Marisol Mares-Javier, C. Guillén-Galván, R. Lemuz-López, J. Debayle
Mathematical Morphology (MM) is a tool that can be applied to many digital image processing tasks that include the reduction of impulsive or salt and pepper noise in grayscale images. The morphological filters used for this task are filters resulting from two basic operators: erosion and dilation. However, when the level of contamination of the image is higher, these filters tend to distort the image. In this work we propose a pair of operators with properties, that better adapt to impulsive noise than other classical morphological filters, it is demonstrated to be increasing idempotent morphological filters. Furthermore, the proposed pair turns out to be a Ʌ-filter and a V-filter which allow to build morphological openings and closings. Finally, they are compared with other filters of the state-of-the-art such as: SMF, PMSF, DBAIN, AMF and NAFSM, and have shown a better performance when the noise level is above 50%.
{"title":"On the Properties of Some Adaptive Morphological Filters for Salt and Pepper Noise Removal","authors":"Marisol Mares-Javier, C. Guillén-Galván, R. Lemuz-López, J. Debayle","doi":"10.5566/IAS.2418","DOIUrl":"https://doi.org/10.5566/IAS.2418","url":null,"abstract":"Mathematical Morphology (MM) is a tool that can be applied to many digital image processing tasks that include the reduction of impulsive or salt and pepper noise in grayscale images. The morphological filters used for this task are filters resulting from two basic operators: erosion and dilation. However, when the level of contamination of the image is higher, these filters tend to distort the image. In this work we propose a pair of operators with properties, that better adapt to impulsive noise than other classical morphological filters, it is demonstrated to be increasing idempotent morphological filters. Furthermore, the proposed pair turns out to be a Ʌ-filter and a V-filter which allow to build morphological openings and closings. Finally, they are compared with other filters of the state-of-the-art such as: SMF, PMSF, DBAIN, AMF and NAFSM, and have shown a better performance when the noise level is above 50%.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"33 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82853513","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}
M. Capek, M. Blažíková, Ivan Novotny, H. Chmelova, D. Svoboda, B. Radochová, J. Janáček, Ondrej Horvath
Filtration of super-resolved microscopic images brings often troubles with removing undesired image parts like, e.g., noise, inhomogenous background and reconstruction artifacts. Standard filtration techniques, e.g., convolution- or Fourier transform-based methods are not always appropriate, since they may lower image resolution that was acquired by hi-tech and expensive microscopy systems. Thus, in this article it is proposed to filter such images using discrete wavelet transform (DWT). Newly developed Wavelet_Denoise plugin for free available Fiji software package demonstrates important possibilities of applying DWT to images: Decomposition of a filtered picture using various wavelet filters and levels of details with showing decomposed images and visualization of effects of back transformation of the picture with chosen level of suppression or denoising of wavelet coefficients. The Fiji framework allows, for example, using a plethora of various microscopic image formats for data opening, users can easily install the plugin through a menu command and the plugin supports processing 3D images in Z-stacks. The application of the plugin for removal of reconstruction artifacts and undesirable background in images acquired by super-resolved structured illumination microscopy is demonstrated as well.
{"title":"The Wavelet-Based Denoising Of Images in Fiji, With Example Applications in Structured Illumination Microscopy","authors":"M. Capek, M. Blažíková, Ivan Novotny, H. Chmelova, D. Svoboda, B. Radochová, J. Janáček, Ondrej Horvath","doi":"10.5566/IAS.2432","DOIUrl":"https://doi.org/10.5566/IAS.2432","url":null,"abstract":"Filtration of super-resolved microscopic images brings often troubles with removing undesired image parts like, e.g., noise, inhomogenous background and reconstruction artifacts. Standard filtration techniques, e.g., convolution- or Fourier transform-based methods are not always appropriate, since they may lower image resolution that was acquired by hi-tech and expensive microscopy systems. Thus, in this article it is proposed to filter such images using discrete wavelet transform (DWT). Newly developed Wavelet_Denoise plugin for free available Fiji software package demonstrates important possibilities of applying DWT to images: Decomposition of a filtered picture using various wavelet filters and levels of details with showing decomposed images and visualization of effects of back transformation of the picture with chosen level of suppression or denoising of wavelet coefficients. The Fiji framework allows, for example, using a plethora of various microscopic image formats for data opening, users can easily install the plugin through a menu command and the plugin supports processing 3D images in Z-stacks. The application of the plugin for removal of reconstruction artifacts and undesirable background in images acquired by super-resolved structured illumination microscopy is demonstrated as well.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"38 1","pages":"3-16"},"PeriodicalIF":0.9,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90277044","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 paper, we propose a new image decolorization method based on image clustering and weight optimization. First, we smooth the color image and cluster it into several classes and get the class centers. Each center can represent a distinctive color in the image. Then the class centers are sorted according to their brightness measured by Euclidean norm. By assuming that the decolorized grayscale image is a linear combination of the three channels of the color image, we propose an optimization problem by forcing the sorted class centers to correspond to specified grayscale values satisfying uniform distribution. Numerically, the problem is solved by quadratic programming. Experiments on two popular data sets demonstrate that the proposed method is competitive with the state-of-the-art decolorization method.
