Domingo Gómez-Pérez, Javier González-Villa, Florian Pausinger
The nucleator is a method to estimate the volume of a particle, i.e. a compact subset of ℝ3, which is widely used in Stereology. It is based on geometric sampling and known to be unbiased. However, the prediction of the variance of this estimator is non-trivial and depends on the underlying sampling scheme.We propose well established tools from quasi-Monte Carlo integration to address this problem. In particular, we show how the theory of reproducing kernel Hilbert spaces can be used for variance prediction and how the variance of estimators based on the nucleator idea can be reduced using lattice (or lattice-like) points. We illustrate and test our results on various examples.
{"title":"ESTIMATION OF VOLUME USING THE NUCLEATOR AND LATTICE POINTS","authors":"Domingo Gómez-Pérez, Javier González-Villa, Florian Pausinger","doi":"10.5566/IAS.2012","DOIUrl":"https://doi.org/10.5566/IAS.2012","url":null,"abstract":"The nucleator is a method to estimate the volume of a particle, i.e. a compact subset of ℝ3, which is widely used in Stereology. It is based on geometric sampling and known to be unbiased. However, the prediction of the variance of this estimator is non-trivial and depends on the underlying sampling scheme.We propose well established tools from quasi-Monte Carlo integration to address this problem. In particular, we show how the theory of reproducing kernel Hilbert spaces can be used for variance prediction and how the variance of estimators based on the nucleator idea can be reduced using lattice (or lattice-like) points. We illustrate and test our results on various examples.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"31 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81758090","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}
Design unbiased estimation of population size by stereological methods is an efficient alternative to automatic computer vision methods, which are generally biased. Moreover, stereological methods offer the possibility of predicting the error variance from a single sample. Here we explore the statistical performance of two alternative variance estimators on a dataset of 26 labelled crowd pictures. The empirical mean square errors of the variance predictors are compared by means of Monte Carlo resampling.
{"title":"VARIANCE PREDICTION FOR POPULATION SIZE ESTIMATION","authors":"Ana I Gómez, Marcos Cruz, L. Cruz-Orive","doi":"10.5566/IAS.1991","DOIUrl":"https://doi.org/10.5566/IAS.1991","url":null,"abstract":"Design unbiased estimation of population size by stereological methods is an efficient alternative to automatic computer vision methods, which are generally biased. Moreover, stereological methods offer the possibility of predicting the error variance from a single sample. Here we explore the statistical performance of two alternative variance estimators on a dataset of 26 labelled crowd pictures. The empirical mean square errors of the variance predictors are compared by means of Monte Carlo resampling.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"21 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81577882","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}
Djibril Kaba, N.J.B. McFarlane, Feng-lin Dong, N. Graf, Xujiong Ye
The annotation of the tumour from medical scans is a crucial step in nephroblastoma treatment. Therefore, an accurate and reliable segmentation method is needed to facilitate the evaluation and the treatments of the tumour. The proposed method serves this purpose by performing the segmentation of nephroblastoma in MRI scans. The segmentation is performed by adapting and a 2D free hand drawing tool to select a region of interest in the scan slices. Results from 24 patients show a mean root-mean-square error of 0.0481 ± 0.0309, an average Dice coefficient of 0.9060 ± 0.0549 and an average accuracy of 99.59% ± 0.0039. Thus the proposed method demonstrated an effective agreement with manual annotations.
