Traditional stability methods, while valuable, often overlook the nuanced impact of individual units, particularly in spatial contexts. In this paper, we explore the concept of unit relevance in clustering analysis, emphasizing its importance in capturing the spatio-temporal nature of the clustering problem. We propose a simple measure of unit relevance, the Unit Relevance Index (URI), and define an overall measure of clustering stability based on the aggregation of computed URIs. Considering two experiments on real datasets with geo-referenced time series, we find that the use of spatial constraints in the clustering task yields more stable results. Therefore, the inclusion of the spatial dimension can be seen as a way to stabilize the clustering.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"66 ","pages":"Article 100880"},"PeriodicalIF":2.1,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143151695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-10DOI: 10.1016/j.spasta.2025.100879
Garry Jacyna, Damon Frezza, David M. Slater, James R. Thompson
We derive the Multifractal Gaussian Mixture Model algorithm for decomposing data sets into different multifractal regimes building on the empirical observation that simulated multifractals have log wavelet leaders that are well-approximated by a Gaussian distribution. We test the algorithm on composite images constructed from multifractal random walks with known multifractal spectra. The algorithm is able to correctly segment the pixels corresponding to different multifractals when the constituent multifractals are most distinct from each other. It also estimates the multifractal parameters with minimal error when compared to the theoretical spectra used to generate the original multifractal random walks. We also apply the algorithm to satellite images with varying degrees of cloud cover taken from the LandSat 8 Cloud Validation Data set. The algorithm is able to segment the pixels into their corresponding cloud mask category, and it detects different texture and features in the images that are unrelated to clouds. The results indicate that the Multifractal Gaussian Mixture Model algorithm is well-suited for semi-automated unsupervised data segmentation when the data being analyzed exhibit complex, scale-invariant characteristics.
{"title":"The Multifractal Gaussian Mixture Model for unsupervised segmentation of complex data sets","authors":"Garry Jacyna, Damon Frezza, David M. Slater, James R. Thompson","doi":"10.1016/j.spasta.2025.100879","DOIUrl":"10.1016/j.spasta.2025.100879","url":null,"abstract":"<div><div>We derive the Multifractal Gaussian Mixture Model algorithm for decomposing data sets into different multifractal regimes building on the empirical observation that simulated multifractals have log wavelet leaders that are well-approximated by a Gaussian distribution. We test the algorithm on composite images constructed from multifractal random walks with known multifractal spectra. The algorithm is able to correctly segment the pixels corresponding to different multifractals when the constituent multifractals are most distinct from each other. It also estimates the multifractal parameters with minimal error when compared to the theoretical spectra used to generate the original multifractal random walks. We also apply the algorithm to satellite images with varying degrees of cloud cover taken from the LandSat 8 Cloud Validation Data set. The algorithm is able to segment the pixels into their corresponding cloud mask category, and it detects different texture and features in the images that are unrelated to clouds. The results indicate that the Multifractal Gaussian Mixture Model algorithm is well-suited for semi-automated unsupervised data segmentation when the data being analyzed exhibit complex, scale-invariant characteristics.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"66 ","pages":"Article 100879"},"PeriodicalIF":2.1,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143151694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-27DOI: 10.1016/j.spasta.2024.100878
Guowang Luo , Mixia Wu
In this paper, bias-corrected instrumental variable estimation methods, specifically the bias-corrected two-stage least square (2SLS) estimation and the bias-corrected asymptotically best 2SLS estimation, are proposed for spatial autoregressive (SAR) models with covariate measurement errors, utilizing available information regarding the variance of the measurement error. Under mild assumptions, the consistency and asymptotic normality of the proposed estimators are derived. Simulation studies further reveal that the proposed methods exhibit robustness regardless of the presence of spatial dependence in the model. Additionally, a real data example is utilized to illustrate the developed methods.
