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Integral geometry originated with problems on geometrical probability and convex bodies. Its later developments have proved to be useful in several fields ranging from pure mathematics (measure theory, continuous groups) to technical and applied disciplines (pattern recognition, stereology). The book is a systematic exposition of the theory and a compilation of the main results in the field. The volume can be used to complement courses on differential geometry, Lie groups, or probability or differential geometry. It is ideal both as a reference and for those wishing to enter the field.Read more
- The standard reference for the area now available in the Cambridge Mathematical Library
- Ideal as a reference for researchers or for graduate students wishing to enter the area
- Subject finds applications in many other areas
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- Edition: 2nd Edition
- Date Published: November 2004
- format: Paperback
- isbn: 9780521523448
- length: 428 pages
- dimensions: 219 x 156 x 21 mm
- weight: 0.59kg
- contains: 55 b/w illus.
- availability: Available
Table of Contents
Part I. Integral Geometry in the Plane:
1. Convex sets in the plane
2. Sets of points and Poisson processes in the plane
3. Sets of lines in the plane
4. Pairs of points and pairs of lines
5. Sets of strips in the plane
6. The group of motions in the plane: kinematic density
7. Fundamental formulas of Poincaré and Blaschke
8. Lattices of figures
Part II. General Integral Geometry:
9. Differential forms and Lie groups
10. Density and measure in homogenous spaces
11. The affine groups
12. The group of motions in En
Part III. Integral Geometry in En:
13. Convex sets in En
14. Linear subspaces, convex sets and compact manifolds
15. The kinematic density in En
16. Geometric and statistical applications: stereology
Part IV. Integral Geometry in Spaces of Constant Curvature:
17. Noneuclidean integral geometry
18. Crofton's formulas and the kinematic fundamental formula in noneuclidean spaces
19. Integral geometry and foliated spaces: trends in integral geometry.
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