{"title":"NEPHROBLASTOMA ANALYSIS IN MRI IMAGES","authors":"Djibril Kaba, N.J.B. McFarlane, Feng-lin Dong, N. Graf, Xujiong Ye","doi":"10.5566/IAS.2000","DOIUrl":"https://doi.org/10.5566/IAS.2000","url":null,"abstract":"The annotation of the tumour from medical scans is a crucial step in nephroblastoma treatment. Therefore, an accurate and reliable segmentation method is needed to facilitate the evaluation and the treatments of the tumour. The proposed method serves this purpose by performing the segmentation of nephroblastoma in MRI scans. The segmentation is performed by adapting and a 2D free hand drawing tool to select a region of interest in the scan slices. Results from 24 patients show a mean root-mean-square error of 0.0481 ± 0.0309, an average Dice coefficient of 0.9060 ± 0.0549 and an average accuracy of 99.59% ± 0.0039. Thus the proposed method demonstrated an effective agreement with manual annotations.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"309 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73470965","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}
We study nonparametric estimation of the length distribution for stationary line segment processes in the d-dimensional Euclidean space. Several methods have been proposed in the literature. We review different approaches (Horvitz-Thompson type estimator, reduced-sample estimator, Kaplan-Meier estimator, nonparametric maximum likelihood estimator, stochastic restoration estimation) and compare the finite sample behaviour by means of a simulation study for stationary line segment processes in 2D and 3D. Several data generating processes (Poisson point process, Matérn cluster process and Matérn hard-core process II) are considered with both independent and dependent segments. Our finite sample comparison reveals that the nonparametric likelihood estimator provides the most preferable method which works reasonably also if its assumptions are not satisfied.
{"title":"A COMPARISON OF NONPARAMETRIC ESTIMATORS FOR LENGTH DISTRIBUTION IN LINE SEGMENT PROCESSES","authors":"Z. Pawlas, M. Zikmundová","doi":"10.5566/IAS.1889","DOIUrl":"https://doi.org/10.5566/IAS.1889","url":null,"abstract":"We study nonparametric estimation of the length distribution for stationary line segment processes in the d-dimensional Euclidean space. Several methods have been proposed in the literature. We review different approaches (Horvitz-Thompson type estimator, reduced-sample estimator, Kaplan-Meier estimator, nonparametric maximum likelihood estimator, stochastic restoration estimation) and compare the finite sample behaviour by means of a simulation study for stationary line segment processes in 2D and 3D. Several data generating processes (Poisson point process, Matérn cluster process and Matérn hard-core process II) are considered with both independent and dependent segments. Our finite sample comparison reveals that the nonparametric likelihood estimator provides the most preferable method which works reasonably also if its assumptions are not satisfied. ","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"37 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86828405","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}
A few words on the present special topic, devoted to the multiscale modeling of granular media, and published in honor of Prof. Dominique Jeulin’s enduring contribution to the wide field of image analysis, random structures and material science.
{"title":"SPECIAL TOPIC ON MULTISCALE MODELING OF GRANULAR MEDIA: A TRIBUTE TO PROF. DOMINIQUE JEULIN","authors":"J. Serra, F. Willot","doi":"10.5566/IAS.2146","DOIUrl":"https://doi.org/10.5566/IAS.2146","url":null,"abstract":"A few words on the present special topic, devoted to the multiscale modeling of granular media, and published in honor of Prof. Dominique Jeulin’s enduring contribution to the wide field of image analysis, random structures and material science.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"892 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77020685","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}
Zuzana Kubínová, Natália Glanc, B. Radochová, Z. Lhotáková, J. Janáček, L. Kubínová, J. Albrechtová
The main objective of this study was to find out whether the selected chloroplast characteristics measured in the mesophyll layer nearest to the needle surface (i.e., the first mesophyll layer) could be representative for the whole needle cross section. Two chloroplast sampling approaches were applied on Norway spruce needles during the investigation of the effects of different levels of air CO2 concentration and irradiance: (i) sampling only from the first mesophyll layer, and (ii) systematic uniform random (SUR) sampling. The selected characteristics were: (i) chloroplast area, (ii) starch grain area, and (iii) starch areal density on median chloroplast cross sections, and (iv) chloroplast number per unit of needle volume. It was shown that the first mesophyll layer was not representative for estimating all evaluated characteristics except the chloroplast area. Sampling only there caused obtaining slightly biased results, while SUR sampling gave unbiased estimations at the cost of longer measuring time. The major effect of studied factors was in starch areal density and starch grain area, which were larger in sun needles in elevated CO2 concentration in comparison with sun needles in ambient CO2 concentration. In conclusion, it was demonstrated that the first layer of mesophyll is not always representative for the needle cross section. If technically feasible, SUR is recommended for analysis of chloroplast ultrastructure. The simplified sampling design can be applied, e.g., for comparisons of many different treatments. However, it should be combined with other approaches to characterize the chloroplast function and the results carefully considered and interpreted.
