We show that O(n) exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled pseudo-triangulation into any other with O(n log c+h log h) flips, where c is the number of convex layers and h is the number of points on the convex hull.

The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts. We show here that the same is true in any Rn —the Riesz transforms can be obtained as the results of averaging of dyadic shifts. The goal of this paper is almost entirely methodological: we simplify the previous approach, rather than presenting the new...

Fourier descriptors are powerful features for the recognition of two-dimensional connected shapes. In this article, we propose a method to define Fourier descriptors even for broken shapes, i.e. shapes that can have more than one contour. The method is based on the convex hull of the shape and the distance to the closest actual contour point along the convex hull. We define different invariant ...

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

We prove large deviations principles (LDPs) for the perimeter and area of convex hull a planar random walk with finite Laplace transform its increments.

The problem of finding the convex hull of a planar set of points P, that is, finding the smallest convex region enclosing P, arises frequently in computer graphics. For example, to fit P into a square or a circle, it is necessary and sufficient that H(P), the convex hull of P, fits; and since it is usually the case that H(P) has many fewer points than P has, it is a simpler object to manipulate...

The authors describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited-angle or sparse-angle tomography. The algorithm estimates an object's mass, center of mass, and convex hull from the available projections, and uses this information, along with fundamental mathematical constraints, to estimate a full set of smoothed projections. The mass and center of mass...

The hybrid Radon-Fourier technique has been proposed for the discrimination and tracking of deforming and compound targets. The current work investigates the technique’s unique statistical properties which make it inherently robust with respect to performance. The Radon transform is used to generate the geometric signature waveform of the convex hull of the target, this then becomes the input t...

Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare ...

In this paper, the reassigned local polynomial periodogram along the frequency direction (RfLPP) is shown to be able to perfectly localize the chirp signal. Due to this property, the RfLPP is combined with the Hough transform for chirp signal detection in the parameter domain. Simulations of the RfLPP-Hough transform are given for chirp signal detection in white Gaussian noise and impulsive noi...