Concepedia

Crofton Formula

The Crofton Formula is a fundamental result in integral geometry that expresses the length of a curve as an integral over the space of lines, weighted by the number of intersections between the curve and each line, thereby relating geometric measures to kinematic averages.

42

Publications

3.2K

Citations

47

Authors

36

Institutions

Publications per year

2017–2026

5

Variants

Crofton's Formula

Parents

Publications

42

Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces

David G. Kendall · Bulletin of the London Mathematical Society · 1984 · 1.5K citations

, , +13

Computing geodesics and minimal surfaces via graph cuts

Boykov, Kolmogorov · 2003 · 562 citations

, , +12

Crofton measures and Minkowski valuations

Franz E. Schuster · Duke Mathematical Journal · 2010 · 158 citations · Full text

, , +11

Crofton's function and inversion formulas in real integral geometry

I. M. Gel'fand · Functional Analysis and Its Applications · 1991 · 72 citations

, , +8

4 KINEMATIC FORMULAS FOR TENSOR VALUATIONS

Andreas Bernig, Daniel Hug · 2016 · 58 citations

, , +12

1–5 of 42

Authors

47

  1. RS
    Rolf Schneider

    University of Freiburg, Germany

    4 publications · 52 citations

    4

    h-index

  2. DH
    Daniel Hug

    University of Freiburg, Germany

    2 publications · 73 citations

    2

    h-index

  3. AB
    Andreas Bernig

    Goethe University Frankfurt, Germany

    2 publications · 103 citations

    2

    h-index

  4. GR
    Glen R. Hall

    Boston University, United States

    2 publications · 42 citations

    2

    h-index

  5. EF
    E. Fernandes

    Laboratoire Paul Painlevé, France

    2 publications · 80 citations

    2

    h-index

1–5 of 47

Institutions

36

  1. University of Freiburg

    Freiburg im Breisgau, Germany

    5 h-index

    5 publications

    80 citations

  2. Concordia University

    Montreal, Canada

    2 h-index

    2 publications

    80 citations

  3. Goethe University Frankfurt

    Frankfurt am Main, Germany

    2 h-index

    2 publications

    78 citations

  4. University of Minnesota System

    Minneapolis, United States

    2 h-index

    2 publications

    42 citations

  5. Université Claude Bernard Lyon 1

    Villeurbanne, France

    2 h-index

    2 publications

    68 citations

  6. Siemens (United States)

    Princeton, United States

    1 h-index

    1 publications

    562 citations

  7. Leibniz University Hannover

    Hanover, Germany

    1 h-index

    1 publications

    29 citations

  8. Charles University

    Prague, Czechia

    1 h-index

    1 publications

    10 citations

1–8 of 36

Venues

  1. Journal of Applied Probability

    JAP · 6 publications · 167 citations

    6

    h-index

  2. Advances in Applied Probability

    AAP · 3 publications · 78 citations

    3

    h-index

  3. FreiDok plus (Universitätsbibliothek Freiburg)

    Repository · 2 publications · 30 citations

    2

    h-index

  4. Duke Mathematical Journal

    DMJ · 2 publications · 180 citations

    2

    h-index

  5. Advances in Mathematics

    2 publications · 71 citations

    2

    h-index

1–5