{"title":"Bias-corrected instrumental variable estimation for spatial autoregressive models with measurement errors","authors":"Guowang Luo , Mixia Wu","doi":"10.1016/j.spasta.2024.100878","DOIUrl":"10.1016/j.spasta.2024.100878","url":null,"abstract":"<div><div>In this paper, bias-corrected instrumental variable estimation methods, specifically the bias-corrected two-stage least square (2SLS) estimation and the bias-corrected asymptotically best 2SLS estimation, are proposed for spatial autoregressive (SAR) models with covariate measurement errors, utilizing available information regarding the variance of the measurement error. Under mild assumptions, the consistency and asymptotic normality of the proposed estimators are derived. Simulation studies further reveal that the proposed methods exhibit robustness regardless of the presence of spatial dependence in the model. Additionally, a real data example is utilized to illustrate the developed methods.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100878"},"PeriodicalIF":2.1,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The timely and efficient administration of rabies vaccinations to animals in rural villages is necessary to attain a state of herd immunity. Efficient sampling of households in a rural village is of utmost importance in reaching the most animals for vaccination, with the least effort, and in the lowest time. This research seeks to both optimise the spatial sampling scheme used to sample households, as well as the route travelled by persons performing door-to-door vaccinations. The walking time in minutes is regarded as the cost of a vaccination scheme and is minimised in this paper. The distribution of houses in a rural village constitutes a spatial point pattern in , and as such, spatial point pattern analysis techniques as well as some spatial sampling schemes are applied throughout this research. The penultimate aim of this work is to provide policy makers with additional tools to combat rabies, a disease which remains endemic to some countries in West and Central Africa, and Asia.
{"title":"An optimised rabies vaccination schedule for rural settlements","authors":"Rian Botes , Inger Fabris-Rotelli , Kabelo Mahloromela , Ding-Geng Chen","doi":"10.1016/j.spasta.2024.100877","DOIUrl":"10.1016/j.spasta.2024.100877","url":null,"abstract":"<div><div>The timely and efficient administration of rabies vaccinations to animals in rural villages is necessary to attain a state of herd immunity. Efficient sampling of households in a rural village is of utmost importance in reaching the most animals for vaccination, with the least effort, and in the lowest time. This research seeks to both optimise the spatial sampling scheme used to sample households, as well as the route travelled by persons performing door-to-door vaccinations. The walking time in minutes is regarded as the cost of a vaccination scheme and is minimised in this paper. The distribution of houses in a rural village constitutes a spatial point pattern in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and as such, spatial point pattern analysis techniques as well as some spatial sampling schemes are applied throughout this research. The penultimate aim of this work is to provide policy makers with additional tools to combat rabies, a disease which remains endemic to some countries in West and Central Africa, and Asia.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100877"},"PeriodicalIF":2.1,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-12-17DOI: 10.1016/j.spasta.2024.100876
Thomas Suesse , Alexander Brenning
Determining exceedance regions, such as regions where a specified threshold of a pollutant in the environment is exceeded, is of critical importance for decision-making in environmental management and public health. Inner and outer predicted exceedance sets express the uncertainties in predicted exceedance regions as they sandwich the unknown true exceedance region with high confidence, analogous to confidence regions for point estimates. It is therefore desirable to reduce the uncertainty about the locations of the true exceedance region, resulting in a narrow band between the inner and outer sets. However, in practice this is not often the case mainly due to the strict statistical subset criteria being set, which are equivalent to a multiple testing problem controlling the familywise error rate (FWER). It is well known that the FWER leads to fewer rejections compared to other criteria; in the context of exceedance regions, this would correspond to an extremely small, conservative inner predicted exceedance region. In this paper, we loosen the criteria slightly to obtain a narrower band between inner and outer sets, allowing for more nuanced uncertainty assessments. A new algorithm is proposed to construct these exceedance sets, and the methods are compared in a simulation study to assess whether they indeed control the new criteria. The methods are illustrated on two data sets: average rainfall in the state of Paraná, Brazil, and nitrogen dioxide air pollution in Germany in the year 2018.
