Early History of Geometric Probability and Stereology

Hykšová, Magdalena; Kalousová, Anna; Saxl, Ivan

doi:10.5566/ias.v31.p1-16

Cited by 16 publications

(13 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…1 is useful to estimate curve length, but sampling and estimation were established only in the 20th century. As detailed by Hykšová et al (2012), it is noteworthy that Joseph-Émile Barbier (1839Barbier ( -1889 anticipated results like Eq. 1, its three dimensional (3D) version for surface area, and other important ideas (Barbier, 1860).…”

Section: Crofton Formulaementioning

confidence: 99%

“…As pointed out by Hykšová et al (2012), however, toward 1664-1666Isaac Newton (1643-1727 apparently formulated the principle that a 'random' point hitting a domain of area A > 0 will hit a subdomain of area a ≤ A with a probability equal to a/A. This may not be surprising inasmuch as probability was developing at Newton's time, notably with Blaise Pascal , and with the early members of the Bernoulli family.…”

Section: Geometrical Probability and Integral Geometry The Birth Of Gmentioning

confidence: 99%

See 1 more Smart Citation

Stereology: A Historical Survey

Cruz‐Orive

2017

Image Anal Stereol

View full text Add to dashboard Cite

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.

show abstract

Section: Crofton Formulaementioning

confidence: 99%

Section: Geometrical Probability and Integral Geometry The Birth Of Gmentioning

confidence: 99%

Stereology: A Historical Survey

Cruz‐Orive

2017

Image Anal Stereol

View full text Add to dashboard Cite

show abstract

“…His proof procedure involves decomposing the curve into infinitesimal portions and proving the result for each portion. This article is considered by specialists in geometric probability to be a foundational text in that field; see e.g., [Hykšová et al 2012]. 6 Thus Schubring's claim (3) to the effect that Cauchy's infinitesimals appear only in textbooks is not merely inaccurate, revealing an incomplete knowledge of the original documents on his part, but more importantly it obscures the fundamental role of infinitesimals in Cauchy's thinking.…”

Section: Schubring Vs Laugwitzmentioning

confidence: 99%

Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts

Błaszczyk

Kanovei²,

Katz

et al. 2015

Found Sci

View full text Add to dashboard Cite

Abstract. Foundations of Science recently published a rebuttal to a portion of our essay it published two years ago. The author, G. Schubring, argues that our 2013 text treated unfairly his 2005 book, Conflicts between generalization, rigor, and intuition. He further argues that our attempt to show that Cauchy is part of a long infinitesimalist tradition confuses text with context and thereby misunderstands the significance of Cauchy's use of infinitesimals. Here we defend our original analysis of various misconceptions and misinterpretations concerning the history of infinitesimals and, in particular, the role of infinitesimals in Cauchy's mathematics. We show that Schubring misinterprets Proclus, Leibniz, and Klein on non-Archimedean issues, ignores the Jesuit context of Moigno's flawed critique of infinitesimals, and misrepresents, to the point of caricature, the pioneering Cauchy scholarship of D. Laugwitz.

show abstract

“…Along each test line the number of intersections between the line and each grain boundary is counted, identifying the type of boundary intercepted as a phase-to-phase contact or a phaseto-background contact (Pérez-Barnuevo et al, 2012). These counts are used by stereology to compute perimeters (Hyksova et al, 2012), and overall are used to compute the well-known stereological parameter Sv or surface area per unit volume (Underwood, 1970). The computation of perimeters is especially useful to estimate the exposed perimeter proportion of the MOl in each particle ( Fig.…”

Section: Textural Descríptors Methodologymentioning

confidence: 99%

Automated characterisation of intergrowth textures in mineral particles. A case study

Pérez-Barnuevo

Pirard

Castroviejo

2013

Minerals Engineering

View full text Add to dashboard Cite

The characterisation of mineral texture has been a major concern for process mineralogists, as liberation characteristics of the ores are intimately related to the mineralogical texture. While a great effort has been done to automatically characterise texture in unbroken ores, the characterisation of textural attributes in mineral particles is usually descriptive. However, the quantitative characterisation of texture in mineral particles is essential to improve and predict the performance of minerallurgical processes (Le. all the processes involved in the liberation and separation of the mineral of interest) and to achieve a more accurate geometallurgical model.Driven by this necessity of achieving a more complete characterisation oftextural attributes in mineral particles, a methodology has been recently developed to automatically characterise the type of intergrowth between mineral phases within particles by means of digital image analysis. In this methodology, a set of minerallurgical indices has been developed to quanti(y different mineralogical features and to identi(y the intergrowth pattern by discriminant analysis. The paper shows the application ofthe methodology to the textural characterisation of chalcopyrite in the rougher concentrate ofthe Kansanshi copper mine (Zambia). In this sample, the variety of intergrowth patterns of chalcopyrite with the other minerals has been used to illustrate the methodology. The results obtained show that the method identifies the intergrowth type and provides quantitative information to achieve a complete and detailed mineralogical characterisation. Therefore, the use of this methodology as a routinely tool in automated mineralogy would contribute to a better understanding of the ore behaviour during liberation and separation processes.

show abstract

Early History of Geometric Probability and Stereology

Cited by 16 publications

References 46 publications

Stereology: A Historical Survey

Stereology: A Historical Survey

Controversies in the Foundations of Analysis: Comments on Schubring’s Conflicts

Automated characterisation of intergrowth textures in mineral particles. A case study

Contact Info

Product

Resources

About