Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated with Legendre multiresolution analysis is a linear phase finite impulse response filter (FIR).Comment: 6 pages, 6 figures, 1 table In: Computational Methods in Circuits and Systems Applications, WSEAS press, pp.211-215, 2003. ISBN: 960-8052-88-

Zernike velocity moments for sequence-based description of moving features

The increasing interest in processing sequences of images motivates development of techniques for sequence-based object analysis and description. Accordingly, new velocity moments have been developed to allow a statistical description of both shape and associated motion through an image sequence. Through a generic framework motion information is determined using the established centralised moments, enabling statistical moments to be applied to motion based time series analysis. The translation invariant Cartesian velocity moments suffer from highly correlated descriptions due to their non-orthogonality. The new Zernike velocity moments overcome this by using orthogonal spatial descriptions through the proven orthogonal Zernike basis. Further, they are translation and scale invariant. To illustrate their benefits and application the Zernike velocity moments have been applied to gait recognition—an emergent biometric. Good recognition results have been achieved on multiple datasets using relatively few spatial and/or motion features and basic feature selection and classification techniques. The prime aim of this new technique is to allow the generation of statistical features which encode shape and motion information, with generic application capability. Applied performance analyses illustrate the properties of the Zernike velocity moments which exploit temporal correlation to improve a shape's description. It is demonstrated how the temporal correlation improves the performance of the descriptor under more generalised application scenarios, including reduced resolution imagery and occlusion

Design of Geometric Molecular Bonds

An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the affinity of the DNA base A for T, but not for C, G, or another A. Recent experimental breakthroughs in DNA nanotechnology demonstrate that a particular nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the ends of any pair of DNA double-helices) can be used to create specific "macrobonds" by careful geometric arrangement of many nonspecific blunt ends, motivating the need for sets of macrobonds that are orthogonal: two macrobonds not intended to bind should have relatively low binding strength, even when misaligned. To address this need, we introduce geometric orthogonal codes that abstractly model the engineered DNA macrobonds as two-dimensional binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung, Salehi, and Wei. The main technical difference is the importance of 2D geometry in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and Multi-Scale Communication

Reconstructing Galaxy Spectral Energy Distributions from Broadband Photometry

We present a novel approach to photometric redshifts, one that merges the advantages of both the template fitting and empirical fitting algorithms, without any of their disadvantages. This technique derives a set of templates, describing the spectral energy distributions of galaxies, from a catalog with both multicolor photometry and spectroscopic redshifts. The algorithm is essentially using the shapes of the templates as the fitting parameters. From simulated multicolor data we show that for a small training set of galaxies we can reconstruct robustly the underlying spectral energy distributions even in the presence of substantial errors in the photometric observations. We apply these techniques to the multicolor and spectroscopic observations of the Hubble Deep Field building a set of template spectra that reproduced the observed galaxy colors to better than 10%. Finally we demonstrate that these improved spectral energy distributions lead to a photometric-redshift relation for the Hubble Deep Field that is more accurate than standard template-based approaches.Comment: 23 pages, 8 figures, LaTeX AASTeX, accepted for publication in A

Exceptional orthogonal polynomials and the Darboux transformation

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction

Sidescan Sonar Image Enchancement Using a Decomposition Based on Orthogonal Functions. Applications with Chebyshev Polynomials

A method is presented to remove from sidescan sonar images of the seafloor, artifacts that are clearly unrelated to the backscattering properties of the seafloor. A spectral analysis performed on a ping by ping basis proved to be well suited to the problem. The technique relies on a decomposition using Chebyshev polynomials. This stochastic method does not require a priori knowledge of deterministic parameters. It deals with the low spatial frequency components of the image whose wavelengths are not very small compared to the swath width. Applications to sidescan sonar images obtained with the SeaMARC LI system are presented