An Introduction to Remotely Sensed Data Analysis - Sampling Spatial Units for Agricultural Surveys - page 77

these into the original image to highlight the contrast near an edge. The main
objective is to produce a line drawing of a scene. To ensure an optimal edge
detection, we must minimize the probability of false positives (detecting
unauthentic edges caused by noise) and false negatives (missing real edges),
identify the edges as close as possible to the true edges, and return one point for
each true edge point minimizing the number of local maxima. Different methods
can be used to identify the edges. In particular, we can use an edge-detecting
template, apply a spatial derivatives method, or subtract a smoothed image from
its original.
For the edge-detecting template method, a value is computed for a central pixel
using a template of pixels on three adjacent rows. In other words, this method
applies a weighted average to the original pixels, where the weights are defined by a
template. Consider, for example, a 3

3 template

−10 1
−1 0 1
−10 1

This template detects vertical edges. The new value for the central pixel (in light
gray) is represented by a weighted average of eight pixels with the weights defined
by the template

s values. For horizontal and diagonal edge detectors, the reader can
see Richards and Jia ( 2006 ).
The second type of edge detector considers an image to be a 2D continuous
brightness function of a pair of continuous coordinates. So the edges can be
described using partial derivatives. In particular, points on an edge appear as
maxima of the first derivative and zero crossings 2 of the second derivative (Marr
and Hildreth 1980 ; Cumani 1991 ).
Finally, the technique of subtracting a smoothed image from its original leads to
the enhancement of edges, lines, and points of high gradient. In fact, a smoothed
image preserves all the low spatial frequency information but has reduced edges
and lines (i.e., high frequency features). As a consequence, the resultant difference
image will mostly only contain the edges and lines.

'

4.5 Multispectral Transformations

There is a widespread tendency for multispectral images to be redundant when the
bands are very close to each other in the electromagnetic range. In this situation,
some of the original bands may be highly correlated. To save on data storage space
and computing time, these bands can be combined into new less correlated images

2 The point at which the value of a function changes from positive to negative (or vice versa) is
known as zero crossing.