Radon transform of Lp -functions on the Lobachevsky space and hyperbolic wavelet transforms

1999 ◽  
Vol 11 (5) ◽  
Author(s):  
C. A. Berenstein ◽  
B. Rubin
Keyword(s):  
Radon Transform ◽  
Wavelet Transforms ◽  
Lobachevsky Space

scholarly journals FACE RECOGNITION SYSTEM BY IMAGE PROCESSING

2020 ◽  
Author(s):  
Bilal Salih Abed Alhayani ◽  
Milind Rane
Keyword(s):  
Face Recognition ◽  
Wavelet Transform ◽  
Radon Transform ◽  
Wavelet Transforms ◽  
Low Frequency ◽  
Principal Component ◽  
Recognition System ◽  
Face Space ◽  
Legitimate User ◽  
Face Images

A wide variety of systems require reliable person recognition schemes to either confirm or determine the identity of an individual requesting their services. The purpose of such schemes is to ensure that only a legitimate user and no one else access the rendered services. Examples of such applications include secure access to buildings, computer systems, laptops, cellular phones, and ATMs. Face can be used as Biometrics for person verification. Face is a complex multidimensional structure and needs a good computing techniques for recognition. We treats face recognition as a two-dimensional recognition problem. A well-known technique of Principal Component Analysis (PCA) is used for face recognition. Face images are projected onto a face space that encodes best variation among known face images. The face space is defined by Eigen face which are eigenvectors of the set of faces, which may not correspond to general facial features such as eyes, nose, lips. The system performs by projecting pre extracted face image onto a set of face space that represent significant variations among known face images. The variable reducing theory of PCA accounts for the smaller face space than the training set of face. A Multire solution features based pattern recognition system used for face recognition based on the combination of Radon and wavelet transforms. As the Radon transform is in-variant to rotation and a Wavelet Transform provides the multiple resolution. This technique is robust for face recognition. The technique computes Radon projections in different orientations and captures the directional features of face images. Further, the wavelet transform applied on Radon space provides multire solution features of the facial images. Being the line integral, Radon transform improves the low-frequency components that are useful in face recognition

Inversion of the Radon Transform on the Free Nilpotent Lie Group of Step Two

2014 ◽  
Vol 66 (3) ◽  
pp. 700-720 ◽  
Author(s):  
Jianxun He ◽  
Jinsen Xiao
Keyword(s):  
Fourier Transform ◽  
Lie Group ◽  
Radon Transform ◽  
Wavelet Transforms ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
Nilpotent Lie Group ◽  
Differentiability Property ◽  
3 Dimensional ◽  
Group Fourier Transform

AbstractLet F2n;2 be the free nilpotent Lie group of step two on 2n generators, and let P denote the affine automorphism group of F2n;2. In this article the theory of continuous wavelet transformon F2n;2 associated with P is developed, and then a type of radial wavelet is constructed. Secondly, the Radon transform on F2n;2 is studied, and two equivalent characterizations of the range for Radon transform are given. Several kinds of inversion Radon transform formulae are established. One is obtained from the Euclidean Fourier transform; the others are from the group Fourier transform. By using wavelet transforms we deduce an inversion formula of the Radon transform, which does not require the smoothness of functions if the wavelet satisfies the differentiability property. In particular, if n = 1, F2;2 is the 3-dimensional Heisenberg group H1, the inversion formula of the Radon transform is valid, which is associated with the sub-Laplacian on F2;2. This result cannot be extended to the case n ≥ 2.

Wavelet Transforms with a Compact Carrier on the Basis of Spline Wavelets

2007 ◽  
Vol 66 (6) ◽  
pp. 505-512
Author(s):  
A. D. Kukharev ◽  
Yu. S. Evstifeev ◽  
V. G. Yakovlev
Keyword(s):  
Wavelet Transforms ◽  
Spline Wavelets
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