{"title":"UNBIASED ESTIMATION OF NORWAY SPRUCE (PICEA ABIES L. KARST.) CHLOROPLAST STRUCTURE: HETEROGENEITY WITHIN NEEDLE MESOPHYLL UNDER DIFFERENT IRRADIANCE AND [CO2]","authors":"Zuzana Kubínová, Natália Glanc, B. Radochová, Z. Lhotáková, J. Janáček, L. Kubínová, J. Albrechtová","doi":"10.5566/IAS.2005","DOIUrl":"https://doi.org/10.5566/IAS.2005","url":null,"abstract":"The main objective of this study was to find out whether the selected chloroplast characteristics measured in the mesophyll layer nearest to the needle surface (i.e., the first mesophyll layer) could be representative for the whole needle cross section. Two chloroplast sampling approaches were applied on Norway spruce needles during the investigation of the effects of different levels of air CO2 concentration and irradiance: (i) sampling only from the first mesophyll layer, and (ii) systematic uniform random (SUR) sampling. The selected characteristics were: (i) chloroplast area, (ii) starch grain area, and (iii) starch areal density on median chloroplast cross sections, and (iv) chloroplast number per unit of needle volume. It was shown that the first mesophyll layer was not representative for estimating all evaluated characteristics except the chloroplast area. Sampling only there caused obtaining slightly biased results, while SUR sampling gave unbiased estimations at the cost of longer measuring time. The major effect of studied factors was in starch areal density and starch grain area, which were larger in sun needles in elevated CO2 concentration in comparison with sun needles in ambient CO2 concentration. In conclusion, it was demonstrated that the first layer of mesophyll is not always representative for the needle cross section. If technically feasible, SUR is recommended for analysis of chloroplast ultrastructure. The simplified sampling design can be applied, e.g., for comparisons of many different treatments. However, it should be combined with other approaches to characterize the chloroplast function and the results carefully considered and interpreted.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"22 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85631830","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}
In this article, we propose a novel, efficient method for computing a random tessellation from its vectorial representation at each voxel of a discretized domain. This method is based upon the resolution of the Eikonal equation and has a complexity in O(N log N), N being the number of voxels used to discretize the domain. By contrast, evaluating the implicit functions of the vectorial representation at each voxel location has a complexity of O(N²) in the general case. The method also enables us to consider the generation of tessellations with rough interfaces between cells by simulating the growth of the germs on a domain where the velocity varies locally. This aspect constitutes the main contribution of the article. A final contribution is the development of an algorithm for estimating the multi-scale tortuosity of the boundaries of the tessellation cells. The algorithm computes the tortuosity of the boundary at several scales by iteratively deforming the boundary until it becomes a straight line. Using this algorithm, we demonstrate that depending on the local velocity model, it is possible to control the roughness amplitude of the cells boundaries.
