The volume tensor provides a robust estimate of the shape and orientation of an object in space. In this paper, we introduce Fakir method for estimating the tensor of an object in 3D data set based on the intersections of objects boundary with virtual lines. We calculate the precision of shape estimates by predicting the variance of estimators of integrals based on systematic sampling. To demonstrate the ability of the Fakir method, we measure changes in shape and orientation of compartments in the pheasant brain during development.
{"title":"VOLUME TENSOR ESTIMATION USING A VIRTUAL LINE GRID: STUDY OF A DEVELOPING PHEASANT BRAIN","authors":"J. Janáček, D. Jirák","doi":"10.5566/ias.1701","DOIUrl":"https://doi.org/10.5566/ias.1701","url":null,"abstract":"The volume tensor provides a robust estimate of the shape and orientation of an object in space. In this paper, we introduce Fakir method for estimating the tensor of an object in 3D data set based on the intersections of objects boundary with virtual lines. We calculate the precision of shape estimates by predicting the variance of estimators of integrals based on systematic sampling. To demonstrate the ability of the Fakir method, we measure changes in shape and orientation of compartments in the pheasant brain during development.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"1 1","pages":"255-260"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88856402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses the geometrical properties of a radiolarian skeletal structure, namely, that of genus Didymocyrtis . We characterized the evolution of skeletal structures and analyzed the structures using geometry. We defined two ratios in order to quantify the geometrical properties of Didymocyrtis and verified that the two ratios changed with their phylogenic evolution. We also used the 3D skeletal data of a specimen of species D. tetrathalamus , which were obtained through micro X-ray CT. The cortical shell obtained in the 3D data was projected onto a spherical surface, and we determined the centers of the pores. Our analysis revealed that the number of pores is approximately 200 and their distribution is not regular. We also determined that the column-like parts of the skeleton, which connect the inner and upper parts of the specimen, do not lie on a plane and their intervals are not equal.
{"title":"Geometrical Properties of Skeletal Structures of Radiolarian Genus Didymocyrtis","authors":"T. Yoshino, A. Matsuoka, N. Kishimoto","doi":"10.5566/ias.2089","DOIUrl":"https://doi.org/10.5566/ias.2089","url":null,"abstract":"This paper discusses the geometrical properties of a radiolarian skeletal structure, namely, that of genus Didymocyrtis . We characterized the evolution of skeletal structures and analyzed the structures using geometry. We defined two ratios in order to quantify the geometrical properties of Didymocyrtis and verified that the two ratios changed with their phylogenic evolution. We also used the 3D skeletal data of a specimen of species D. tetrathalamus , which were obtained through micro X-ray CT. The cortical shell obtained in the 3D data was projected onto a spherical surface, and we determined the centers of the pores. Our analysis revealed that the number of pores is approximately 200 and their distribution is not regular. We also determined that the column-like parts of the skeleton, which connect the inner and upper parts of the specimen, do not lie on a plane and their intervals are not equal.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"132 1","pages":"237-244"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73953437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The estimation of the grain size in granular materials is usually performed by 2D observations. Unfolding the grain size distribution from apparent 2D sizes is commonly referred as the corpuscle problem. For spherical particles, the distribution of the apparent size can be related to that of the actual size thanks to the Wicksell’s equation. The Saltikov method, which is based on Wicksell’s equation, is the most widely used method for resolving corpuscle problems. This method is recursive and works on the finite histogram of the grain size. In this paper, we propose an algorithm based on a minimizing procedure to numerically solve the Wicksell’s equation, assuming a parametric model for the distribution (e.g. lognormal distribution). This algorithm is applied on real material and the results are compared to those found using Saltikov or Saltikov-based stereology techniques. A criterion is proposed for choosing the number of bins in the Saltikov method. The accuracy of the proposed algorithm, depending on the sample size, is studied.
