Neighborhood Processing - Introduction to Video and Image Processing - page 80

Fig. 5.11 A single column of the image is enlarged and presented in a graph. This graph contains
two very significant changes in height, the position of which is marked with circles on the graph.
This is how edges are defined in an image
5.2.2 Edge Detection
Another important application of correlation is edge detection . An edge in an image
is defined as a position where a significant change in gray-level values occur. In
Fig. 5.11 an image is shown to the left. We now take an image slice defined by the
vertical line between the two arrows. This new image will have the same height as
the input image, but only be one pixel wide. In the figure this is illustrated. Note that
we have made it wider in order to be able to actually see it. Imagine now that we
interpret the intensity values as height values. This gives us a different representation
of the image, which is shown in the graph to the right.
What can be seen in the graph is that locations in the original image where we
have a significant change in gray-scale value appear as significant changes in height.
Such positions are illustrated by circles in the figure. It is these positions where we
say we have an edge in an image.
Edges are useful in many applications since they define the contour of an ob-
ject and are less sensitive to changes in the illumination compared to for example
thresholding. Moreover, in many industrial applications image processing (or rather
machine vision) is used to measure some dimensions of objects. It is therefore of
great importance to have a clear definition of where an object starts and ends. Edges
are often used for this purpose.
Gradients
To enable edge detection we utilize the concept of gradients. We first present gra-
dients for a general curve and then turn to gradients in images. In the 1D case we
can define the gradient of a point as the slope of the curve at this point. Concretely