Lightness functions

DOI10.1016/j.aim.2012.08.015zbMath1261.52002OpenAlexW4206148521MaRDI QIDQ1759371

Richard J. Gardner, Markus Kiderlen, Stefano Campi, Paolo Gronchi

Publication date: 20 November 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2012.08.015

zbMATH Keywords

illuminationsurface areaconvex bodiesgeometric tomographyshadow boundaryBlaschke sumbrightness functionBlaschke indecomposable bodiesLambert's cosine lawlightness function

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Reconstruction of convex bodies from surface tensors, Reconstruction problems of convex bodies from surface area measures and lightness functions, Reconstruction of convex bodies from moments

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimates of Loomis-Whitney type for intrinsic volumes
• Recovering a centred convex body from the areas of its shadows: A stability estimate
• Blaschke-decomposable convex bodies
• Approximation of zonoids by zonotopes in fixed directions
• Reconstruction of convex bodies from brightness functions
• Convex bodies with extremal volumes having prescribed brightness in finitely many directions
• Shape estimation from support and diameter functions
• Convergence of algorithms for reconstructing convex bodies and directional measures
• Spherical projections and liftings in geometric tomography
• Stability results for convex bodies in geometric tomography
• Stability estimates for star bodies in terms of their intersection bodies
• Inverse problems of generalized projection operators
• A Generalization of a Theorem of Fenchel
• Measure and integration theory. Transl. from the German by Robert B. Burckel