Image reconstruction from a complete set of similarity invariants extracted from complex moments

Ghorbel, Faouzi; Derrode, Stéphane; Mezhoud, R.; Bannour, Tarak; Dhahbi, Sami

doi:10.1016/j.patrec.2006.01.001

Cited by 55 publications

(21 citation statements)

References 24 publications

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“…Flusser et al proposed a complete set of rotation invariants by normalizing the complex moments [6,7]. The construction of a complete set of similarity (translation, scale and rotation) invariant descriptors by means of some linear combinations of complex moments has been addressed by Ghorbel et al [14].…”

Section: Derivation Of Moment Invariants To Geometric Transformationsmentioning

confidence: 99%

“…We now describe a general approach to derive a complete set of OFMM invariants. We use the same method to achieve the translation invariance as described in [14]. That is, the origin of the coordinate system is located at the center of mass of the object to achieve the translation invariance.…”

Section: Derivation Of a Complete Set Of Orthogonal Fouriermellin Mommentioning

confidence: 99%

“…As noted by Ghorbel et al [5,14], the most important properties to assess by the image descriptors are: (1) invariance against some geometrical transformations; (2) stability to noise, to blur, to non-rigid and small local deformations; and (3) completeness. The objective of this chapter is to present a comprehensive survey of the state-of-the-art on the moment invariants to geometric transformations and to blur in pattern recognition.…”

Section: Introductionmentioning

confidence: 99%

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Derivation of Moment Invariants

Hu¹,

Luo²,

Coatrieux³

2014

Gate to Computer Science and Research

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In most computer vision applications, the extraction of key image features, whatever the transformations applied and the image degradations observed, is of major importance. A large diversity of approaches has been reported in the literature. This chapter concentrates on one particular processing frame: the moment-based methods. It provides a survey of methods proposed so far for the derivation of moment invariants to geometric transforms and blurring eects. Theoretical formulations and some selected examples dealing with very dierent problems are given.

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Section: Derivation Of Moment Invariants To Geometric Transformationsmentioning

confidence: 99%

Section: Derivation Of a Complete Set Of Orthogonal Fouriermellin Mommentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Derivation of Moment Invariants

Hu¹,

Luo²,

Coatrieux³

2014

Gate to Computer Science and Research

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“…In some cases, the set of numbers is complete in the sense that the original shape can be reconstructed from the shape descriptors [1,2], but even in these situations, only a subset of the shape descriptors is typically used in practical applications. The shape descriptors can thus be considered as an approximative description of the shape such that shape similarity somehow corresponds to similarity of the shape descriptors.…”

Section: Introductionmentioning

confidence: 99%

Fourier descriptors for broken shapes

Dalitz

Brandt

Goebbels

et al. 2013

EURASIP J. Adv. Signal Process.

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Fourier descriptors are powerful features for the recognition of two-dimensional connected shapes. In this article, we propose a method to define Fourier descriptors even for broken shapes, i.e. shapes that can have more than one contour. The method is based on the convex hull of the shape and the distance to the closest actual contour point along the convex hull. We define different invariant Fourier descriptors for this three-dimensional representation of a two-dimensional shape and compare them on different data sets. The recognition rates are comparable to normal Fourier descriptors while the new scheme at the same time offers the option to also deal with broken contours. We also discuss and evaluate different normalisation schemes that make the descriptors invariant under scale and rotation.

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“…Flusser [14] discussed the problem of dependence of Hu's invariants and derived a new set of only rotation moment invariants of any order. Derrode et al [15] derived a set of both rotation and scale invariants. Flusser and Suk [16] extended the original work of Flusser [14] and introduced a set of rotationally moment invariants for symmetric objects.…”

Section: Introductionmentioning

confidence: 99%

Optimized Set of RST Moment Invariants

Hosny¹

2008

American J. of Applied Sciences

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Moment invariants are widely used in image processing, pattern recognition and computer vision. Several methods and algorithms have been proposed for fast and efficient calculation of moment's invariants where numerical approximation errors are involved in most of these methods. In this paper, an optimized set of moment invariants with respect to rotation, scaling and translation is presented. An accurate method is used for exact computation of moment invariants for gray level images. A fast algorithm is applied to accelerate the process of computation. Error analysis is presented and a comparison with other conventional methods is performed. The obtained results explain the superiority of the proposed method.

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Image reconstruction from a complete set of similarity invariants extracted from complex moments

Cited by 55 publications

References 24 publications

Derivation of Moment Invariants

Derivation of Moment Invariants

Fourier descriptors for broken shapes

Optimized Set of RST Moment Invariants

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