We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed fram...

This tutorial covers a variety of methods for 3D shape matching and retrieval that are characterized by the use of a real-valued function defined on the shape (mapping function) to derive its signature. The methods are discussed following an abstract conceptual framework that distinguishes among the three main components of these class of shape matching methods: shape analysis, via the applicat...

We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape analysis as well as in investigating how the brain perceives and generates curv...

We propose two differential geometric representations of planar shapes using: (i) direction functions and (ii) curvature functions, of their boundaries. Under either representation, planar shapes are treated as elements of infinite-dimensional shape spaces. Pairwise differences between the shapes are quantified using the lengths of geodesics connecting them on the shape spaces. We specify the g...

The multi-particle Bose-Einstein correlations are the source of "intermittency" in high energy hadronic collisions. The power-law like increase of factorial moments with decreasing bin size was obtained by complete event weighing technique with gaussian approximation of space-time particle emitting source shape. The value of source size parameter was found to be higher than the common one tted ...

In this paper, we propose an efficient and stable algorithm to recover the 3D shape of an unfolded curved book surface from the shading information of a scanner image. This shape from shading problem in a real world environment has a global and complicated interdependency among the shape, the depth and the albcdo distribution of the book surface. Hence, the ovcrall surface shape must be recover...

We present a hypnogram generator fully written in Matlab/Octave programming languages. Our software extracts data from brainwaves during sleep and then classifies wave stretches according to their predominant frequency. Differently from other programs, which rely on heavily numerical data analyses, our approach is the plain shape analysis of the waves. For this purpose we focus on properties of...

We report 5.1 dB of squeezing from a fiber interferometer pumped with a 1-GHz pulse source that successfully eliminates guided-acoustic-wave Brillouin scattering in significant frequency regimes. The pulse source is a diode-pumped Nd:YLF laser actively mode locked at 1.314 microm. The squeezing results are consistent with the limits imposed by the Gaussian pulse shape and the detection quantum ...

The current paper presents a pseudo-sweep algorithm to determine whether a given volume constitutes an approximately swept shape for the purpose of hexahedral finite element mesh generation. The pseudo-swept shape determination approach consists of three steps. Step 1: Determining the source surface, target surface, and lateral surface of a given solid object B. Two requirements: topological an...