Cooperation of the partial differential equation methods and the wavelet transform for the segmentation of multivalued images

  • Authors:

  • Aldo Maalouf;Philippe Carré;Bertrand Augereau;Christine Fernandez-Maloigne

  • Affiliations:

  • Signal-Image-Communication Laboratory, University of Poitiers, SP2MI-2 Bd Marie et Pierre Curie, PO Box 30179, 86962 Futuroscope Chasseneuil, France;Signal-Image-Communication Laboratory, University of Poitiers, SP2MI-2 Bd Marie et Pierre Curie, PO Box 30179, 86962 Futuroscope Chasseneuil, France;Signal-Image-Communication Laboratory, University of Poitiers, SP2MI-2 Bd Marie et Pierre Curie, PO Box 30179, 86962 Futuroscope Chasseneuil, France;Signal-Image-Communication Laboratory, University of Poitiers, SP2MI-2 Bd Marie et Pierre Curie, PO Box 30179, 86962 Futuroscope Chasseneuil, France

  • Venue:
  • Image Communication
  • Year:
  • 2008

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Abstract

In this work, the wavelet transform (WT) and two partial differential equations (PDEs)-based segmentation methods are merged together towards an efficient segmentation paradigm that integrates level-set functions and wavelet-based singularity detection to object extraction from multivalued images. To this end, different interfaces of the image regions are characterized using a wavelet-based multiscale multistructure tensor that is capable of identifying edges in spite of the presence of noise. With this wavelet-based multistructure tensor, the edge structures of a vector-valued image can be studied at different scales. This multiresolution edge-detection approach allows to reconstruct the accumulated orientational information of the multispectral image. Detected edges are then modeled by level-set functions. A functional is defined on these level sets whose minimizers define the optimal classification of objects. In a second step, the cooperation of PDE and WT is used for pioneering active contour segmentation method. For that purpose, foveal wavelets [S. Mallat, Foveal orthonormal wavelets for singularities, Technical Report, Ecole Polytechnique, 2000], known by their high capability to precisely characterize the holder regularity of singularities, are used to detect the image contours. These wavelets are capable of accurately characterizing edges of noisy images. The obtained foveal coefficients are used to guide the curve flow in an active contour segmentation process. Therefore a foveal-wavelet-based snake approach is formulated. The proposed approach is capable of driving the snake curve to the real edges of different regions in a noisy image. Promising experimental results illustrate the potential of the cooperation of the PDE and the WT in the segmentation of multivalued images.