Fingerprint-Matching Algorithm Using Polar Shapelets

An image, such as a fingerprint, can be decomposed into a linear combination of polar shapelet-base functions. This publication describes a fingerprint-matching algorithm that uses polar shapelet-base functions. Using polar shapelet-base functions, a fingerprint image block can be separated into components with explicit rotational symmetries. Polar shapelet-base functions can represent the fingerprint image through compact parameterization or encoder representation due to their interpretation in terms of the rotational angle , and due to their separability by a distance r. Therefore, the use of polar shapelets enables a convenient and robust method to perform fingerprint image manipulation, analysis, and matching. Polar shapelet-base functions are special types of steerable filters that have rotational symmetry. When the fingerprint image is convolved with a polar shapelet-base function, the magnitude of the convolution output is rotationally invariant, and the relative rotation between two fingerprint images is the phase shift in the convolution output, which enables calculating the rotation angle between two matching image blocks with relative ease. Polar shapelet-base functions can be utilized to create a machine-learned (ML) model that is composed of harmonic and rotationally symmetric convolution filters. The fingerprint-matching algorithm pre-specifies the rotation order of each filter, but the size and shape of the convolution filter is optimized using the ML model. Also, the fingerprint-matching algorithm optimizes a TensorFlow implementation for each convolution filter in the radial direction r. The ML model determines an optimized set of filters that can increase the matching between two rotated images. The described fingerprint-matching algorithm offers high-resolution fingerprint images, low computation latency, low image energy residuals, and high matching rates

Analytic structure of radiation boundary kernels for blackhole perturbations

Exact outer boundary conditions for gravitational perturbations of the Schwarzschild metric feature integral convolution between a time-domain boundary kernel and each radiative mode of the perturbation. For both axial (Regge-Wheeler) and polar (Zerilli) perturbations, we study the Laplace transform of such kernels as an analytic function of (dimensionless) Laplace frequency. We present numerical evidence indicating that each such frequency-domain boundary kernel admits a "sum-of-poles" representation. Our work has been inspired by Alpert, Greengard, and Hagstrom's analysis of nonreflecting boundary conditions for the ordinary scalar wave equation.Comment: revtex4, 14 pages, 12 figures, 3 table

Linear inequalities for flags in graded posets

The closure of the convex cone generated by all flag $f$-vectors of graded posets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chain-enumeration functionals on this class of posets. These are in one-to-one correspondence with antichains of intervals on the set of ranks and thus are counted by Catalan numbers. Furthermore, we prove that the convolution operation introduced by Kalai assigns extreme rays to pairs of extreme rays in most cases. We describe the strongest possible inequalities for graded posets of rank at most 5

A General Filter for Stretched-Grid Models: Application in Two-Dimension Polar Geometry

Variable-resolution grids are used in global atmospheric models to improve the representation of regional scales over an area of interest: they have reduced computational cost compared to uniform high-resolution grids, and avoid the nesting issues of limited-area models. To address some concerns associated with the stretching and anisotropy of the variable-resolution computational grid, a general convolution filter operator was developed.\ud \ud The convolution filter that was initially applied in Cartesian geometry in a companion paper is here adapted to cylindrical polar coordinates as an intermediate step toward spherical polar latitude–longitude grids. Both polar grids face the so-called “pole problem” because of the convergence of meridians at the poles.\ud \ud In this work the authors will present some details related to the adaptation of the filter to cylindrical polar coordinates for both uniform as well as stretched grids. The results show that the developed operator is skillful in removing the extraneous fine scales around the pole, with a computational cost smaller than that of common polar filters. The results on a stretched grid for vector and scalar test functions are satisfactory and the filter’s response can be optimized for different types of test function and noise one wishes to remove