An edge point can be regarded as a point in an image where a discontinuity (in gradient) occurs across some line. A discontinuity may be classified as one of three types (see Fig 21):
Fig. 21 The C Compilation Model
- A Gradient Discontinuity
- -- where the gradient of the pixel values changes across a line. This type of discontinuity can be classed as
- roof edges
- ramp edges
- convex edges
- concave edges
- A Jump or Step Discontinuity
- -- where pixel values themselves change suddenly across some line.
- A Bar Discontinuity
- -- where pixel values rapidly increase then decrease again (or vice versa) across some line.
- jump discontinuities occur where one object occludes another (or another part of itself).
- Gradient discontinuities usually occur between adjacent faces of the same object.
- a bar discontinuity would represent cases like a thin black line on a white piece of paper.
- Step edges may separate different objects, or may occur where a shadow falls across an object.
The gradient is a vector, whose components measure how rapidly pixel values are changing with distance in the x and y directions.
Thus, the components of the gradient may be found using the following approximation:
where
and 
measure distance along the x and y directions respectively. In (discrete) images we can consider
and in terms of numbers of pixels between two points. Thus, when 
(pixel spacing) and we are at the point whose pixel coordinates are (i,j) we have 
In order to detect the presence of a gradient discontinuity we must calculate the change in gradient at (i,j). We can do this by finding the following gradient magnitude measure,
and the gradient direction,
, given by 
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