Skip to main content
SpringerLink
Log in

Towards a unitary formulation for invariant image description: application to image coding

Vers une Fomulation Unitaire des Descriptions Invariantes D’image : Application au Codage D’image

  • Published:
Annales Des Télécommunications Aims and scope Submit manuscript

Abstract

Here, we introduce a joint topology and harmonic analysis formulation for the extraction of global shape descriptors which are invariant under a given group of geometrical transformations. The topology approach allows the rigorous definition of the notions of shape, shape space, the invariant features space, and a metric between shapes. Therefore a new definition of completeness is given. A stability criterion is defined mathematically. Using harmonic analysis, a unitary operator that is able to separate the shape information and the geometric transformation, allows us to extract a relevant invariant shape descriptors under a given group of transformations. It also gives a robust method for the evaluation of the global object motion. In the closed curves, some three-dimensional surfaces and planar gray level image cases, such an operator becomes the Fourier transform on a given group. Therefore, under some assumptions, a complete convergent set of invariant features exists and can be constructed. We derived from this a shape metric. Recent developments in image coding domain for moving pictures offer new perspectives to the application of the image invariant representations of regions and contours. Therefore, we intend to illustrate the importance of our approach in image coding and indexing applications.

Résumé

Dans cet article, une formulation conjointe provenant de la topologie et de l’analyse harmonique du problème de l’extraction de primitives invariantes en vue d’une description de forme dans un cadre général est proposée. Ces descripteurs sont invariants par rapport à un groupe de transformations géométriques donné. L’approche topologique permet la définition rigoureuse des notions de forme, d’espace des formes et d’espace des invariants menant à une nouvelle de la complétude et de la stabilité. L’application de l’analyse harmonique, par la construction d’un opérateur qui est capable de séparer l’information de transformation géométrique de celle deforme, permet l’extraction de descripteurs invariants pertinents par rapport à un groupe de transformations donné. Une méthode d’estimation de mouvement robuste est également possible à partir de cet opérateur. Dans le cas des contours fermés, des images planes à niveaux de gris et de certaines surfaces tridimensionnelles, cet opérateur correspond exactement à la transformation de Fourier sur un groupe. On en déduit, alors, quand il est possible, une famille d’invariants complète et convergente ou stable. Les récents développements en codage d’images animées offrent de nouvelles perspectives aux méthodes de représentations invariantes des régions et des objets contours. Dans cet article l’importance de cette approche pour le codage d’image orienté objet ainsi que dans les applications de type indexation est illustrée.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ming-Kuel (H.), Visual pattern recognition by moment invariants,IEEE Trans. IT., pp 179–187, (Feb 1962).

  2. Sadjadi (F. A.) et al , Three dimensional moment invariants,IEEE Trans PAMI, 2, pp. 127–136. (March 1980).

  3. Cheong-Huah et al, 3-D moment forms : their construction and application to object identification and position,IEEE Tram. PAMI 11.no. 10. (Oct. 1989).

  4. Zhan (C. T.) Roskies (R. Z.), Fournier Description for plane closed curves, inIEEE Tram. C,21, n° 3, pp. 261–81, (1972).

    Google Scholar 

  5. Grunlund (G. H.), Fourrier pre processing for hand print character recgnition,IEEE. Trans. C,21, pp. 195–201. (1972).

    Article  Google Scholar 

  6. Persoon (E.) Fu (K. S.), Shape discrimination using Fourrier descriptors,IEEE Trans. SMC 7, n° 3, pp. 170–179. (1977).

    MathSciNet  Google Scholar 

  7. Ghorbel (F.), A complete invariant description for gray-level images by the harmonic analysis approach,Pattern Recognition Letters, pp. 1043–1051. (15 April 1994).

  8. Bougrenet (J. L.de),Ghorbel (F.), Scale invariant pattern recognition applied to image data compresion,Pattern recognition letters,8, pp. 55–58. (1988).

    Article  Google Scholar 

  9. Fonga (H.), Analyse harmonique en reconnaissanse de formes Doctorate thesis,Institut National Polytechnique de Grenoble (France). (1992).