{"title":"Smoothing and Clustering Guided Image Decolorization","authors":"Fang Li, Yuanming Zhu","doi":"10.5566/IAS.2348","DOIUrl":"https://doi.org/10.5566/IAS.2348","url":null,"abstract":"In this paper, we propose a new image decolorization method based on image clustering and weight optimization. First, we smooth the color image and cluster it into several classes and get the class centers. Each center can represent a distinctive color in the image. Then the class centers are sorted according to their brightness measured by Euclidean norm. By assuming that the decolorized grayscale image is a linear combination of the three channels of the color image, we propose an optimization problem by forcing the sorted class centers to correspond to specified grayscale values satisfying uniform distribution. Numerically, the problem is solved by quadratic programming. Experiments on two popular data sets demonstrate that the proposed method is competitive with the state-of-the-art decolorization method.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"49 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82320643","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 have lost one of the greatest founders of modern stereology: Hans Jorgen Gottlieb Gundersen.
我们失去了现代立体学最伟大的奠基人之一:汉斯·约根·戈特利布·冈德森。
{"title":"Obituary for Hans Jørgen Gottlieb Gundersen","authors":"J. Nyengaard","doi":"10.5566/IAS.2540","DOIUrl":"https://doi.org/10.5566/IAS.2540","url":null,"abstract":"We have lost one of the greatest founders of modern stereology: Hans Jorgen Gottlieb Gundersen.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"48 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80605800","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}
Segregation is one of the quality standards that must be monitored during the fabrication and placement of Portland cement concrete. Segregation refers to separation of coarse aggregate from the cement paste, resulting in inhomogeneous mixture. This study introduces a digital imaging based technique to quantify the segregation of Portland cement concrete from 2D digital images of cut sections. In the previous studies, segregation was evaluated based on the existence of coarse aggregate fraction at different geometrical regions of a sample cross section without considering its distribution characteristics. However, it is shown that almost all particle fractions can form clusters and increase the degree of segregation, thus deteriorating the structural performance of concrete. In the proposed methodology, a segregation index is developed by based on the spatial distribution of different size fractions of coarse aggregate within a sample cross section. It is shown that degradation in mixture’s homogeneity is controlled by the combined effect of particle distribution and their relative proportions in the mixture. Hence, a segregation index characterizing the mixture inhomogeneity is developed by considering not only spatial distribution of aggregate particles, but also their size fractions in the mixture. The proposed methodology can be successfully used as a quality control tool for monitoring the segregation level in hardened concrete samples.
