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Mathematical Morphology - Theory and Applications最新文献

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Mathematical Morphology on Irregularly Sampled Data in One Dimension 一维不规则采样数据的数学形态学
Mathematical Morphology - Theory and Applications Pub Date : 2017-12-20 DOI: 10.1515/mathm-2017-0001
Teo Asplund, C. L. Hendriks, M. Thurley, R. Strand
{"title":"Mathematical Morphology on Irregularly Sampled Data in One Dimension","authors":"Teo Asplund, C. L. Hendriks, M. Thurley, R. Strand","doi":"10.1515/mathm-2017-0001","DOIUrl":"https://doi.org/10.1515/mathm-2017-0001","url":null,"abstract":"Abstract Mathematical morphology (MM) on grayscale images is commonly performed in the discrete domain on regularly sampled data. However, if the intention is to characterize or quantify continuous-domain objects, then the discrete-domain morphology is affected by discretization errors that may be alleviated by considering the underlying continuous signal. Given a band-limited image, for example, a real image projected through a lens system, which has been correctly sampled, the continuous signal may be reconstructed. Using information from the continuous signal when applying morphology to the discrete samples can then aid in approximating the continuous morphology. Additionally, there are a number of applications where MM would be useful and the data is irregularly sampled. A common way to deal with this is to resample the data onto a regular grid. Often this creates problems where data is interpolated in areas with too few samples. In this paper, an alternative way of thinking about the morphological operators is presented. This leads to a new type of discrete operators that work on irregularly sampled data. These operators are shown to be morphological operators that are consistent with the regular, morphological operators under the same conditions, and yield accurate results under certain conditions where traditional morphology performs poorly.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122646451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Prior-based Hierarchical Segmentation Highlighting Structures of Interest 基于先验的分层分割突出感兴趣的结构
Mathematical Morphology - Theory and Applications Pub Date : 2017-03-09 DOI: 10.1515/mathm-2019-0002
Amin Fehri, S. Velasco-Forero, F. Meyer
{"title":"Prior-based Hierarchical Segmentation Highlighting Structures of Interest","authors":"Amin Fehri, S. Velasco-Forero, F. Meyer","doi":"10.1515/mathm-2019-0002","DOIUrl":"https://doi.org/10.1515/mathm-2019-0002","url":null,"abstract":"Abstract Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of structures of interest in the images. In this paper, we present a versatile hierarchical segmentation method that takes into account any prior spatial information and outputs a hierarchical segmentation that emphasizes the contours or regions of interest while preserving the important structures in the image. Several applications are presented that illustrate the method versatility and efficiency.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122036117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Efficient Computation of Greyscale Path Openings 灰度路径开口的高效计算
Mathematical Morphology - Theory and Applications Pub Date : 2016-05-05 DOI: 10.1515/mathm-2016-0010
Herman R. Schubert, J. V. D. Gronde, J. Roerdink
{"title":"Efficient Computation of Greyscale Path Openings","authors":"Herman R. Schubert, J. V. D. Gronde, J. Roerdink","doi":"10.1515/mathm-2016-0010","DOIUrl":"https://doi.org/10.1515/mathm-2016-0010","url":null,"abstract":"Abstract Path openings are morphological operators that are used to preserve long, thin, and curved structures in images. They have the ability to adapt to local image structures,which allows them to detect lines that are not perfectly straight. They are applicable in extracting cracks, roads, and similar structures. Although path openings are very efficient to implement for binary images, the greyscale case is more problematic. This study provides an analysis of the main existing greyscale algorithm, and shows that although its time complexity can be quadratic in the number of pixels, this is optimal in terms of the output (if the full opening transform is created). Also, it is shown that under many circumstances the worst-case running time is much less than quadratic. Finally, a new algorithm is provided,which has the same time complexity, but is simpler, faster in practice and more amenable to parallelization","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127959373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Cluster Based Vector Attribute Filtering 基于聚类的矢量属性过滤
Mathematical Morphology - Theory and Applications Pub Date : 2016-04-14 DOI: 10.1515/mathm-2016-0007
Fred N. Kiwanuka, M. Wilkinson
{"title":"Cluster Based Vector Attribute Filtering","authors":"Fred N. Kiwanuka, M. Wilkinson","doi":"10.1515/mathm-2016-0007","DOIUrl":"https://doi.org/10.1515/mathm-2016-0007","url":null,"abstract":"Abstract Morphological attribute filters operate on images based on properties or attributes of connected components. Until recently, attribute filtering was based on a single global threshold on a scalar property to remove or retain objects. A single threshold struggles in case no single property or attribute value has a suitable, usually multi-modal, distribution. Vector-attribute filtering allows better description of characteristic features for 2D images. In this paper, we apply vector-attribute filtering to 3D and incorporate unsupervised pattern recognition, where connected components are classified based on the similarity of feature vectors. Using a single attribute allows multi-thresholding for attribute filters where more than two classes of structures of interest can be selected. In vector-attribute filters automatic clustering avoids the need for either setting very many attribute thresholds, or finding suitable class prototypes in 3D and setting a dissimilarity threshold. Explorative visualization reduces to visualizing and selecting relevant clusters. We show that the performance of these new filters is better than those of regular attribute filters in enhancement of objects in medical images.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"28 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132193514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Statistical attribute filtering to detect faint extended astronomical sources 统计属性过滤，以检测微弱的扩展天文来源
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-30 DOI: 10.1515/mathm-2016-0006
P. Teeninga, U. Moschini, S. Trager, M. Wilkinson
