Generalized Fourier Descriptors with Applications to Objects Recognition in SVM Context

Smach, Fethi; Lemaître, Cédric; Gauthier, Jean-Paul; Mitéran, Johel; Atri, Mohamed

doi:10.1007/s10851-007-0036-3

Cited by 54 publications

(81 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Namely, we propose to use the bispectrum as an invariant under the action of SE(2, N ). These invariants are well established in statistical signal processing [7] and have been introduced and studied in the context of SE(2, N ) and of compact groups in [18]. We mention also [13], devoted to the bispectrum on homogeneous spaces of compact groups.…”

Section: Image Recognitionmentioning

confidence: 99%

Image Processing in the Semidiscrete Group of Rototranslations

Prandi

Boscain

Gauthier

2015

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Section: Image Recognitionmentioning

confidence: 99%

Image Processing in the Semidiscrete Group of Rototranslations

Prandi

Boscain

Gauthier

2015

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

“…where ν is a Haar measure on G. In what follows we only consider the case where G = (R 2 , +) (although more general cases have been already envisaged in image processing, see for instance [13] and [30]). Since G is abelian, every irreducible representation is of dimension one and is given by a continuous group morphism…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Spin Geometry and Image Processing

Berthier

2013

Adv. Appl. Clifford Algebras

View full text Add to dashboard Cite

Abstract. We give a survey of applications of spin geometry to image processing. We mainly focus on the problem of defining geometric Fourier transforms for both grey-level and color images. The definitions we propose rely on a spin generalization of the usual notion of character. We consider three possibilities for the actions of these spin characters: by using the spinor representation of grey-level image surfaces; by considering grey-level and color images as sections of associated bundles built first with standard representations and then with spin representations. Examples of applications to low-pass filtering are presented.Mathematics Subject Classification (2010). Primary 68U10, 53C27; Secondary 53A05, 43A32.

show abstract

“…the definition of the Fourier series. The non abelian case which requires more mathematical developments has been considered for instance in [27] to define generalized Fourier descriptors using the motion group of the plane and in [10] for the construction of so-called shearlets. 3) Very few works are devoted to a mixed approach of signal processing involving both harmonic and Riemannian methods.…”

Section: Introductionmentioning

confidence: 99%

Spinor Fourier Transform for Image Processing

Batard

Berthier

2013

IEEE J. Sel. Top. Signal Process.

View full text Add to dashboard Cite

Abstract-We propose in this paper to introduce a new spinor Fourier transform for both grey-level and color image processing. Our approach relies on the three following considerations: mathematically speaking, defining a Fourier transform requires to deal with group actions; vectors of the acquisition space can be considered as generalized numbers when embedded in a Clifford algebra; the tangent space of the image surface appears to be a natural parameter of the transform we define by means of so-called spin characters. The resulting spinor Fourier transform may be used to perform frequency filtering that takes into account the Riemannian geometry of the image. We give examples of low-pass filtering interpreted as diffusion process. When applied to color images, the entire color information is involved in a really non marginal process.

show abstract

Generalized Fourier Descriptors with Applications to Objects Recognition in SVM Context

Cited by 54 publications

References 35 publications

Image Processing in the Semidiscrete Group of Rototranslations

Image Processing in the Semidiscrete Group of Rototranslations

Spin Geometry and Image Processing

Spinor Fourier Transform for Image Processing

Contact Info

Product

Resources

About