Precision of systematic sampling and transitive methods

Kiêu, Kiên; Souchet, Sandie; Istas, Jacques

doi:10.1016/s0378-3758(98)00193-1

Cited by 65 publications

(73 citation statements)

References 6 publications

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“…17b was q = 0. Theory establishes that, under certain conditions, the trend or 'extension term' of the variance of a Cavalieri estimator is of order O(T 2q+2 ), (Kiêu et al, 1999;García-Fiñana and Cruz-Orive, 2004). In the present study the expected trend of CE 2 { B(ω, x)} should therefore be approximately of O(E(I) −(2q+2) ) = O(E(I) −2 ).…”

Section: Buffon-steinhaus Estimatormentioning

confidence: 55%

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On the Precision of Curve Length Estimation in the Plane

2016

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The estimator of planar curve length based on intersection counting with a square grid, called the BuffonSteinhaus estimator, is simple, design unbiased and efficient. However, the prediction of its error variance from a single grid superimposition is a non trivial problem. A previously published predictor is checked here by means of repeated Monte Carlo superimpositions of a curve onto a square grid, with isotropic uniform randomness relative to each other. Nine curvilinear features (namely flattened DNA molecule projections) were considered, and complete data are shown for two of them. Automatization required image processing to transform the original tiff image of each curve into a polygonal approximation consisting of between 180 and 416 straight line segments or 'links' for the different curves. The performance of the variance prediction formula proved to be satisfactory for practical use (at least for the curves studied).

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Section: Buffon-steinhaus Estimatormentioning

confidence: 55%

“…12b is the standard Cavalieri estimator of it. Moreover, because the measurement function I Y ω (z) is integer valued it will exhibit jumps, and therefore its smoothness constant will be q = 0 (Kiêu et al, 1999;García-Fiñana and Cruz-Orive, 2004). In consequence, the σ 2 i are computed with q = 0.…”

Section: Remarksmentioning

confidence: 99%

On the Precision of Curve Length Estimation in the Plane

2016

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“…In this work, the precision of the estimates of neuronal densities, nuclear volumes, and total neuron numbers from each sample was estimated as the coefficient of error (CE). Various error estimators of volume, neuronal densities, and total neuron numbers by Cavalieri's, fractionator, or disector methods have been reported in the literature (Gundersen and Jensen, 1987;Braendgaard et al, 1990;Cruz-Orive, 1990, 1999, 2004, 2006Guntinas-Lichius and Neiss, 1996;Gundersen et al, 1999;Kieu et al, 1999;GualArnau and Cruz-Orive, 2006). In this work, the CE for …”

Section: Methodsmentioning

confidence: 99%

Morphometric Analysis of Infant and Adult Medullary Nuclei Through Optical Disector Method

Porzionato

Macchi

Parenti

et al. 2009

The Anatomical Record

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In the literature, comprehensive and comparative morphometric studies of infant and adult medullary nuclei performed with unbiased methods are still lacking. In this study, the unbiased quantitative method of the optical disector was applied to analyze neuronal densities, nuclear volumes, and total neuron numbers of the hypoglossal nucleus (XII), dorsal motor nucleus of the vagus (DMNV), nucleus tractus solitarii (NTS), medial vestibular nucleus (MedVe), cuneate nucleus (Cu), nucleus of the spinal trigeminal tract, principal inferior olivary nucleus (PION), medial inferior olivary nucleus (MION), and dorsal inferior olivary nucleus (DION) in adults (16 male, six female; mean age: 37 years) and infants (five male, five female; mean age: 5 months). In both infants and adults, higher neuronal densities were found in the more ventrally located nuclei of the spinal trigeminal tract (mean values (coefficient of variation): 20,947 (0.29) and 8,990 (0.18) neurons/mm 3 , respectively) and inferior olivary complex (PION: 20,010 (0.15) and 9,076 (0.10); MION: 18,667 (0.20) and 9,989 (0.13); DION: 22,424 (0.17) and 10,986 (0.20), respectively) than in the nuclei of the medullary tegmentum, that is, XII (2,747 (0.39) and 1,026 (0.31)), DMNV (2,876 (0.19) and 1,553 (0.26)), NTS (7,993 (0.17) and 2,877 (0.13)), MedVe (7,010 (0.17) and 2,918 (0.12)), and Cu (2,563 (0.23) and 1,038 (0.16)). All the medullary nuclei showed higher volumes and lower neuronal densities in adults than in infants, without statistically significant differences in total neuron numbers, probably because of postnatal development of the neuropil and microvascularization. Anat Rec, 292:1619Rec, 292: -1629Rec, 292: , 2009. V V C 2009 Wiley-Liss, Inc.Key words: morphometry; optical disector; medulla oblongata; human; infantThe medulla oblongata is involved in many different and complex functions as it contains nuclei involved in cardiac and respiratory control, nervous centers providing sensory and motor innervation of peripheral structures, groups of neurons receiving inputs related to the special senses of hearing, vestibular function and taste, or providing/receiving efferent/afferent cerebellar projections. There have been a few studies in the literature detailing morphometric parameters, such as neuronal density, nuclear volume, and total neuron number, in the medullary nuclei considered in this study (e.g

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“…For a survey of G. Matheron's transitive theory see Cruz-Orive (1989b). Souchet (1995), Kiêu (1997) and Kiêu et al (1999) related the degree of Matheron's polynomial model with the shape (more precisely with the smoothness constant q ∈ [0, 1]) of the function A, and improved Gundersen and Jensen's estimator (which implied the value q = 0) with a numerical coefficient depending on q. On empirical grounds supplied by Neil Roberts, Cruz-Orive (1993) had considered the alternative q = 1 for fairly smooth measurement functions, but Kiên Kiêu's theory significantly contributed to better understand the problem.…”

Section: Error Variance Prediction Under Systematic Samplingmentioning

confidence: 99%

Stereology: A Historical Survey

Cruz‐Orive

2017

Image Anal Stereol

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Stereology is the science of geometric sampling, with applications to the statistical analysis of microstructures in biology and materials science. Subsidiary disciplines are image analysis, quantitative microscopy, and radiology. This survey is organized chronologically within a series of topics which cover most aspects of stereology. Each topic is described informally to make it accessible to scientists of different disciplines.

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Precision of systematic sampling and transitive methods

Abstract: To cite this version:Kiên Kiêu, Sandie Souchet, Jacques Istas. Precision of systematic sampling and transitive methods.

Cited by 65 publications

References 6 publications

On the Precision of Curve Length Estimation in the Plane

On the Precision of Curve Length Estimation in the Plane

Morphometric Analysis of Infant and Adult Medullary Nuclei Through Optical Disector Method

Stereology: A Historical Survey

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