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We describe a methodology for the interactive definition of curves and motion paths using a stochastic formulation of optimal control. We demonstrate how the same optimization framework can be used in different ways to generate curves and traces that are g ...
We prove formulas for power moments for point counts of elliptic curves over a finite field k such that the groups of k-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain con ...
Photon-counting imaging technology has applications in many fields such as fluorescence lifetime imaging microscopy (FLIM), time-resolved Raman spectroscopy, 3D imaging, and even space communications. The requirement to detect single photons with picosecon ...
Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...
The performance of post-processing techniques carried out on the Brillouin gain spectrum to estimate the Brillouin frequency shift (BFS) in standard Brillouin distributed sensors is evaluated. Curve fitting methods with standard functions such as polynomia ...
We present a method for the interactive generation of stylised letters, curves and motion paths that are similar to the ones that can be observed in art forms such as graffiti and calligraphy. We define various stylisations of a letter form over a common g ...
Nowadays, massive amounts of point cloud data can be collected thanks to advances in data acquisition and processing technologies like dense image matching and airborne LiDAR (Light Detection and Ranging) scanning. With the increase in volume and precision ...
We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...
We establish obstructions for groups to act by homeomorphisms on dendrites. For instance, lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for irreducible lattices in products of connected groups. Further results ...
In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer n≥3, we define e(n) to be the minimum positive integer such that an ...
