EM 1110-2-2907
1 October 2003
c. Image Enhancement #3: Spatial Filters. It is occasionally advantageous to reduce
the detail or exaggerate particular features in an image. This can be done by a convolu-
tion method creating an altered or "filtered" output image data file. Numerous spatial
filters have been developed and can be automated within software programs. A user can
also develop his or her own spatial filter to control the output data set. Presented below
is a short introduction to the method of convolution and a few commonly used spatial
filters.
(1) Spatial Frequency. Spatial frequency describes the pattern of digital values
observed across an image. Images with little contrast (very bright or very dark) have
zero spatial frequency. Images with a gradational change from bright to dark pixel val-
ues have low spatial frequency; while those with large contrast (black and white) are
said to have high spatial frequency. Images can be altered from a high to low spatial fre-
quency with the use of convolution methods.
(2) Convolution.
(a) Convolution is a mathematical operation used to change the spatial fre-
quency of digital data in the image. It is used to suppress noise in the data or to exagger-
ate features of interest. The operation is performed with the use of a spatial kernel. A
kernel is an array of digital number values that form a matrix with odd numbered rows
and columns (Table 5-2). The kernel values, or coefficients, are used to average each
pixel relative to its neighbor across the image. The output data set will represent the av-
eraging effect of the kernel coefficients. As a spatial filter, convolution can smooth or
blur images, thereby reducing image noise. In feature detection, such as an edge en-
hancement, convolution works to exaggerate the spatial frequency in the image. Kernels
can be reapplied to an image to further smooth or exaggerate spatial frequency.
(b) Low pass filters apply a small gain to the input data (Table 5-2a). The re-
sulting output data will decrease the spatial frequency by de-emphasizing relatively
bright pixels. Two types of low pass filters are the simple mean and center-weighted
mean methods (Table 5-2a and b). The resultant image will appear blurred. Alterna-
tively, high pass frequency filters (Table 5-2c) increase image spatial frequency. These
types of filters exaggerate edges without reducing image details (an advantage over the
Laplacian filter discussed below).
(2) Laplacian or Edge Detection Filter.
(a) The Laplacian filter detects discrete changes in spectral frequency and is
used for highlighting edge features in images. This type of filter works well for deline-
ating linear features, such as geologic strata or urban structures. The Laplacian is calcu-
lated by an edge enhancement kernel (Table 5-2d and e); the middle number in the ma-
trix is much higher or lower than the adjacent coefficients. This type of kernel is
sensitive to noise and the resulting output data will exaggerate the pixel noise. A
smoothing convolution filter can be applied to the image in advance to reduce the edge
filter's sensitivity to data noise.
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