{"title":"Resolution of the Wicksell's equation by Minimum Distance Estimation","authors":"D. Depriester, R. Kubler","doi":"10.5566/ias.2133","DOIUrl":"https://doi.org/10.5566/ias.2133","url":null,"abstract":"The estimation of the grain size in granular materials is usually performed by 2D observations. Unfolding the grain size distribution from apparent 2D sizes is commonly referred as the corpuscle problem. For spherical particles, the distribution of the apparent size can be related to that of the actual size thanks to the Wicksell’s equation. The Saltikov method, which is based on Wicksell’s equation, is the most widely used method for resolving corpuscle problems. This method is recursive and works on the finite histogram of the grain size. In this paper, we propose an algorithm based on a minimizing procedure to numerically solve the Wicksell’s equation, assuming a parametric model for the distribution (e.g. lognormal distribution). This algorithm is applied on real material and the results are compared to those found using Saltikov or Saltikov-based stereology techniques. A criterion is proposed for choosing the number of bins in the Saltikov method. The accuracy of the proposed algorithm, depending on the sample size, is studied.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"229 1","pages":"213-226"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82809881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝ d is estimated using a periodic grid in an isotropic uniform random position. Extension term in the estimator variance is proportional to the integral of the squared modulus of the function over the object boundary and to the grid scaling factor raised to the power of d +1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.
{"title":"VARIANCE OF THE ISOTROPIC UNIFORM SYSTEMATIC SAMPLING","authors":"J. Janáček, D. Jirák","doi":"10.5566/ias.2218","DOIUrl":"https://doi.org/10.5566/ias.2218","url":null,"abstract":"The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝ d is estimated using a periodic grid in an isotropic uniform random position. Extension term in the estimator variance is proportional to the integral of the squared modulus of the function over the object boundary and to the grid scaling factor raised to the power of d +1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"1 1","pages":"261-267"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89361378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Markus Kronenberger, K. Schladitz, O. Wirjadi, Christopher Weber, B. Hamann, H. Hagen
This paper introduces a method for detecting endpoints of partially overlapping straight fibers in three-dimensional voxel image data. The novel approach directly determines fiber endpoints without the need for more expansive single-fiber segmentation. In the context of fiber-reinforced polymers, endpoint information is of practical significance as it can indicate potential damage in endless fiber systems, or can serve as input for estimating statistical fiber length distribution. We tackle this challenge by exploiting Gaussian curvature of the surface of the fibers. Fiber endpoints have high positive curvature, allowing one to distinguish them from the rest of a structure. Accuracy data of the proposed method are presented for various data sets. For simulated fiber systems with fiber volume fractions of less than 20 %, true positive rates above 94 % and false positive rates below 5 % are observed. Two well-resolved real data sets show a reduction of the first rate to 90.3 % and an increase of the second rate to 13.1 %.
{"title":"Endpoint Detection of Partially Overlapping Straight Fibers using High Positive Gaussian Curvature in 3D images","authors":"Markus Kronenberger, K. Schladitz, O. Wirjadi, Christopher Weber, B. Hamann, H. Hagen","doi":"10.5566/ias.2197","DOIUrl":"https://doi.org/10.5566/ias.2197","url":null,"abstract":"This paper introduces a method for detecting endpoints of partially overlapping straight fibers in three-dimensional voxel image data. The novel approach directly determines fiber endpoints without the need for more expansive single-fiber segmentation. In the context of fiber-reinforced polymers, endpoint information is of practical significance as it can indicate potential damage in endless fiber systems, or can serve as input for estimating statistical fiber length distribution. We tackle this challenge by exploiting Gaussian curvature of the surface of the fibers. Fiber endpoints have high positive curvature, allowing one to distinguish them from the rest of a structure. Accuracy data of the proposed method are presented for various data sets. For simulated fiber systems with fiber volume fractions of less than 20 %, true positive rates above 94 % and false positive rates below 5 % are observed. Two well-resolved real data sets show a reduction of the first rate to 90.3 % and an increase of the second rate to 13.1 %.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"346 1","pages":"245-253"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75158354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces improvements to the algorithm that was proposed in 2001 by Chen and Chen. The algorithm constructs a quadtree directly from Freeman chain code in four directions. We have improved the algorithm in two ways: Firstly, a time efficient solution using the space filling Z-order curve is proposed for a self-intersection case that was not considered by Chen and Chen. Secondly, the algorithm is expanded to handle geometric objects containing holes. The computational efficiency of the extended algorithm was confirmed by the experiments.
