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14 September 1993 Discrete image stacks verifying the diffusion equation for mulitresolution image processing
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In practical situations, images are discrete and only discrete filtering can be performed, such that the above theory must be adapted accordingly. In this paper, we derive the filter family which must replace the Gaussian kernel, in this case. The result can be understood because the Fourier transform of the second derivative corresponds to the multiplication by the square of the frequency, such that our filter is the discrete version of a Gaussian. In other words, our approach consistently generalizes the continuous theory to the discrete case. When the discrete equivalent of the Laplacian is defined on the basis of n-order B-spline interpolating functions, the image stack exactly verifies the continuous diffusion equation at the spatially sampled points. These results are generalized to any linear partial differential operator corresponding to another requirement on the image stack, just by defining the discrete equivalent operator.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Christophe Dary, Yves J. Bizais, Jeanpierre V. Guedon, and Laurent Bedat "Discrete image stacks verifying the diffusion equation for mulitresolution image processing", Proc. SPIE 1898, Medical Imaging 1993: Image Processing, (14 September 1993);

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