33 research outputs found
Perceptually Motivated Shape Context Which Uses Shape Interiors
In this paper, we identify some of the limitations of current-day shape
matching techniques. We provide examples of how contour-based shape matching
techniques cannot provide a good match for certain visually similar shapes. To
overcome this limitation, we propose a perceptually motivated variant of the
well-known shape context descriptor. We identify that the interior properties
of the shape play an important role in object recognition and develop a
descriptor that captures these interior properties. We show that our method can
easily be augmented with any other shape matching algorithm. We also show from
our experiments that the use of our descriptor can significantly improve the
retrieval rates
The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach
This paper develops the theory behind the bispectrum, a concept that is well
established in statistical signal processing but not, until recently, extended
to computer vision as a source of frequency-domain invariants. Recent papers on
using the bispectrum in vision show good results when the bispectrum is applied
to spherical harmonic models of three-dimensional (3-D) shapes, in particular
by improving discrimination over previously-proposed magnitude invariants, and
also by allowing detection of neutral pose in human activity detection. The
bispectrum has also been formulated for vector spherical harmonics, which have
been used in medical imaging for 3-D anatomical modeling. In a paper published
in this journal, Smach {\it et al.} use duality theory to establish the
completeness of second-order invariants which, as shown here, are the same as
the bispectrum. This paper unifies earlier works of various researchers by
deriving the bispectrum formula for all compact groups. It also provides a
constructive algorithm for recovering functions from their bispectral values on
SO(3). The main theoretical result shows that the bispectrum serves as a
complete source of invariants for homogeneous spaces of compact groups,
including such important domains as the sphere
Signal analysis using a multiresolution form of the singular value decomposition
This paper proposes a multiresolution form of the singular value decomposition (SVD) and shows how it may be used for signal analysis and approximation. It is well-known that the SVD has optimal decorrelation and subrank approximation properties. The multiresolution form of SVD proposed here retains those properties, and moreover, has linear computational complexity. By using the multiresolution SVD, the following important characteristics of a signal may be measured, at each of several levels of resolution: isotropy, sphericity of principal components, self-similarity under scaling, and resolution of mean-squared error into meaningful components. Theoretical calculations are provided for simple statistical models to show what might be expected. Results are provided with real images to show the usefulness of the SVD decomposition
Bispectrum on finite groups
The algebraic theory of finite groups appears in signal processing problems involving the statistical analysis of ranked
data and the construction of invariants for pattern recognition. Standard signal processing techniques involving spectral
analysis are, in theory, possible for data defined on finite groups by using the Fourier transform provided by group representations. However, one such technique, the bispectrum, which is useful for analysing non-Gaussian data as well as
for constructing geometric invariants, has not been explored in detail for finite groups. This paper shows how to construct
the bispectrum on an arbitrary finite group or homogeneous space and explores its properties. Examples are given using
the symmetric group as well as wreath-product groups.Accepted versio
Interpreting the Phase Spectrum in Fourier Analysis of Partial Ranking Data
Whenever ranking data are collected, such as in elections, surveys, and database searches, it is frequently the case that partial rankings are available instead of, or sometimes in addition to, full rankings. Statistical methods for partial rankings have been discussed in the literature. However, there has been relatively little published on their Fourier analysis, perhaps because the abstract nature of the transforms involved impede insight. This paper provides as its novel contributions an analysis of the Fourier transform for partial rankings, with particular attention to the first three ranks, while emphasizing on basic signal processing properties of transform magnitude and phase. It shows that the transform and its magnitude satisfy a projection invariance and analyzes the reconstruction of data from either magnitude or phase alone. The analysis is motivated by appealing to corresponding properties of the familiar DFT and by application to two real-world data sets