{"title":"Extended algorithm to construct a quadtree from Freeman chain code in four directions","authors":"Andrej Nerat, D. Strnad, Eva Zupancic, B. Žalik","doi":"10.5566/ias.2095","DOIUrl":"https://doi.org/10.5566/ias.2095","url":null,"abstract":"This paper introduces improvements to the algorithm that was proposed in 2001 by Chen and Chen. The algorithm constructs a quadtree directly from Freeman chain code in four directions. We have improved the algorithm in two ways: Firstly, a time efficient solution using the space filling Z-order curve is proposed for a self-intersection case that was not considered by Chen and Chen. Secondly, the algorithm is expanded to handle geometric objects containing holes. The computational efficiency of the extended algorithm was confirmed by the experiments.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"47 1","pages":"227-235"},"PeriodicalIF":0.9,"publicationDate":"2019-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73815393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Old theorems by Cavalieri, Buffon and Cauchy that have been mentioned earlier for their relevance to materials engineering are discussed herein, whereby it is indicated how we applied them on cementbased materials. Specifically, relevant problems treated by the present author are surveyed. Particularly in the presently explored field of porosimetry and permeability estimation of virtual representations of the cement-based materials, it is demonstrated how the stereological framework - in which the theorems are embedded to day - develops with respect to the discussed problems.
{"title":"FAMOUS “PRE-STEREOLOGICAL” TOOLS: SURVEY OF APPLICATIONS ON CEMENT-BASED MATERIALS DURING PAST HALF OF A CENTURY","authors":"P. Stroeven","doi":"10.5566/ias.2207","DOIUrl":"https://doi.org/10.5566/ias.2207","url":null,"abstract":"Old theorems by Cavalieri, Buffon and Cauchy that have been mentioned earlier for their relevance to materials engineering are discussed herein, whereby it is indicated how we applied them on cementbased materials. Specifically, relevant problems treated by the present author are surveyed. Particularly in the presently explored field of porosimetry and permeability estimation of virtual representations of the cement-based materials, it is demonstrated how the stereological framework - in which the theorems are embedded to day - develops with respect to the discussed problems.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"23 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76859548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maciej Skwirczynski, T. Gaciarz, M. Skomorowski, W. Wojciechowski
Radiographic measurements of foot deformities are used to determine, among other things, such conditions as flatfoot, high arch, or calcaneal fracture. Those measurements are achieved by estimating four angles. Manual assessment of those angles is time-consuming not to mention inevitable errors of such approximation. To the best of the authors knowledge, currently there is no research focusing on finding those four angles. In this paper an algorithm for automatic assessment of those angles, based on extremely randomized trees, is being proposed. Moreover this diagnostic assisting system was intended to be as generic as possible and could be applied, to some degree, to other similar problems. To demonstrate usefulness of this method, correlations of automated measurements with manual ones against correlations of manual measurements with manual ones are being compared. The significance level for manual-manual measurements comparison is less than 0.001 in case of all four angles. The significance level for automated-manual measurements comparison is also less than 0.001 in all cases. The results show that the search for the aforementioned angles can be automated. Even with the use of a generic algorithm a high degree of precision can be achieved, allowing for a more efficient diagnosis.
