We provide a reformulation and formalization of the classical result by Juhani Karhum\"aki characterizing intersections two languages form $\{x,y\}^*\cap \{u,v\}^*$. use terminology morphisms which allows to formulate in shorter more transparent way, we formalize proof assistant Isabelle/HOL.

We discuss two ways to determine, given I ⊂ S, whether I ∈ I. The first method is based on the previous lecture, where we considered the set Ŝ = ∪̇Ŝi, a union of disjoint copies of the Si. Formally, we write Ŝ = {(e, i) : e ∈ Si}. There is a natural mapping f : Ŝ → ∪Si which maps (e, i) to e. We can now define a partition matroid Mp over the ground set Ŝ, where I(Mp) = { I ⊆ Ŝ s.t. ∀e ∈ S : |I ∩...

The number of intersection accidents around the world has reached a plateau and has not decreased in spite of the innovation and improvement in road and vehicle safety technologies. Therefore, intersection collision warning and avoidance systems that are able to warn potential drivers of an impending collision are required. The existing systems have not utilized recent innovations in vehicular ...

In this mini-project, we have defined the problem of inferring a spatially varying function given a finite set of noisy sensor observations. The challenge lies in the nonuniform noise in the input space of the observed data. The assumption is that samples generated along a particular trajectory tend to experience similar levels of noise in their location information. Therefore, we design an inf...

This paper describes how the generation of 3-D models may be achieved from a small number of images. It uses an automatic segmentation technique and a two stage iterative camera calibration and volumetric intersection algorithm to produce a set of 3-D points in the form of a cloud of voxels. From this, a polygonal or B-spline based surface representation of an object can be generated. The B-spl...

Based on the optimality criteria established in Part I, we show a primal-type cyclecanceling algorithm and a primal-dual-type augmenting algorithm for the valuated independent assignment problem: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectively, find a matching M(⊆ A) that maximizes ∑ {w(a) | a ∈ M}+ ω(∂M) + ω−(∂−M), w...

Data imprecision constitutes an important gap between theory and practice in computational geometry. A lot of research about imprecision in computational geometry is directed at computing the convex hull of imprecise points rather than imprecise line segment intersection. In this paper we introduce an algorithm to construct the convex hull for a set of imprecise line segment intersection in time.