{"title":"Quantification of Segregation in Portland Cement Concrete Based on Spatial Distribution of Aggregate Size Fractions","authors":"M. Ozen, M. Guler","doi":"10.5566/ias.2318","DOIUrl":"https://doi.org/10.5566/ias.2318","url":null,"abstract":"Segregation is one of the quality standards that must be monitored during the fabrication and placement of Portland cement concrete. Segregation refers to separation of coarse aggregate from the cement paste, resulting in inhomogeneous mixture. This study introduces a digital imaging based technique to quantify the segregation of Portland cement concrete from 2D digital images of cut sections. In the previous studies, segregation was evaluated based on the existence of coarse aggregate fraction at different geometrical regions of a sample cross section without considering its distribution characteristics. However, it is shown that almost all particle fractions can form clusters and increase the degree of segregation, thus deteriorating the structural performance of concrete. In the proposed methodology, a segregation index is developed by based on the spatial distribution of different size fractions of coarse aggregate within a sample cross section. It is shown that degradation in mixture’s homogeneity is controlled by the combined effect of particle distribution and their relative proportions in the mixture. Hence, a segregation index characterizing the mixture inhomogeneity is developed by considering not only spatial distribution of aggregate particles, but also their size fractions in the mixture. The proposed methodology can be successfully used as a quality control tool for monitoring the segregation level in hardened concrete samples.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"175 1","pages":"147-159"},"PeriodicalIF":0.9,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79762782","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}
Deep learning techniques such as Deep Convolutional Networks have achieved great success in skin lesion segmentation towards melanoma detection. The performance is however restrained by distinctive and challenging features of skin lesions such as irregular and fuzzy border, noise and artefacts presence and low contrast between lesions. The methods are also restricted with scarcity of annotated lesion images training dataset and limited computing resources. Recent research in convolutional neural network (CNN) has provided a variety of new architectures for deep learning. One interesting new architecture is the local binary convolutional neural network (LBCNN), which can reduce the workload of CNNs and improve the classification accuracy. The proposed framework employs the local binary convolution on U-net architecture instead of the standard convolution in order to reduced-size deep convolutional encoder-decoder network that adopts loss function for robust segmentation. The proposed framework replaced the encoder part in U-net by LBCNN layers. The approach automatically learns and segments complex features of skin lesion images. The encoder stage learns the contextual information by extracting discriminative features while the decoder stage captures the lesion boundaries of the skin images. This addresses the issues with encoder-decoder network producing coarse segmented output with challenging skin lesions appearances such as low contrast between healthy and unhealthy tissues and fine grained variability. It also addresses issues with multi-size, multi-scale and multi-resolution skin lesion images. The deep convolutional network also adopts a reduced-size network with just five levels of encoding-decoding network. This reduces greatly the consumption of computational processing resources. The system was evaluated on publicly available dataset of ISIC and PH2. The proposed system outperforms most of the existing state-of-art.
{"title":"Skin Lesion Segmentation Using Local Binary Convolution-Deconvolution Architecture","authors":"Omran Salih, Serestina Viriri","doi":"10.5566/ias.2397","DOIUrl":"https://doi.org/10.5566/ias.2397","url":null,"abstract":"Deep learning techniques such as Deep Convolutional Networks have achieved great success in skin lesion segmentation towards melanoma detection. The performance is however restrained by distinctive and challenging features of skin lesions such as irregular and fuzzy border, noise and artefacts presence and low contrast between lesions. The methods are also restricted with scarcity of annotated lesion images training dataset and limited computing resources. Recent research in convolutional neural network (CNN) has provided a variety of new architectures for deep learning. One interesting new architecture is the local binary convolutional neural network (LBCNN), which can reduce the workload of CNNs and improve the classification accuracy. The proposed framework employs the local binary convolution on U-net architecture instead of the standard convolution in order to reduced-size deep convolutional encoder-decoder network that adopts loss function for robust segmentation. The proposed framework replaced the encoder part in U-net by LBCNN layers. The approach automatically learns and segments complex features of skin lesion images. The encoder stage learns the contextual information by extracting discriminative features while the decoder stage captures the lesion boundaries of the skin images. This addresses the issues with encoder-decoder network producing coarse segmented output with challenging skin lesions appearances such as low contrast between healthy and unhealthy tissues and fine grained variability. It also addresses issues with multi-size, multi-scale and multi-resolution skin lesion images. The deep convolutional network also adopts a reduced-size network with just five levels of encoding-decoding network. This reduces greatly the consumption of computational processing resources. The system was evaluated on publicly available dataset of ISIC and PH2. The proposed system outperforms most of the existing state-of-art.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"136 1","pages":"169-185"},"PeriodicalIF":0.9,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77449758","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}
Francisco José Fumero Batista, T. Díaz-Alemán, J. Sigut, S. Alayón, R. Arnay, D. Ángel-Pereira
The first version of the Retinal IMage database for Optic Nerve Evaluation (RIM-ONE) was published in 2011. This was followed by two more, turning it into one of the most cited public retinography databases for evaluating glaucoma. Although it was initially intended to be a database with reference images for segmenting the optic disc, in recent years we have observed that its use has been more oriented toward training and testing deep learning models. The recent REFUGE challenge laid out some criteria that a set of images of these characteristics must satisfy to be used as a standard reference for validating deep learning methods that rely on the use of these data. This, combined with the certain confusion and even improper use observed in some cases of the three versions published, led us to consider revising and combining them into a new, publicly available version called RIM-ONE DL (RIM-ONE for Deep Learning). This paper describes this set of images, consisting of 313 retinographies from normal subjects and 172 retinographies from patients with glaucoma. All of these images have been assessed by two experts and include a manual segmentation of the disc and cup. It also describes an evaluation benchmark with different models of well-known convolutional neural networks.