  10. Timoty (P.). Wallace,Three dimensional shape analysis using local shape description,IEEE Trans. PAMI,3, (May, 1981) pp. 310–322.

    Google Scholar 

  11. Burdin (V), Modélisation et analyse de structure tridimensionnelles : application à la morphométrie des os longs,Doctorate thesis, Université Rennes I. (1992).

  12. Weiss (I), Noise resistant invariant of curves.Geometric in Computer Vision, edited by Joseph L. Mundly and Andrew Zisserman, Artificial Intelligence series,MIT Press, (1992).

  13. Gourd (F.).Gautier (J. P.), Une méthode d’analyse harmonique en reconnaissance de formes.Traitement du signal,6, no3, pp. 161–178 (1989).

    MATH  MathSciNet  Google Scholar 

  14. Ghorbel (F.), Vers une approche mathématique unifiée des aspects géométriques et reconnaissance de formes planes,Doctorate thesis, Université Rennes I. (1990).

  15. Gautier (J. P.), Bornard (G), Silbermann (M). Motion and Pattern analysis : harmonic analysis on motion groups and their homogenoeus spaces,IEEE Trans. SMC21, no 1 (Jan/Feb 1991).

  16. Lenz-Groups representations and their homogeneous spaces,Lecture Notes in Computer Science, Springer. (1991).

  17. Ghorbel (F.), Stability of invariants Fourrier descriptors and its interference on the shape classification,11th International Conference on Pattern Recognition, (ICPR), 30 August-3 September, The Hague (NL). (1992).

  18. Ghorbel (F.) (1992), Distance et invariance pour la clasification d’objets dans les images,International meeting on distance analysis distancia ’92, June 22-26, 1992, Rennes.

  19. Ghorbel (F.).Budin (V.), Invariant curve approximation vith radial representation, Wavelets, Images, and Surface fitting, Pierre-Jean Laurent/Alain Le Méhauté Larry L. Schumaker (eds). 269–276.AK Peters Ltd, Wellesley USA(1994).

    Google Scholar 

  20. Bez (H. E.), A unified of invariance for the curve and surface defining algorithms,IMAJ Appl Maths,30, pp. 325–341. (1983).

    Article  MATH  MathSciNet  Google Scholar 

  21. Bez (H. E.), On invariant curve forms,Computer Geometrical Design,3, pp. 193–204. (1986).

    Article  MATH  MathSciNet  Google Scholar 

  22. Pavilidis (T.). Structural recognition,Springer Verlag, Berlin. (1977).

    Google Scholar 

  23. Deudonné (J.).Élément d’analyse moderne, Gautier-Villars. (1974).

  24. Arbter (K.), Snyder (W. E.), Burkhardt (H.).Hirzinger (G.), Application of affine-invaraint Fourrier Description to Recognition of 3-D objects,IEEE Tram., PAM1-12, no. 7, pp. 640–647. (July 1990).

    Google Scholar 

  25. Ghorbel (F.), Bougrenet de la tocnaye (J. L. de), Automatic control of lamellibranch larva growth using contour invariant feature extraction,Pattern Recognition,23, no. 2, (March 1990).

  26. Segman (Jos), Rubinstein (J), Zeevi (Y. Y.), The canonical coordinates method for pattern deformation: theoretical and computational considerations,IEEE Trans PAMI,14, 12, pp. 1171–1183. (1992).

    Google Scholar 

  27. Segman (Jos) Zeevi (Y. Y.), Image analysis by wavelet-type transforms : group théorie approach,Mathematical Imaging and vision, (1993).

  28. Meyer (F.) et al, Morphological segmentation,J. Visual Communication and Image Representation,1 no. 1, pp. 21–46, (Sept. 1990).

    Article  Google Scholar 

  29. Salembie (P.) et al, Morphological multiscale image segmentation, SPIE vol.18,Visual Communications and Image Processing, pp. 620–627 (1992).

