Image Processing

Adaptive bidirectional diffusion for image restoration

“…As early as in 1955, Kovasznay and Joseph [20] introduced the idea of "anti-diffusion" in image processing, where they assumed an image degrading process by the heat diffusion equation, and proposed a contour enhancing operator by expanding u(x, t) into a Taylor series. Afterwards there are different approaches leading to diffusion processing for image restoration, such as variational regularization, stochastic regularization, scale space filtering, anisotropic diffusion, etc.…”

“…(20) Here, N l (i) denotes neighborhood points in the l ∈ {x, y} direction. Then, we rewrite (17) as…”

From Image Analysis to Computer Vision: An Annotated Bibliography, 1955–1979

“…Such a boundary is called an edge; pixels that lie on edges can be detected by the fact that there are large differences in the image gray levels in their neighborhoods. The highest directional rate of change of a function f in the neighborhood of a point is called the gradient of f ; the usefulness of the gradient for edge detection was pointed out as early as the 1950s by Kovasznay and Joseph [101]. (That paper also discussed the Laplacian of an image and its use for approximate inversion of diffusion blur.)…”

Solving the backward heat equation on the unit sphere

“…In hydrologic inversion [1], sources of groundwater pollution are sought by reconstructing the contaminant history. Kovasznay and Joseph [6] proposed the use of a backward diffusion equation to restore blurred images. Backward parabolic problems on a spherical domain have potential applications in atmospheric modelling, when a global temperature from the past is to be determined by current temperature data.…”