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  • 1
    In: Journal of Microscopy, January 1999, Vol.193(1), pp.89-90
    Keywords: Biology;
    ISSN: 0022-2720
    E-ISSN: 1365-2818
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  • 2
    Language: English
    In: Image Analysis and Stereology, 01 March 2013, Vol.32(1), pp.45-55
    Description: A new method is presented for estimating the specific fiber length from 3D images of macroscopically homogeneous fiber systems. The method is based on a discrete version of the Crofton formula, where local knowledge from 3x3x3-pixel configurations of the image data is exploited. It is shown that the relative error resulting from the discretization of the outer integral of the Crofton formula amonts at most 1.2%. An algorithmic implementation of the method is simple and the runtime as well as the amount of memory space are low. The estimation is significantly improved by considering 3x3x3-pixel configurations instead of 2x2x2, as already studied in literature.〈br /〉〈br /〉
    Keywords: Image Analysis ; Integral of Mean Curvature ; Crofton Formula ; Systematic Error ; Engineering
    ISSN: 1580-3139
    E-ISSN: 1854-5165
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  • 3
    Language: English
    In: Imaging & Microscopy, August 2007, Vol.9(3), pp.20-20
    Description: The 14 workshop “Quantitative Image Analysis” has been held at the University of Applied Sciences in Darmstadt on 15 June 2007. Image Analysis works on complex images as 3D‐images, massive mosaics and video sequences.
    ISSN: 1439-4243
    ISSN: Imaging & Microscopy
    E-ISSN: 1863-7809
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  • 4
    Language: English
    In: Advances in Applied Probability, 06/1998, Vol.30(2), pp.289-290
    ISSN: 0001-8678
    E-ISSN: 1475-6064
    Source: CrossRef
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  • 5
    Language: English
    In: Advances in Applied Probability, 1 June 1998, Vol.30(2), pp.289-290
    Keywords: Mathematics -- Applied mathematics -- Statistics ; Information science -- Information management -- Data management ; Mathematics -- Applied mathematics -- Statistics ; Mathematics -- Mathematical expressions -- Mathematical functions ; Mathematics -- Applied mathematics -- Statistics
    ISSN: 00018678
    E-ISSN: 14756064
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  • 6
    Language: English
    In: Physica A: Statistical Mechanics and its Applications, 1996, Vol.233(1), pp.1-18
    Description: The fractal dimension of a set in the Euclidean n -space may depend on the applied concept of fractal dimension. Several concepts are considered here, and in a first part, properties are given for sets such that they have the same fractal dimension for all concepts. In particular, self-similar sets hold these properties. The second part deals with the measurement of fractal dimension. An often-used method to empirically compute the fractal dimension of a set E is the box-counting method where the slope of a regression line gives the estimate of the fractal dimension. A new interpretation, which concentrates on the visible complexity of the set, uses counted boxes to define generators for adjacent self-similar sets. Their maximal fractal dimension is assigned to the set as a measurement of fractal dimension or of visible complexity. The results from the first part guarantee that all measurements are independent of the considered concepts. The construction suggests a new method, which is called extended box-counting method, to estimate fractal dimension or to measure complexity of an image in a given range of magnification. The method works without linear regression and has the advantage to nearly preserve the union stability (maximum property).
    Keywords: Box Counting Method ; Fractal Sets ; Hausdorff Dimension ; Metric Dimension ; Maximum Property ; Physics
    ISSN: 0378-4371
    E-ISSN: 1873-2119
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  • 7
    Language: English
    In: Biometrical Journal, 1993, Vol.35(6), pp.649-660
    Description: In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width is of interest. The fissures are mathematically generalized to flat bodies which form a stationary weighted surface process with the weight “thickness”. Because of stationarity a joint distribution of spatial direction and thickness exists in a “typical point” of the surface process. A suitable parametric family of distributions is assumed. The corresponding parameters can be estimated from measurements on the vertical sections. But on the sections only the visible thickness and the visible angle of a fissure can be measured. Therefore the joint distribution of these variables is expressed by the joint spatial distribution of spatial direction and thickness. This derived distribution depends on the same parameters. The Chi‐Square method is proposed for the parameter estimation. The estimation procedure is demonstrated using the Bingham‐Mardia distribution for the direction and the lognormal distribution for the thickness and by defining a way to correlate the mean thickness and the direction.
    Keywords: Weighted Surface Process ; Stereology ; Vertical Section ; Bingham‐Mardia Distribution ; Parameter Estimation
    ISSN: 0323-3847
    E-ISSN: 1521-4036
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  • 8
    Language: French
    In: Acta Stereologica, 01 February 1996, Vol.15, pp.83-90
    Description: The fractal dimension of sets is used in praxis e.g. as a roughness parameter for surfaces, as a texture parameter or for classifying the complexity of line structures. An essential property of fractal dimension is that the most complex-structured part of a set determines tl1e dimension, mathematically described by the maximum property. The most popular methods to measure fractal dimension are the divider stepping method, the sausage method and the box-counting method. Measurements with these methods depend on the range of magnification and on the way the (necessary) linear regression is done. All these methods do not fulfill the maximum property. A new method based on the box counting theorem is represented here, called extended counting method. It avoids the linear regression, is increasing and even has a quasi maximum property, i.e. the maximum property is fulfilled except of a correction term, which tends to zero if the range of magnification tends to infinity. Several examples are shown demonstrating the method and its properties.
    Keywords: Complexity ; Box Counting Method ; Fractal Dimension ; Maximum Property ; Self-Similar
    ISSN: 0351-580X
    Source: University of Liège Library (ULiège Library)
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  • 9
    Language: English
    In: Advances in Applied Probability, 06/1996, Vol.28(02), pp.341-342
    ISSN: 0001-8678
    E-ISSN: 1475-6064
    Source: CrossRef
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  • 10
    Language: English
    In: Advances in Applied Probability, 1 June 1996, Vol.28(2), pp.341-342
    Keywords: Mathematics -- Applied mathematics -- Statistics ; Mathematics -- Applied mathematics -- Statistics ; Mathematics -- Pure mathematics -- Geometry ; Mathematics -- Pure mathematics -- Geometry;
    ISSN: 00018678
    E-ISSN: 14756064
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