Discrete image stacks verifying the diffusion equation for mulitresolution image processing

Christophe Dary; Yves J. Bizais; Jeanpierre V. Guedon; Laurent Bedat

doi:10.1117/12.154544

14 September 1993 Discrete image stacks verifying the diffusion equation for mulitresolution image processing

Christophe Dary, Yves J. Bizais, Jeanpierre V. Guedon, Laurent Bedat

Proceedings Volume 1898, Medical Imaging 1993: Image Processing; (1993) https://doi.org/10.1117/12.154544
Event: Medical Imaging 1993, 1993, Newport Beach, CA, United States

Abstract

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.

Citation Download Citation

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); https://doi.org/10.1117/12.154544

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available