  30. Serra (J.), Image analysis and mathetical morphology, Vol II,Theoretical Advances, Academic Press. (1988).

  31. Freeman (H.), Shape description via use of critical points,Pattern recognition, 10, pp. 159–156, (1978).

    Article  MATH  Google Scholar 

  32. Villenkin, Fonctions spéciales et théorie de la représentation des groupes,Dunod, Paris. (1969).

    Google Scholar 

  33. DieudonnÉ (J.) Carrell J., Invariant theory old and new,Academic press, New York. (1971).

    MATH  Google Scholar 

  34. Crimmins (T. R.), A complete set of Fourrier descriptors for two-dimensional shapes,IEEE Trans., SMC-12, no. 6, pp. 848–55, (Nov/Dec. 1982).

    MathSciNet  Google Scholar 

  35. Yip (R. K. K.), Tam (P. K. S.), Leung (D. N. K.), Application of elliptic Fourier descriptors to symmetry detection under parallel projection,IEEE, Trans. PAMI,16 no. 3. (March 1994).

  36. Sekita (I.), Kurita (T.), Ostsu (N.), Complex autoregressive model for shape recognition,IEEE Trans., PAMI,14, pp. 489–496, (April. 1992).

    Google Scholar 

  37. DieudonnÉ (J.), Elements d’analyseGauthier-Villars Tome II, (Collection cahier scientifique), Paris I. (1974).

  38. DieudonnÉ (J.),Elements d’analyse, Gauthier-Villars Tome VI, (Collection cahier scientifique), Paris I. (1974).

  39. Sheng (Y), Processeur optique en temps réel d’image video : application optique des moments bidimentionneles,Doctorate thesis, Faculté des sciences et Techniques, Université de Franche-comté (1986).

  40. Chen (S.), A new vision system and the Fourier descriptors method by group representations theory,CDC Conference, Las Vegas, USA. (1985).

  41. Sadjadi (F. A.) et al. Three dimensional moment invariants,IEEE Trans PAMI.,2, pp. 127–136. (March 1980).

    MATH  Google Scholar 

  42. Chong-Huah et al, 3-D moment forms : their construction and application to object identification and positioning,IEEE Trans PAMI.11, no 10. (Oct. 1989).

  43. You (Y. C.) et al (1979), A syntactic approach to shape recognition using attributed grammars,IEEE Trans PAMI. SMC,9, pp. 334–345, (June 1973).

    Google Scholar 

  44. Barr, (A. H.) Superquadrics and angle-preserving transformations IEEE TransCGA.,1, pp. 11–23. (1986).

    Google Scholar 

  45. Solina (F) Bajcsy (R), Recovery of parametric models from range images: the case for superquadricks with global deformations,IEEE trans PAMI.,12, no 2, pp 131–47, (1990).

    Google Scholar 

  46. Zribi (M.), Fonga(H.) Ghorbel (F), Invariant description for 3D gray level volumes under a general 3D Euclidean motion,Internationat Conference on Pattern Recognition ICPR, Austria. (1996).

  47. (J) Osterman, Based analysis-synthesis coding (obase) based on source model of moving flexible 3D Objects,IEEE Trans. IP,3. no 5. (Sept 1994).

  48. Banham (M. R.) et al, Low bit rate video coding using robust motion vector regeneration in the decoder,IEEE Trans. IP,3, no 5 (Sept 1994.).

  49. Ghorbel (F), Daoudi (M), Mokadem (A.) Avaro (O), Global planar rigid motion estimation, applied to object-oriented coding,International Conference on Pattern Recognition ICPR, Austria (Aug 1996).

  50. Mokadem (A.), Daoudi (M), Ghorbel (F.) ; A shape distance by complete and stable invarient description for contour tracking,International Conference on Pattern ICPR, Austria. August (1996).

Download references

Author information

Authors and Affiliations

  1. Groupe de Recherche Images et Formes de Tunisie de l’École Nationale des Sciences de l’Informatique (ENSI), Centre des Études et de Recherche des Télécommunications (CERT)/Direction des Études et de la Recherche, 42, rue Asdrubal, 1002, Tunis, Tunisie

    Faouzi Ghorbel

Authors
  1. Faouzi Ghorbel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghorbel, F. Towards a unitary formulation for invariant image description: application to image coding. Ann. Télécommun. 53, 242–260 (1998). https://doi.org/10.1007/BF02997680

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02997680

Key words

Mots-clés

Search

Navigation