79,540 research outputs found
A similarity-based approach to perceptual feature validation
Which object properties matter most in human perception may well vary according to sensory modality, an important consideration for the design of multimodal interfaces. In this study, we present a similarity-based method for comparing the perceptual importance of object properties across modalities and show how it can also be used to perceptually validate computational measures of object properties. Similarity measures for a set of three-dimensional (3D) objects varying in shape and texture were gathered from humans in two modalities (vision and touch) and derived from a set of standard 2D and 3D computational measures (image and mesh subtraction, object perimeter, curvature, Gabor jet filter responses, and the Visual Difference Predictor (VDP)). Multidimensional scaling (MDS) was then performed on the similarity data to recover configurations of the stimuli in 2D perceptual/computational spaces. These two dimensions corresponded to the two dimensions of variation in the stimulus set: shape and texture. In the human visual space, shape strongly dominated texture. In the human haptic space, shape and texture were weighted roughly equally. Weights varied considerably across subjects in the haptic experiment, indicating that different strategies were used. Maps derived from shape-dominated computational measures provided good fits to the human visual map. No single computational measure provided a satisfactory fit to the map derived from mean human haptic data, though good fits were found for individual subjects; a combination of measures with individually-adjusted weights may be required to model the human haptic similarity judgments. Our method provides a high-level approach to perceptual validation, which can be applied in both unimodal and multimodal interface design
Equation-Free Dynamic Renormalization: Self-Similarity in Multidimensional Particle System Dynamics
We present an equation-free dynamic renormalization approach to the
computational study of coarse-grained, self-similar dynamic behavior in
multidimensional particle systems. The approach is aimed at problems for which
evolution equations for coarse-scale observables (e.g. particle density) are
not explicitly available. Our illustrative example involves Brownian particles
in a 2D Couette flow; marginal and conditional Inverse Cumulative Distribution
Functions (ICDFs) constitute the macroscopic observables of the evolving
particle distributions.Comment: 7 pages, 5 figure
Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts
In this paper, we study the benefits of using polyharmonic splines and node
layouts with smoothly varying density for developing robust and efficient
radial basis function generated finite difference (RBF-FD) methods for pricing
of financial derivatives. We present a significantly improved RBF-FD scheme and
successfully apply it to two types of multidimensional partial differential
equations in finance: a two-asset European call basket option under the
Black--Scholes--Merton model, and a European call option under the Heston
model. We also show that the performance of the improved method is equally high
when it comes to pricing American options. By studying convergence,
computational performance, and conditioning of the discrete systems, we show
the superiority of the introduced approaches over previously used versions of
the RBF-FD method in financial applications
On the optimality of shape and data representation in the spectral domain
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami
operator (LBO) in representing smooth functions on surfaces is provided and
adapted to the field of applied shape and data analysis. It is based on the
Courant-Fischer min-max principle adapted to our case. % The theorem we present
supports the new trend in geometry processing of treating geometric structures
by using their projection onto the leading eigenfunctions of the decomposition
of the LBO. Utilisation of this result can be used for constructing numerically
efficient algorithms to process shapes in their spectrum. We review a couple of
applications as possible practical usage cases of the proposed optimality
criteria. % We refer to a scale invariant metric, which is also invariant to
bending of the manifold. This novel pseudo-metric allows constructing an LBO by
which a scale invariant eigenspace on the surface is defined. We demonstrate
the efficiency of an intermediate metric, defined as an interpolation between
the scale invariant and the regular one, in representing geometric structures
while capturing both coarse and fine details. Next, we review a numerical
acceleration technique for classical scaling, a member of a family of
flattening methods known as multidimensional scaling (MDS). There, the
optimality is exploited to efficiently approximate all geodesic distances
between pairs of points on a given surface, and thereby match and compare
between almost isometric surfaces. Finally, we revisit the classical principal
component analysis (PCA) definition by coupling its variational form with a
Dirichlet energy on the data manifold. By pairing the PCA with the LBO we can
handle cases that go beyond the scope defined by the observation set that is
handled by regular PCA
FiEstAS sampling -- a Monte Carlo algorithm for multidimensional numerical integration
This paper describes a new algorithm for Monte Carlo integration, based on
the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed
in detail, and its performance is evaluated in the context of Bayesian
analysis, with emphasis on multimodal distributions with strong parameter
degeneracies. Source code is available upon request.Comment: 18 pages, 3 figures, submitted to Comp. Phys. Com
Spectral Generalized Multi-Dimensional Scaling
Multidimensional scaling (MDS) is a family of methods that embed a given set
of points into a simple, usually flat, domain. The points are assumed to be
sampled from some metric space, and the mapping attempts to preserve the
distances between each pair of points in the set. Distances in the target space
can be computed analytically in this setting. Generalized MDS is an extension
that allows mapping one metric space into another, that is, multidimensional
scaling into target spaces in which distances are evaluated numerically rather
than analytically. Here, we propose an efficient approach for computing such
mappings between surfaces based on their natural spectral decomposition, where
the surfaces are treated as sampled metric-spaces. The resulting spectral-GMDS
procedure enables efficient embedding by implicitly incorporating smoothness of
the mapping into the problem, thereby substantially reducing the complexity
involved in its solution while practically overcoming its non-convex nature.
The method is compared to existing techniques that compute dense correspondence
between shapes. Numerical experiments of the proposed method demonstrate its
efficiency and accuracy compared to state-of-the-art approaches
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