Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction

International audienceThis paper addresses the gray-level image representation ability of the Fourier-Mellin Transform (FMT) for pattern recognition, reconstruction and image database retrieval. The main practical di±culty of the FMT lies in the accuracy and e±ciency of its numerical approximation and we propose three estimations of its analytical extension. Comparison of these approximations is performed from discrete and ¯nite-extent sets of Fourier- Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities. Experimental results on real gray-level images show that it is possible to recover an image to within a speci¯ed degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, illustrating both theoretical and numerical results in the context of content-based image retrieval

A Compact and Complete AFMT Invariant with Application to Face Recognition

In this paper, we present a complete set of hybrid similarity invariants under the Analytical Fourier-Mellin Transform (AFMT) framework, and apply it to invariant face recognition. Because the magnitude and phase spectra are not processed separately, this invariant descriptor is complete. In order to simplify the invariant feature data for recognition and discrimination, a 2D-PCA approach is introduced into this complete invariant descriptor. The experimental results indicate that the presented invariant descriptor is complete and similarityinvariant. Its compact representation through the 2D-PCA preserves the essential structure of an object. Furthermore, we apply this compact form into ORL, Yale and BioID face databases for experimental verification, and achieve the desired results

Spectral representation of fingerprints

Most fingerprint recognition systems are based on the use of a minutiae set, which is an unordered collection of minutiae locations and directions suffering from various deformations such as translation, rotation and scaling. The spectral minutiae representation introduced in this paper is a novel method to represent a minutiae set as a fixed-length feature vector, which is invariant to translation, and in which rotation and scaling become translations, so that they can be easily compensated for. These characteristics enable the combination of fingerprint recognition systems with a template protection scheme, which requires a fixed-length feature vector. This paper introduces the idea and algorithm of spectral minutiae representation. A correlation based spectral minutiae\ud matching algorithm is presented and evaluated. The scheme shows a promising result, with an equal error rate of 0.2% on manually extracted minutiae

Fingerprint Verification Using Spectral Minutiae Representations

Most fingerprint recognition systems are based on the use of a minutiae set, which is an unordered collection of minutiae locations and orientations suffering from various deformations such as translation, rotation, and scaling. The spectral minutiae representation introduced in this paper is a novel method to represent a minutiae set as a fixed-length feature vector, which is invariant to translation, and in which rotation and scaling become translations, so that they can be easily compensated for. These characteristics enable the combination of fingerprint recognition systems with template protection schemes that require a fixed-length feature vector. This paper introduces the concept of algorithms for two representation methods: the location-based spectral minutiae representation and the orientation-based spectral minutiae representation. Both algorithms are evaluated using two correlation-based spectral minutiae matching algorithms. We present the performance of our algorithms on three fingerprint databases. We also show how the performance can be improved by using a fusion scheme and singular points

Construction of a complete set of orthogonal Fourier-Mellin moment invariants for pattern recognition applications

International audienceThe completeness property of a set of invariant descriptors is of fundamental importance from the theoretical as well as the practical points of view. In this paper, we propose a general approach to construct a complete set of orthogonal Fourier-Mellin moment (OFMM) invariants. By establishing a relationship between the OFMMs of the original image and those of the image having the same shape but distinct orientation and scale, a complete set of scale and rotation invariants is derived. The efficiency and the robustness to noise of the method for recognition tasks are shown by comparing it with some existing methods on several data sets

Adjoint Operators of Two Dimensional Fractional Fourier-Mellin Transform

Methods based on the Fourier transform and Mellin transform are used in virtually all areas of engineering and science and by virtually all engineers and scientists. These transform play a important role in signal processing, algorithm, watermarking, pattern recognition, correlators, navigation, vowel recognition, cryptographic scheme, quantum calculus, radar system and have applications in agriculture, medical stream, detection of watermark in images regardless of the scaling and rotation. In this paper we present an adjiont shifting operator, adjoint scaling operator and adjoint shifting-scaling operator of two dimensional fractional Fourier-Mellin transform. Also we discuss some transform formulae using adjoint differential operator

A Fast Mellin and Scale Transform

A fast algorithm for the discrete-scale (and -Mellin) transform is proposed. It performs a discrete-time discrete-scale approximation of the continuous-time transform, with subquadratic asymptotic complexity. The algorithm is based on a well-known relation between the Mellin and Fourier transforms, and it is practical and accurate. The paper gives some theoretical background on the Mellin, -Mellin, and scale transforms. Then the algorithm is presented and analyzed in terms of computational complexity and precision. The effects of different interpolation procedures used in the algorithm are discussed

Reconnaissance de formes par invariants complets et convergents ; Application à l'indexation de bases d'objets à niveaux de gris

La recherche d'images par le contenu est un domaine de recherche émergent et particulièrement dynamique du fait de l'essor de grandes bases d'images. Elle requiert un ensemble de descripteurs, une méthode robuste pour les extraire et, enfin, une mesure de similarité rapide qui traduit la ressemblance visuelle entre les formes. Dans ce travail, nous présentons et comparons deux familles complètes et convergentes de descripteurs globaux pour la recherche et l'archivage d'objets à niveaux de gris. Notre approche est invariante aux similitudes planes. La robustesse et la performance des descripteurs sont illustrées par plusieurs expériences numériques sur deux bases