Anisotropic diffusions are classified by the second eigenvalue of the Hessian matrix associated with the diffusivity function into two categories: one incapable of edge-sharpening and the other capable of selective edge-sharpening. A third class is proposed: the eigenvalue starts with a small value and decreases monotonically with image gradient magnitude, so that the stronger the edge is, the more it is sharpened. Two families of such diffusivity functions are proposed. Numerical simulations indicate that the noise removal performance of anisotropic diffusion does not correlate with the shape of the diffusivity function, but is, instead, determined by the shape of the second eigenvalue function. Diffusivity functions in the third category produce the best maximum peak signal-to-noise ratio in numerical simulations.
Through its evolution with time, anisotropic diffusion provides multi-scale edge-sensitive smoothing of noisy
images. Depending on the type of equation used, such a procedure may also have the ability to sharpen the
edges. This paper characterizes the edge-sharpening abilities of a well-known diffusion equation based on the
characteristics of the second eigenvalue of the Hessian of a function related to the diffusivity function. It
then proposes a new way of diffusivity function design based on the natural requirement of the degree of edge
sharpening monotonically related to the strength of edges. A comparative example based on the Structural
Similarity Index (SSIM) is also presented.
A fourth order PDE is proposed as the regularization operator for image restoration in order to alleviate the
"blocky" effects that frequently mar restored images regularized with anisotropic difusion (a second order PDE).
This is motivated by its desirable property of evolving toward an image consisting of piecewise planar areas
which is a less blocky and better approximation to natural images. In order to mitigate speckle artifacts that
it frequently brings about, image gradient magnitude is added as an additional variable of the nonlinearity
function that controls its behavior. A numerical implementation method is presented and simulation results
indicate that the proposed method tend to produce restored images which are smoother in smooth areas and
sharper in feature-rich areas. However, speckle artifacts need to be carefully addressed.
This paper presents modifications of the continuous Hopfield and Hartline-Ratliff networks for use in signal restoration and parameter estimation. The particular parameter estimation problem of interest is concerned with the estimation of the directions of arrival of an unknown number of plane waves in unknown noise. Restoration of linearly distorted noisy images is considered as an example of regularized restoration of a signal with known dynamic range.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
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.