{"title":"AUTOMATED MEASUREMENT OF FOOT DEFORMITIES: FLATFOOT, HIGH ARCH, CALCANEAL FRACTURE","authors":"Maciej Skwirczynski, T. Gaciarz, M. Skomorowski, W. Wojciechowski","doi":"10.5566/IAS.1980","DOIUrl":"https://doi.org/10.5566/IAS.1980","url":null,"abstract":"Radiographic measurements of foot deformities are used to determine, among other things, such conditions as flatfoot, high arch, or calcaneal fracture. Those measurements are achieved by estimating four angles. Manual assessment of those angles is time-consuming not to mention inevitable errors of such approximation. To the best of the authors knowledge, currently there is no research focusing on finding those four angles. In this paper an algorithm for automatic assessment of those angles, based on extremely randomized trees, is being proposed. Moreover this diagnostic assisting system was intended to be as generic as possible and could be applied, to some degree, to other similar problems. To demonstrate usefulness of this method, correlations of automated measurements with manual ones against correlations of manual measurements with manual ones are being compared. The significance level for manual-manual measurements comparison is less than 0.001 in case of all four angles. The significance level for automated-manual measurements comparison is also less than 0.001 in all cases. The results show that the search for the aforementioned angles can be automated. Even with the use of a generic algorithm a high degree of precision can be achieved, allowing for a more efficient diagnosis.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81678710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Texture segmentation is one of the main tasks in image applications, specifically in remote sensing, where the objective is to segment high-resolution images of natural landscapes into different cover types. Often the focus is on the selection of discriminant textural features, and although these are really fundamental, there is another part of the process that is also influential, partitioning different homogeneous textures into groups. A methodology based on archetype analysis (AA) of the local textural measurements is proposed. AA seeks the purest textures in the image and it can find the borders between pure textures, as those regions composed of mixtures of several archetypes. The proposed procedure has been tested on a remote sensing image application with local granulometries, providing promising results.
{"title":"ARCHETYPAL ANALYSIS: AN ALTERNATIVE TO CLUSTERING FOR UNSUPERVISED TEXTURE SEGMENTATION","authors":"Ismael Cabero, I. Epifanio","doi":"10.5566/IAS.2052","DOIUrl":"https://doi.org/10.5566/IAS.2052","url":null,"abstract":"Texture segmentation is one of the main tasks in image applications, specifically in remote sensing, where the objective is to segment high-resolution images of natural landscapes into different cover types. Often the focus is on the selection of discriminant textural features, and although these are really fundamental, there is another part of the process that is also influential, partitioning different homogeneous textures into groups. A methodology based on archetype analysis (AA) of the local textural measurements is proposed. AA seeks the purest textures in the image and it can find the borders between pure textures, as those regions composed of mixtures of several archetypes. The proposed procedure has been tested on a remote sensing image application with local granulometries, providing promising results.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"146 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74701220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Random sets play an essential role in modelling several phenomena in biology, medicine and material science. However, sometimes it is hard to describe them using a specific model. Therefore it can also be difficult to classify them or to compare their realisations. This contribution proposes a similarity measure between two random sets whose realisations consist of many components based on just one realisation of each of them. The similarity measure is obtained in a non-parametric way taking into account the shapes and the positions of the components. The procedure is justified by a simulation study and consequently applied to real biomedical data of histological images of mammary tissue.
{"title":"SIMILARITY BETWEEN RANDOM SETS CONSISTING OF MANY COMPONENTS","authors":"Vesna Gotovac","doi":"10.5566/IAS.2017","DOIUrl":"https://doi.org/10.5566/IAS.2017","url":null,"abstract":"Random sets play an essential role in modelling several phenomena in biology, medicine and material science. However, sometimes it is hard to describe them using a specific model. Therefore it can also be difficult to classify them or to compare their realisations. This contribution proposes a similarity measure between two random sets whose realisations consist of many components based on just one realisation of each of them. The similarity measure is obtained in a non-parametric way taking into account the shapes and the positions of the components. The procedure is justified by a simulation study and consequently applied to real biomedical data of histological images of mammary tissue.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"44 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73692246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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