{"title":"Statistical attribute filtering to detect faint extended astronomical sources","authors":"P. Teeninga, U. Moschini, S. Trager, M. Wilkinson","doi":"10.1515/mathm-2016-0006","DOIUrl":"https://doi.org/10.1515/mathm-2016-0006","url":null,"abstract":"Abstract In astronomy, sky surveys contain a large number of light-emitting sources, often with intensities close to the noise level. Automatic extraction of astronomical objects is therefore needed. SExtractor is a widely used program for automated source extraction and cataloguing, but it is not optimal with faint extended sources. Using SExtractor as a reference, the paper describes an improvement of a previous method proposed by the authors. It is a Max-Tree-based method for extraction of faint extended sources without using a stronger image smoothing. The Max-Tree structure is a hierarchical representation of an image, in which attributes can be computed in every node. Object detection is performed on the nodes of the tree and it relies on the distribution of a statistic calculated using the power attribute, compared to the expected distribution in case of noise. Statistical tests are presented, a comparison with the object extraction of SExtractor is shown and results are discussed.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123956030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Morphological probabilistic hierarchies for texture segmentation 纹理分割的形态学概率层次
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-30 DOI: 10.1515/mathm-2016-0012
D. Jeulin
{"title":"Morphological probabilistic hierarchies for texture segmentation","authors":"D. Jeulin","doi":"10.1515/mathm-2016-0012","DOIUrl":"https://doi.org/10.1515/mathm-2016-0012","url":null,"abstract":"Abstract A general methodology is introduced for texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations on images. Starting from a fine partition of the image in regions, hierarchical segmentations are designed in a probabilistic framework by means of probabilistic distances conveying the textural or morphological information, and of random markers accounting for the morphological content of the regions and of their spatial arrangement. The probabilistic hierarchies are built from binary or multiple fusion of regions.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129786158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Tracking sub-atomic particles through the Attribute Space 通过属性空间跟踪亚原子粒子
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-26 DOI: 10.1515/mathm-2016-0009
M. Babai, N. Kalantar-Nayestanaki, J. Messchendorp, M. Wilkinson
{"title":"Tracking sub-atomic particles through the Attribute Space","authors":"M. Babai, N. Kalantar-Nayestanaki, J. Messchendorp, M. Wilkinson","doi":"10.1515/mathm-2016-0009","DOIUrl":"https://doi.org/10.1515/mathm-2016-0009","url":null,"abstract":"Abstract In this paper, we present the results of an application of attribute space morphological filters for tracking sub-atomic particles in magnetic fields. For this purpose, we have applied the concept of attribute space and connectivity to the binary images produced by charged particles passing through the tracking detector for the future experiment PANDA. This detector could be considered as an undirected graph with irregular neighbourhood relations. For this project, we rely only on the detector geometry. In addition, we have extended the graph to estimate the z-coordinates of the particle paths. The result is an O(n2), proof of concept algorithm with a total error of approximately 0.17; this value depends on track multiplicity and particle type and its parameters. The results look promising; however, more work needs to be done to make this algorithm applicable for the real-life case.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128570776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Quantile Filtering of Colour Images via Symmetric Matrices 基于对称矩阵的彩色图像分位数滤波
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-19 DOI: 10.1515/mathm-2016-0008
M. Welk, A. Kleefeld, M. Breuß
{"title":"Quantile Filtering of Colour Images via Symmetric Matrices","authors":"M. Welk, A. Kleefeld, M. Breuß","doi":"10.1515/mathm-2016-0008","DOIUrl":"https://doi.org/10.1515/mathm-2016-0008","url":null,"abstract":"Abstract Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2 × 2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these.We consider variants of these filters based on three matrix norms – the nuclear, Frobenius, and spectral norm – and study their differences. We investigate the properties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba structuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are presented to demonstrate the favourable properties of the filters, and compare them to existing approaches in colour morphology.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129046499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
N-ary Mathematical Morphology n元数学形态学
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-18 DOI: 10.1515/mathm-2016-0003
Emmanuel Chevallier, Augustin Chevallier, J. Angulo
{"title":"N-ary Mathematical Morphology","authors":"Emmanuel Chevallier, Augustin Chevallier, J. Angulo","doi":"10.1515/mathm-2016-0003","DOIUrl":"https://doi.org/10.1515/mathm-2016-0003","url":null,"abstract":"Abstract Mathematical morphology on binary images can be fully described by set theory. However, it is not sufficient to formulate mathematical morphology for grey scale images. This type of images requires the introduction of the notion of partial order of grey levels, together with the definition of sup and inf operators. More generally, mathematical morphology is now described within the context of the lattice theory. For a few decades, attempts are made to use mathematical morphology on multivariate images, such as color images, mainly based on the notion of vector order. However, none of these attempts has given fully satisfying results. Instead of aiming directly at the multivariate case we propose first an extension of binary mathematical morphology to an intermediary situation: images composed of a finite number of independent unordered labels. We propose then an second extension to a continuous case.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131288709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations 定义和计算实线和圆上分布之间的豪斯多夫距离:最优输运和形态扩张之间的联系
Mathematical Morphology - Theory and Applications Pub Date : 2016-01-18 DOI: 10.1515/mathm-2016-0005
I. Bloch, J. Atif
{"title":"Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations","authors":"I. Bloch, J. Atif","doi":"10.1515/mathm-2016-0005","DOIUrl":"https://doi.org/10.1515/mathm-2016-0005","url":null,"abstract":"Abstract Comparing probability or possibility distributions is important in many fields of information processing under uncertainty. In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We propose several dilations of distributions, and exhibit some links between Lévy-Prokhorov distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology. As an illustration, the proposed approaches are applied to the comparison of spatial relations between objects in an image or a video sequence, when these relations are represented as distributions.","PeriodicalId":244328,"journal":{"name":"Mathematical Morphology - Theory and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134334752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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