# 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.

castleman@earthlink.net