We present a unified feature extraction architecture consisting of only three core algorithms that allows to extract and track a rich variety of geometrically defined, local and global features evolving in scalar and vector fields. The architecture builds upon the concepts of Feature Flow Fields and Connectors, which can be implemented using the three core algorithms finding zeros, integrating ...

Complex movies with different parallel lines of action, only intersecting in a small number of scenes, can be difficult to analyze. The present study sets out to provide the viewer with assisted automatic procedures designed to decompose and analyze the narrative from different possible perspectives. We propose a model for narrative decomposition, based on the interaction of characters. The pro...

In curve design such as highway design andmotion planning of autonomous vehicles, it may be important to minimize the maximum curvature. In this paper we address the problem of minimizing the maximum curvature of a quadratic Bézier curve within a boundary constraint determined by a tetragonal concave polygon. The curve is parameterized by lengths between its control points, called the ‘‘control...

This entry provides a geometric proof of the intersecting chords theorem. The theorem states that when two chords intersect each other inside a circle, the products of their segments are equal. After a short review of existing proofs in the literature [1, 3–5], I decided to use a proof approach that employs reasoning about lengths of line segments, the orthogonality of two lines and Pythagoras ...

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a, b, c, d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindström-GesselViennot theorem leads to a formula as a sum of...

We prove Erdős-Ko-Rado and Hilton-Milner type theorems for t-intersecting k-chains in posets using the kernel method. These results are common generalizations of the original EKR and HM theorems, and our earlier results for intersecting k-chains in the Boolean algebra. For intersecting k-chains in the c-truncated Boolean algebra we also prove an exact EKR theorem (for all n) using the shift met...

We present two 1/8 supersymmetric intersecting p-brane solutions of 11-dimensional supergravity which upon compactification to four dimensions reduce to extremal dyonic black holes with finite area of horizon. The first solution is a configuration of three intersecting 5-branes with an extra momentum flow along the common string. The second describes a system of two 2-branes and two 5-branes. R...

We show some combinatorial and algorithmic results concerning sets of lines and polyhedral objects in 3-space. Our main results include: (1) An O(n 3 2 c p log n) upper bound on the worst case complexity of the set of lines missing a star-shaped compact polyhedron with n edges, where c is a suitable constant. (2) An O(n 3 2 c p log n) upper bound on the worst case complexity of the set of lines...

Combined visualizations of filamentous structures and surrounding volumetric objects are common in biological and medical applications. Often, the structures’ spatial relationships remain unclear to the viewer. In this paper, we discuss and evaluate techniques to emphasize spatial relationships. We concentrate on the visualization of transparent objects and intersecting lines. Among various tec...