Space-variant Image Enhancement

Using Linear Combination Filters


Simple Linear Combination Filtering: (a) Input image; (b) Laplacian of (a); (c) Spatially invariant high-pass filtering [sum of (a) and (b)]; (d) Mask image [Sobel gradient of (a) smoothed by a 5x5 box filter]; (e) Product of (b) and (d); (f) Space-variant enhancement [sum of (a) and (e)].

Adding the Laplacian to the original implements ordinary (spatially invariant) high-pass filtering in (c). Notice that in areas having little detail in the original, this mainly enhances noise.

The mask image, (d), takes on high values where there is detail present in the input image, and low values where there is none. Multiplying the Laplacian by the mask before adding it to the original preserves the smoothness of flat areas, while still enhancing detail where it is present [see (f)].

Linear combination filtering is discussed further in [1,2]. See also [3].

1. K. R. Castleman, Digital Image Processing, Prentice-Hall, 1996.
2. K. R. Castleman, Digital Image Processing, Prentice-Hall, 1979.
3. Paul Haeberli and Douglas Voorhies, "Image Processing By Interpolation and Extrapolation," in Grafica Obscura.

Last updated 04 June, 2011.
Copyright © 1995 Kenneth R. Castleman
Permission granted for noncommercial educational use.