Related papers: Capturing the Shape of a Point Set with a Line Seg…
A topological shape analysis is proposed and utilized to learn concepts that reflect shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects. Therein constellations…
The distant graph $G = G(\mathbb{P}(Z),\triangle)$ of the projective line over the ring of integers is considered. The shortest path problem in this graph is solved by use of Klein's geometric interpretation of Euclidean continued…
We consider the problem of segmenting objects in videos based on their motion and no other forms of supervision. Prior work has often approached this problem by using the principle of common fate, namely the fact that the motion of points…
Let $P$ be a polygonal curve in $\mathbb{R}^D$ of length $n$, and $S$ be a point set of size $k$. The Curve/Point Set Matching problem consists of finding a polygonal curve $Q$ on $S$ such that its Fr\'echet distance from $P$ is less than a…
Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a…
Object shape and pose estimation is a foundational robotics problem, supporting tasks from manipulation to scene understanding and navigation. We present a fast local solver for shape and pose estimation which requires only category-level…
Let $P$ be a set of $n$ points in the plane where each point $p$ of $P$ is associated with a radius $r_p>0$.The transmission graph $G=(P,E)$ of $P$ is defined as the directed graph such that $E$ contains an edge from $p$ to $q$ if and only…
An interesting class of orthogonal representations consists of the so-called turn-regular ones, i.e., those that do not contain any pair of reflex corners that "point to each other" inside a face. For such a representation H it is possible…
A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are…
We consider the following problem: Given a finite set of straight line segments in the plane, determine the positions of a minimal number of points on the segments, from which guards can see all segments. This problem can be interpreted as…
We address the problem of one dimensional segment detection and estimation, in a regression setup. At each point of a fixed or random design, one observes whether that point belongs to the unknown segment or not, up to some additional…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
This paper presents a novel approach to computing vector road maps from satellite remotely sensed images, building upon a well-defined Patched Line Segment (PaLiS) representation for road graphs that holds geometric significance. Unlike…
Visual data, such as an image or a sequence of video frames, is often naturally represented as a point set. In this paper, we consider the fundamental problem of finding a nearest set from a collection of sets, to a query set. This problem…
Object detection or localization is an incremental step in progression from coarse to fine digital image inference. It not only provides the classes of the image objects, but also provides the location of the image objects which have been…
The visual complexity of a graph drawing is defined as the number of geometric objects needed to represent all its edges. In particular, one object may represent multiple edges, e.g., one needs only one line segment to draw two collinear…
It is at times important to detect human presence automatically in secure environments. This needs a shape recognition algorithm that is robust, fast and has low error rates. The algorithm needs to process camera images quickly to detect…
In this paper, we propose a novel image set representation and classification method by maximizing the margin of image sets. The margin of an image set is defined as the difference of the distance to its nearest image set from different…
Tubular structure tracking is a crucial task in the fields of computer vision and medical image analysis. The minimal paths-based approaches have exhibited their strong ability in tracing tubular structures, by which a tubular structure can…
Motion trajectory recognition is important for characterizing the moving property of an object. The speed and accuracy of trajectory recognition rely on a compact and discriminative feature representation, and the situations of varying…