MaPhySto and StocLab Summer School on
Stereology and Geometric Tomography
Sandbjerg Manor, 20-25 May, 2000
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MaPhySto and StocLab Summer School onStereology and Geometric TomographySandbjerg Manor, 20-25 May, 2000 |
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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.
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| 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
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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
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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)
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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
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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
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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)
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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
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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.
Please make
further inquiries to MaPhySto (maphysto@maphysto.dk) or to the organizer
Eva B. Vedel Jensen.
Pictures from the Summer School