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To appear in Proc. International Conference on Image Processing, ICIP-2000, Sep. 10-13, 2000 Vancouver, Canada
WAVELET-BASED RECONSTRUCTION OF IRREGULARLY-SAMPLED IMAGES: APPLICATION TO STEREO IMAGING Carlos V´azquez, Janusz Konrad
Eric Dubois
Institut National de la Recherche Scientifique Place Bonaventure, P.O. Box 644, Montreal QC, H5A 1C6, Canada vazquez,
[email protected]
School of Information Technology and Engineering (SITE), University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada
[email protected]
ABSTRACT We are concerned with the reconstruction of a regularly-sampled image based on irregularly-spaced samples thereof. We propose a new iterative method based on a wavelet representation of the image. For this representation we use a biorthogonal spline wavelet basis implemented on an oversampled grid. We apply the developed algorithm to disparity-compensated stereoscopic image interpolation. Under disparity compensation, the resulting sampling grids are irregular and require the irregular/regular inte rpolation. We show experimental results on real-world images and we compare our results with other methods proposed in the literature.
In the irregular sampling case, however, Shannon’s sampling theory is not applicable, and the main goal is to reconstruct the underlying continuous function Ic from an irregular set of samples 2 I [ i ]; i is an irregular sampling i2Z , where grid defined on 2 . The irregular sampling theory specifies the conditions that an irregular sampling set must respect to assure perfect reconstruction. Since in the applications mentioned above the irregular sampling grid is determined by a motion or disparity vector field, the spatial distribution of image samples may be quite arbitrary, often precluding perfect reconstruction. Instead, an approximation needs to be computed.
f x x 2X
