MaPhySto and StocLab Summer School on
Stereology and Geometric Tomography
Sandbjerg Manor, 20-25 May, 2000
The aim of the summer school was to give an overview of modern stereology and its relation to geometric tomography, including both the mathematical and statistical theory and the practical applications.
Stereology is the area of stochastics dealing with statistical inference about spatial structures from geometric samples of the structure such as two-dimensional sections and one-dimensional probes. The development of stereological methods involve the use of advanced mathematical tools, especially from geometric measure theory and integral geometry. Stereology is now in world-wide use in many areas of biology and medicine, most importantly in neuroscience and cancer grading. Other areas of application are geology, metallography and mineralogy.
|A disector consists of a reference plane and a look-up plane, a distance h apart.||Illustration of the sampling relevant for estimation of length in R3, based on projections on a vertical plane.|
Geometric tomography is closely related to stereology, as is apparent from its definition: ``geometric tomography is the area of mathematics dealing with the retrieval of information about a geometric object from data about its sections, or projections, or both''. Geometric tomography has connections with convex geometry, geometric probing in robotics, computerized tomography, and other areas. The area is surveyed in the book Geometric Tomography by Richard Gardner.
The summer school was held at Sandbjerg Manor, a conference centre owned by University of Aarhus, situated in the southern part of Jutland, Denmark. The summer school was organized by StocLab (Laboratory for Computational Stochastics) and by MaPhySto (Centre for Mathematical Physics and Stochastics), both Department of Mathematical Sciences, University of Aarhus.
The teaching team consisted of
Lectures by invited researchers in related fields such as convex geometry, stochastic geometry and spatial statistics were given, as well as lectures by the participants of the summer school.
(L) : Lectures (TE) : Theoretical Exercises (SL) : Special Invited Lectures (PL) : Participants' Lectures (PE) : Practical Exercises ________________________________________________________________________________ Saturday 20 May 2000 15.00-16.00 Coffee 16.00-16.30 Welcome Presentation of teachers and participants 16.30-17.10 Eva B. Vedel Jensen: Introduction to stereology Richard Gardner: Introduction to geometric tomography 17.15-18.00 Adrian Baddeley: Analogy between stereology and survey sampling (L) 18.00 Dinner 20.30- Get-together ________________________________________________________________________________ Sunday 21 May 2000 09.00-09.45 Richard Gardner: Star bodies, chord functions, and section functions (L) 10.00-10.45 Eva B. Vedel Jensen: Stereological estimation of number (L) 10.45-11.15 Coffee 11.15-12.00 Niels Væver Hartvig: Stereological estimation of number (TE) 12.00-14.00 Lunch 14.00-14.45 Richard Gill: Quantum tomography (SL) 14.45-15.15 Coffee 15.15-16.00 Aljosa Volcic: Determination of a convex body by sections I (SL) 16.10-16.50 Markus Kiderlen: Endomorphisms of convex bodies (PL) 17.00-17.30 Boris Rubin: Arithmetrical properties of generalized Minkowski-Funk transforms and small denominators on the sphere (PL) 18.00 Dinner 20.00-21.00 Adrian Baddeley: The fractionator (PE) _______________________________________________________________________________ Monday 22 May 2000 09.00-09.45 Richard Gardner: The spherical Radon transform and Funk's theorem (L) 10.00-10.45 Hans Jørgen G. Gundersen: Counting and sampling in 3D (demonstration at the microscope) 10.45-11.15 Coffee 11.15-12.00 Adrian Baddeley: Stereological sampling designs, volume estimation (L) 12.00-14.00 Lunch 14.00-14.45 Aljosa Volcic: Determination of a convex body by sections II 14.45-15.15 Coffee 15.15-16.00 Martin Bøgsted Hansen Statistical aspects of inverse problems (SL) 16.10-16.50 Niels Holm Olsen: 3D-reconstruction, light microscopy and optics of embryo (PL) 17.00-17.30 Andrew Olenko: Closeness of random fields in different multidimensional metrics (PL) 19.00- Summer school dinner ________________________________________________________________________________ Tuesday 23 May 2000 09.00-09.45 Richard Gardner: Determination by chord and section functions (L) 10.00-10.45 Eva B. Vedel Jensen: Length and surface area estimation under isotropy (L) 10.45-11.15 Coffee 11.15-12.00 Kien Kieu: Length and surface area estimation under isotropy (TE) 12.00-13.00 Lunch 13.00-17.30 Excursion 18.00 Dinner ________________________________________________________________________________ Wednesday 24 May 2000 09.00-09.45 Richard Gardner: Affine inequalities and volume estimates (L) 10.00-10.45 Adrian Baddeley: Vertical sections (L) 10.45-11.15 Coffee 11.15-12.00 Kien Kieu Variance of planar area estimators based on systematic sampling (L) 12.00-14.00 Lunch 14.00-14.45 Boris Rubin: Continuous wavelet transforms in geometric tomography (SL) 14.45-15.15 Coffee 15.15-15.45 Eugene Spodarev: One isoperimetrical problem for stationary flat processes (PL) 15.45-16.15 Martin Bøgsted Hansen: Nonparametric estimation of the chord length distribution (PL) 16.30-17.00 Marta Garcia-Finana: Fractional trend of the variance under systematic sampling on R (PL) 17.00-17.30 Stephan Boehm: On Laslett's test for Boolean model (PL) 18.00 Dinner 20.00-21.00 Hans Jørgen G. Gundersen: How to estimate the volume and surface area of a banana (PE) ________________________________________________________________________________ Thursday 25 May 2000 09.00-09.45 Eva B. Vedel Jensen: Local stereology (L) 10.00-10.45 Kien Kieu: Variance of planar area estimators based on systematic sampling (TE) 10.45-11.15 Coffee 11.15-12.00 Hans Jorgen G. Gundersen Connectivity (L) 12.00-14.00 Lunch _______________________________________________________________________________
For the Summer School a small booklet was made, in which the program, abstracts, small notes, list of participants, etc. were included. You may download the (revised and expanded) booklet.
further inquiries to MaPhySto (
firstname.lastname@example.org) or to the organizer
Eva B. Vedel Jensen.
Pictures from the Summer School