第一版视神经评估视网膜图像数据库(RIM-ONE)于2011年发布。随后又进行了两项研究，使其成为评估青光眼的最常被引用的公共视网膜造影数据库之一。虽然它最初的目的是作为视盘分割参考图像的数据库，但近年来我们观察到它的使用更倾向于训练和测试深度学习模型。最近的REFUGE挑战提出了一些标准，这些特征的一组图像必须满足这些标准，才能作为验证依赖于这些数据使用的深度学习方法的标准参考。这一点，再加上在某些情况下观察到的三个版本的某些混淆甚至不当使用，导致我们考虑修改并将它们合并成一个新的，公开可用的版本，称为RIM-ONE DL (RIM-ONE for Deep Learning)。本文描述了这组图像，包括313张正常受试者的视网膜造影和172张青光眼患者的视网膜造影。所有这些图像都经过了两位专家的评估，包括对椎间盘和椎间盘杯的人工分割。描述了一种基于不同模型的卷积神经网络评估基准。
{"title":"RIM-ONE DL: A Unified Retinal Image Database for Assessing Glaucoma Using Deep Learning","authors":"Francisco José Fumero Batista, T. Díaz-Alemán, J. Sigut, S. Alayón, R. Arnay, D. Ángel-Pereira","doi":"10.5566/ias.2346","DOIUrl":"https://doi.org/10.5566/ias.2346","url":null,"abstract":"The first version of the Retinal IMage database for Optic Nerve Evaluation (RIM-ONE) was published in 2011. This was followed by two more, turning it into one of the most cited public retinography databases for evaluating glaucoma. Although it was initially intended to be a database with reference images for segmenting the optic disc, in recent years we have observed that its use has been more oriented toward training and testing deep learning models. The recent REFUGE challenge laid out some criteria that a set of images of these characteristics must satisfy to be used as a standard reference for validating deep learning methods that rely on the use of these data. This, combined with the certain confusion and even improper use observed in some cases of the three versions published, led us to consider revising and combining them into a new, publicly available version called RIM-ONE DL (RIM-ONE for Deep Learning). This paper describes this set of images, consisting of 313 retinographies from normal subjects and 172 retinographies from patients with glaucoma. All of these images have been assessed by two experts and include a manual segmentation of the disc and cup. It also describes an evaluation benchmark with different models of well-known convolutional neural networks.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"81 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83870078","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}
Intersection formulae of Croton type for general geometric probes are well known in integral geometry. For the special case of cylinders with non necessarily convex direktrix, however, no equivalent formula seems to exist in the literature. We derive such formula resorting to motion invariant probability elements associated with test systems, instead of using a traditional approach. Because cylinders are seldom used as probes in stereological practice, however, this note is mainly of a theoretical nature.
{"title":"Stereology with cylinder probes","authors":"L. Cruz-Orive, X. Gual-Arnau","doi":"10.5566/ias.2433","DOIUrl":"https://doi.org/10.5566/ias.2433","url":null,"abstract":"Intersection formulae of Croton type for general geometric probes are well known in integral geometry. For the special case of cylinders with non necessarily convex direktrix, however, no equivalent formula seems to exist in the literature. We derive such formula resorting to motion invariant probability elements associated with test systems, instead of using a traditional approach. Because cylinders are seldom used as probes in stereological practice, however, this note is mainly of a theoretical nature.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"12 1","pages":"213-218"},"PeriodicalIF":0.9,"publicationDate":"2020-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90704086","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}
J. Schreier, O. Furat, M. Cankaya, V. Schmidt, U. Bröckel
This study aims to an automated evaluation of contact angles in a three-phase system of selective agglomeration in liquids. Wetting properties, quantified by contact angles, are essential in many industries and their processes. Selective agglomeration as a three-phase system consists of a suspension liquid, a heterogeneous solid phase and an immiscible binding liquid. It offers the chance of establishing more efficient separation processes because of the shape-dependent wetting properties of fine particles (size ≤ 10 µm). In the present paper, an experimental setup for contact angle measurements of fine particles based on the Sessile Drop Method is described. Moreover, a new algorithm is discussed, which can be used to automatically compute contact angles from image data captured by a high-speed camera. The algorithm uses a marker-based watershed transform to segment the image data into regions representing the droplet, the carrier plate coated by fine particles, and the background. The main idea is a parametric modelling approach for the time-dependent droplet’s contour by an ellipse. The results show that the development of the dynamic contact angles towards a static contact angle can be efficiently determined based on this novel technique. These findings are useful for a detailed discrimination of wetting properties of spherical and irregularly shaped particles as well as their wetting kinetics. Also, a better understanding of selective agglomeration processes will be promoted by this user-friendly method.
