We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field Fpn of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over Fpn with a rational Weierstrass point is O(g4+ǫn3+ǫ).

We propose a linear-time algorithm for curve segmentation which is based on constructive polynomial fitting. This work extends previous work on constructive fitting by taking the topological properties of a digitized curve into account. The algorithm uses uniform (or L∞) fitting and it works for segments of arbitrary thickness. We illustrate the algorithm with the segmentation of contours into ...

We construct a polynomial of degree d in two variables whose Hessian curve has (d − 2) connected components using Viro patchworking. In particular, this implies the existence of a smooth real algebraic surface of degree d in RP 3 whose parabolic curve is smooth and has d(d− 2) connected components. “Salut à toi Che Guevara”

We describe a new explicit function that given an elliptic curve E defined over Fpn , maps elements of Fpn into E in deterministic polynomial time and in a constant number of operations over Fpn . The function requires to compute a cube root. As an application we show how to hash deterministically into an elliptic curve.

We propose a symbolic computation algorithm for computing local parametrization of analytic branches and real analytic branches of a curve in n-dimensional space, which is de ned by implicit polynomial equations. The algorithm can be used in space curve tracing near a singular point, as an alternative to symbolic computations based on resolutions of singularities.

Cheng and Uchiyama show that if one is given an elliptic curve, depending on a prime p, that is defined over a number field and has certain properties, then one can solve the Decision Diffie-Hellman Problem (DDHP) in Fp in polynomial time. We show that it is unlikely that an elliptic curve with the desired properties exists.

Tissue deformation in ultrasound imaging is an inevitable phenomenon and poses challenges to the development of many techniques related to ultrasound image registration, including multimodal image fusion, freehand three-dimensional ultrasound, and quantitative measurement of tissue geometry. In this thesis, a novel trajectory-based method to correct tissue deformation in ultrasound B-mode imagi...