{"title":"Softening the criteria for determining inner and outer predicted exceedance sets","authors":"Thomas Suesse , Alexander Brenning","doi":"10.1016/j.spasta.2024.100876","DOIUrl":"10.1016/j.spasta.2024.100876","url":null,"abstract":"<div><div>Determining exceedance regions, such as regions where a specified threshold of a pollutant in the environment is exceeded, is of critical importance for decision-making in environmental management and public health. Inner and outer predicted exceedance sets express the uncertainties in predicted exceedance regions as they sandwich the unknown true exceedance region with high confidence, analogous to confidence regions for point estimates. It is therefore desirable to reduce the uncertainty about the locations of the true exceedance region, resulting in a narrow band between the inner and outer sets. However, in practice this is not often the case mainly due to the strict statistical subset criteria being set, which are equivalent to a multiple testing problem controlling the familywise error rate (FWER). It is well known that the FWER leads to fewer rejections compared to other criteria; in the context of exceedance regions, this would correspond to an extremely small, conservative inner predicted exceedance region. In this paper, we loosen the criteria slightly to obtain a narrower band between inner and outer sets, allowing for more nuanced uncertainty assessments. A new algorithm is proposed to construct these exceedance sets, and the methods are compared in a simulation study to assess whether they indeed control the new criteria. The methods are illustrated on two data sets: average rainfall in the state of Paraná, Brazil, and nitrogen dioxide air pollution in Germany in the year 2018.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100876"},"PeriodicalIF":2.1,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-26DOI: 10.1016/j.spasta.2024.100875
Qingqing Li, Ruizhuo Zheng, Aibing Ji, Hongyan Ma
Interval-valued data has garnered attention across various applications, leading to increased research into spatial interval-valued data models. The integration of uncertainty variables into spatial panel data models has become crucial. This paper presents a spatial panel interval-valued autoregressive model with fixed effects, utilizing the parametric method. The quasi-maximum likelihood method is employed for parameter estimation, and its consistency and asymptotic properties are discussed. Additionally, three special cases and two degenerated models derived from our framework are presented, elucidating their significance in spatial statistics. Monte Carlo simulations are used to validate the fitting and forecasting performance of our proposed models across diverse scenarios. Furthermore, the models are implemented in real-world air quality and house price datasets for forecasting purposes. Through rigorous experimentation, the superior performance of the models is demonstrated. These results highlight the practical utility of the spatial panel interval-valued autoregressive models in addressing spatial data challenges.
{"title":"Fixed effects spatial panel interval-valued autoregressive models and applications","authors":"Qingqing Li, Ruizhuo Zheng, Aibing Ji, Hongyan Ma","doi":"10.1016/j.spasta.2024.100875","DOIUrl":"10.1016/j.spasta.2024.100875","url":null,"abstract":"<div><div>Interval-valued data has garnered attention across various applications, leading to increased research into spatial interval-valued data models. The integration of uncertainty variables into spatial panel data models has become crucial. This paper presents a spatial panel interval-valued autoregressive model with fixed effects, utilizing the parametric method. The quasi-maximum likelihood method is employed for parameter estimation, and its consistency and asymptotic properties are discussed. Additionally, three special cases and two degenerated models derived from our framework are presented, elucidating their significance in spatial statistics. Monte Carlo simulations are used to validate the fitting and forecasting performance of our proposed models across diverse scenarios. Furthermore, the models are implemented in real-world air quality and house price datasets for forecasting purposes. Through rigorous experimentation, the superior performance of the models is demonstrated. These results highlight the practical utility of the spatial panel interval-valued autoregressive models in addressing spatial data challenges.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100875"},"PeriodicalIF":2.1,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142747091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-23DOI: 10.1016/j.spasta.2024.100874
Pierpaolo D’Urso , Livia De Giovanni , Lorenzo Federico , Vincenzina Vitale
A fuzzy clustering model for data with mixed features and spatial constraints is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute employing a weighting scheme, to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. A spatial term is taken into account, considering a wide definition of contiguity, either physical contiguity or the adjacency matrix in a network. Simulation studies and two empirical applications, including both physical and abstract definitions of contiguity are presented that show the effectiveness of the proposed clustering model.
{"title":"Fuzzy clustering of mixed data with spatial regularization","authors":"Pierpaolo D’Urso , Livia De Giovanni , Lorenzo Federico , Vincenzina Vitale","doi":"10.1016/j.spasta.2024.100874","DOIUrl":"10.1016/j.spasta.2024.100874","url":null,"abstract":"<div><div>A fuzzy clustering model for data with mixed features and spatial constraints is proposed. The clustering model allows different types of variables, or attributes, to be taken into account. This result is achieved by combining the dissimilarity measures for each attribute employing a weighting scheme, to obtain a distance measure for multiple attributes. The weights are objectively computed during the optimization process. The weights reflect the relevance of each attribute type in the clustering results. A spatial term is taken into account, considering a wide definition of contiguity, either physical contiguity or the adjacency matrix in a network. Simulation studies and two empirical applications, including both physical and abstract definitions of contiguity are presented that show the effectiveness of the proposed clustering model.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100874"},"PeriodicalIF":2.1,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-22DOI: 10.1016/j.spasta.2024.100873
Lucas Michelin , Lucas C. Godoy , Heitor S. Ramos , Marcos O. Prates
Extracting geological resources like hydrocarbon fluids requires significant investments and precise decision-making processes. To optimize the efficiency of the extraction process, researchers and industry experts have explored innovative methodologies, including the prediction of optimal drilling locations. Porosity, a key attribute of reservoir rocks, plays a crucial role in determining fluid storage capacity. Geostatistical techniques, such as kriging, have been widely used for estimating porosity by capturing spatial dependence in sampled point-referenced data. However, the reliance on geographical coordinates for determining spatial distances may present challenges in scenarios with small and widely separated samples. In this paper, we develop a mixture model that combines the covariance generated by geographical space and the covariance generated in an appropriate feature space to enhance estimation accuracy. Developed within the Bayesian framework, our approach utilizes flexible Markov Chain Monte Carlo (MCMC) methods and leverages the Nearest-Neighbor Gaussian Process (NNGP) strategy for scalability. We present a controlled empirical comparison, considering various data generation configurations, to assess the performance of the mixture model in comparison to the marginal models. Applying our models to a three-dimensional reservoir demonstrates its practical applicability and scalability. This research presents a novel approach for improved porosity estimation by integrating spatial and covariate information, offering the potential for optimizing reservoir exploration and extraction activities.