{"title":"Automated Evaluation of Contact Angles in a Three-Phase System of Selective Agglomeration in Liquids","authors":"J. Schreier, O. Furat, M. Cankaya, V. Schmidt, U. Bröckel","doi":"10.5566/IAS.2403","DOIUrl":"https://doi.org/10.5566/IAS.2403","url":null,"abstract":"This study aims to an automated evaluation of contact angles in a three-phase system of selective agglomeration in liquids. Wetting properties, quantified by contact angles, are essential in many industries and their processes. Selective agglomeration as a three-phase system consists of a suspension liquid, a heterogeneous solid phase and an immiscible binding liquid. It offers the chance of establishing more efficient separation processes because of the shape-dependent wetting properties of fine particles (size ≤ 10 µm). In the present paper, an experimental setup for contact angle measurements of fine particles based on the Sessile Drop Method is described. Moreover, a new algorithm is discussed, which can be used to automatically compute contact angles from image data captured by a high-speed camera. The algorithm uses a marker-based watershed transform to segment the image data into regions representing the droplet, the carrier plate coated by fine particles, and the background. The main idea is a parametric modelling approach for the time-dependent droplet’s contour by an ellipse. The results show that the development of the dynamic contact angles towards a static contact angle can be efficiently determined based on this novel technique. These findings are useful for a detailed discrimination of wetting properties of spherical and irregularly shaped particles as well as their wetting kinetics. Also, a better understanding of selective agglomeration processes will be promoted by this user-friendly method.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85649000","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}
Motivated by the stereological problem of volume estimation from parallel section profiles, the so-called Newton-Cotes integral estimators based on random sampling nodes are analyzed. These estimators generalize the classical Cavalieri estimator and its variant for non-equidistant sampling nodes, the generalized Cavalieri estimator, and have typically a substantially smaller variance than the latter. The present paper focuses on the following points in relation to Newton-Cotes estimators: the treatment of dropouts, the construction of variance estimators, and, finally, their application in volume estimation of convex bodies. Dropouts are eliminated points in the initial stationary point process of sampling nodes, modeled by independent thinning. Among other things, exact representations of the variance are given in terms of the thinning probability and increments of the initial points under two practically relevant sampling models. The paper presents a general estimation procedure for the variance of Newton-Cotes estimators based on the sampling nodes in a bounded interval. Finally, the findings are illustrated in an application of volume estimation for three-dimensional convex bodies with sufficiently smooth boundaries.
{"title":"Improving the Cavalieri estimator under non-equidistant sampling and dropouts","authors":"Mads Stehr, M. Kiderlen","doi":"10.5566/IAS.2422","DOIUrl":"https://doi.org/10.5566/IAS.2422","url":null,"abstract":"Motivated by the stereological problem of volume estimation from parallel section profiles, the so-called Newton-Cotes integral estimators based on random sampling nodes are analyzed. These estimators generalize the classical Cavalieri estimator and its variant for non-equidistant sampling nodes, the generalized Cavalieri estimator, and have typically a substantially smaller variance than the latter. The present paper focuses on the following points in relation to Newton-Cotes estimators: the treatment of dropouts, the construction of variance estimators, and, finally, their application in volume estimation of convex bodies. Dropouts are eliminated points in the initial stationary point process of sampling nodes, modeled by independent thinning. Among other things, exact representations of the variance are given in terms of the thinning probability and increments of the initial points under two practically relevant sampling models. The paper presents a general estimation procedure for the variance of Newton-Cotes estimators based on the sampling nodes in a bounded interval. Finally, the findings are illustrated in an application of volume estimation for three-dimensional convex bodies with sufficiently smooth boundaries.","PeriodicalId":49062,"journal":{"name":"Image Analysis & Stereology","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88283314","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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