{"title":"EIKONAL-BASED MODELS OF RANDOM TESSELLATIONS","authors":"B. Figliuzzi","doi":"10.5566/IAS.2061","DOIUrl":"https://doi.org/10.5566/IAS.2061","url":null,"abstract":"In this article, we propose a novel, efficient method for computing a random tessellation from its vectorial representation at each voxel of a discretized domain. This method is based upon the resolution of the Eikonal equation and has a complexity in O(N log N), N being the number of voxels used to discretize the domain. By contrast, evaluating the implicit functions of the vectorial representation at each voxel location has a complexity of O(N²) in the general case. The method also enables us to consider the generation of tessellations with rough interfaces between cells by simulating the growth of the germs on a domain where the velocity varies locally. This aspect constitutes the main contribution of the article. A final contribution is the development of an algorithm for estimating the multi-scale tortuosity of the boundaries of the tessellation cells. The algorithm computes the tortuosity of the boundary at several scales by iteratively deforming the boundary until it becomes a straight line. Using this algorithm, we demonstrate that depending on the local velocity model, it is possible to control the roughness amplitude of the cells boundaries.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"4 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75586953","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}
Approaches for analyzing digital images of moving and burning fuel droplets, with the goal of accurately measuring droplet edge coordinates, are discussed. Strategies for locating droplet edges in the presence of obscuration from soot and also backlight diffraction at the droplet edge are described. An outlier detection method is employed to identify outliers in droplet edge coordinates, and the resulting data can have significantly smaller standard deviations in droplet diameters if outliers are rejected, especially for droplets that exhibit significant soot formation. The approaches described herein are applied to images from droplet combustion experiments performed on the International Space Station as well as to synthetic image sequences that were generated to enable the accuracy of the algorithms to be assessed.
{"title":"DIGITAL IMAGE ANALYSIS OF BURNING DROPLETS IN THE PRESENCE OF BACKLIGHT DIFFRACTION AND SOOT","authors":"Ramya Bhaskar, B. Shaw","doi":"10.5566/IAS.2015","DOIUrl":"https://doi.org/10.5566/IAS.2015","url":null,"abstract":"Approaches for analyzing digital images of moving and burning fuel droplets, with the goal of accurately measuring droplet edge coordinates, are discussed. Strategies for locating droplet edges in the presence of obscuration from soot and also backlight diffraction at the droplet edge are described. An outlier detection method is employed to identify outliers in droplet edge coordinates, and the resulting data can have significantly smaller standard deviations in droplet diameters if outliers are rejected, especially for droplets that exhibit significant soot formation. The approaches described herein are applied to images from droplet combustion experiments performed on the International Space Station as well as to synthetic image sequences that were generated to enable the accuracy of the algorithms to be assessed.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"100 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85862884","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}
Etienne Decencière, Amira Belhedi, S. Koudoro, F. Flament, Ghislain François, Virginie Rubert, Isabelle Pecile, Julien Pierre
Wrinkles or creases are common structures on surfaces. Their detection is often challenging, and can be an important step for many different applications. For instance, skin wrinkle segmentation is a crucial step for quantifying changes in skin wrinkling and assessing the beneficial effects of dermatological and cosmetic anti-ageing treatments. A 2.5D approach is proposed in this paper to segment individual wrinkles on facial skin surface described by 3D point clouds. The method, based on mathematical morphology, only needs a few physical parameters as input, namely the maximum wrinkle width, the minimum wrinkle length, and the minimum wrinkle depth. It has been applied to data acquired from eye wrinkles using a fringe projection system. An accurate evaluation was made possible thanks to manual annotations provided by three different experts. Results demonstrate the accuracy of this novel method.
{"title":"A 2.5D APPROACH TO SKIN WRINKLES SEGMENTATION","authors":"Etienne Decencière, Amira Belhedi, S. Koudoro, F. Flament, Ghislain François, Virginie Rubert, Isabelle Pecile, Julien Pierre","doi":"10.5566/IAS.1925","DOIUrl":"https://doi.org/10.5566/IAS.1925","url":null,"abstract":"Wrinkles or creases are common structures on surfaces. Their detection is often challenging, and can be an important step for many different applications. For instance, skin wrinkle segmentation is a crucial step for quantifying changes in skin wrinkling and assessing the beneficial effects of dermatological and cosmetic anti-ageing treatments. A 2.5D approach is proposed in this paper to segment individual wrinkles on facial skin surface described by 3D point clouds. The method, based on mathematical morphology, only needs a few physical parameters as input, namely the maximum wrinkle width, the minimum wrinkle length, and the minimum wrinkle depth. It has been applied to data acquired from eye wrinkles using a fringe projection system. An accurate evaluation was made possible thanks to manual annotations provided by three different experts. Results demonstrate the accuracy of this novel method.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"4 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80091424","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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