{"title":"Fast mixture spatial regression: A mixture in the geographical and feature space applied to predict porosity in the post-salt","authors":"Lucas Michelin , Lucas C. Godoy , Heitor S. Ramos , Marcos O. Prates","doi":"10.1016/j.spasta.2024.100873","DOIUrl":"10.1016/j.spasta.2024.100873","url":null,"abstract":"<div><div>Extracting geological resources like hydrocarbon fluids requires significant investments and precise decision-making processes. To optimize the efficiency of the extraction process, researchers and industry experts have explored innovative methodologies, including the prediction of optimal drilling locations. Porosity, a key attribute of reservoir rocks, plays a crucial role in determining fluid storage capacity. Geostatistical techniques, such as kriging, have been widely used for estimating porosity by capturing spatial dependence in sampled point-referenced data. However, the reliance on geographical coordinates for determining spatial distances may present challenges in scenarios with small and widely separated samples. In this paper, we develop a mixture model that combines the covariance generated by geographical space and the covariance generated in an appropriate feature space to enhance estimation accuracy. Developed within the Bayesian framework, our approach utilizes flexible Markov Chain Monte Carlo (MCMC) methods and leverages the Nearest-Neighbor Gaussian Process (NNGP) strategy for scalability. We present a controlled empirical comparison, considering various data generation configurations, to assess the performance of the mixture model in comparison to the marginal models. Applying our models to a three-dimensional reservoir demonstrates its practical applicability and scalability. This research presents a novel approach for improved porosity estimation by integrating spatial and covariate information, offering the potential for optimizing reservoir exploration and extraction activities.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100873"},"PeriodicalIF":2.1,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-20DOI: 10.1016/j.spasta.2024.100869
Mariem Abaach , Hermine Biermé , Elena Di Bernardino , Anne Estrade
In this paper we consider the so-called directional perimeters of a thresholded gray-level image. These geometrical quantities are built by considering separately the horizontal and vertical contributions of the pixel. We explicitly compute the first two moments of the directional perimeter under the hypothesis of an underlying discrete Gaussian stationary random field. We establish a central limit theorem (CLT), as the number of pixels goes to infinity, for the joint directional perimeters at various levels under a weak summability condition of the covariance function. By using the CLT previously established, we construct a consistent pixel isotropy test, based on the ratio of the directional perimeters. Our theoretical study is completed by extensive numerical illustrations based on simulated data. Finally, we apply our method to detect pixel anisotropy in calcaneus X-ray images.
{"title":"Pixel isotropy test based on directional perimeters","authors":"Mariem Abaach , Hermine Biermé , Elena Di Bernardino , Anne Estrade","doi":"10.1016/j.spasta.2024.100869","DOIUrl":"10.1016/j.spasta.2024.100869","url":null,"abstract":"<div><div>In this paper we consider the so-called directional perimeters of a thresholded gray-level image. These geometrical quantities are built by considering separately the horizontal and vertical contributions of the pixel. We explicitly compute the first two moments of the directional perimeter under the hypothesis of an underlying discrete Gaussian stationary random field. We establish a central limit theorem (CLT), as the number of pixels goes to infinity, for the joint directional perimeters at various levels under a weak summability condition of the covariance function. By using the CLT previously established, we construct a consistent pixel isotropy test, based on the ratio of the directional perimeters. Our theoretical study is completed by extensive numerical illustrations based on simulated data. Finally, we apply our method to detect pixel anisotropy in calcaneus X-ray images.</div></div>","PeriodicalId":48771,"journal":{"name":"Spatial Statistics","volume":"65 ","pages":"Article 100869"},"PeriodicalIF":2.1,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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