**Leo Dorst** (University of Amsterdam)

**"How Rounds Can Be Fit by Squaring the Circle"**

**Abstract**

When reading Kanatani's Bible on Stochastical Optimization for Geometric Optimization, one is struck by the general sophisticated statistics, applied to geometric coordinate representations that are hand-picked rather specifically for the problems at hand. In geometric algebra, on the other hand, we have a unified framework of coordinate-free representation for geometry, but are lacking the statistics. These fields clearly need to merge. As a first puzzle, we study the problem of fitting a model to data, which can be give both geometrical and statistical motivation.

In this talk, I show how to solve the optimal least squares fitting to a set of data points of k-spheres (`rounds') in n-D (for instance, circles in 3D), using an isometric model of Euclidean space as provided by the (n+2)-D space of conformal geometric algebra (CGA). As an aside, this leads to a compact characterization of curved point data by a `conformal covariance'. Such tools might play an elementary role in a future `algebra of uncertain geometry'.

**Vaclav Hlavac** (Czech Technical University in Prague)

**"Percepts and Structure; In and Out of a Few Personal Traps"**

**Abstract**

Structural pattern recognition was forecasted a bright future after seminal contributions by Kung Sun Fu in 1970th. I learned in mid-1990th about the alternative approach to the subject allowing joint use of statistical and structural methods from my co-author while writing the book Schlesinger M.I., Hlavac V.: Ten lectures on statistical and structural pattern recognition, Kluwer 2002. Prof. Kenichi Kanatani was a conscientious reader of this book. I like to tell him and the audience of a seminar honoring him what I have learned about the subject since. I will mention several traps I fell to on my way.

I will talk about my view of the subject in the reflection of our work: (1) in using 2D context-free grammars for analysis of mathematical formulae, (2) in using structure (pose primitives) in analysis of human activity from video; and (3) in recent project aiming at dual-robot manipulation with soft materials as pieces of garment.

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