# Edges and Corners

## Edges

Edges are defined by single lines:

*e*(*x*, *y*) = *ax* + *by* + *c*
The edge image is defined by

The figure below shows a generated edge image:

See MATLAB code that generated this image.

## Corners

Corners are defined by two intersecting lines:

represented graphically by

The edge function is given by the product of the lines, and can be
reduced to a general quadratic as shown below.

If the lines are perpendicular, the corresponding vectors must have a zero dot product,
as shown below

This eliminates a term proportional to *x*^{2} + *y*^{2}.

The figure below shows a generated corner image determined by *xy*:

See MATLAB code that generated this image.

## Examples

### Example 1

pixels in the right-hand image above are interpolated

### Example 2

pixels in the right-hand image above are replicated

Maintained by John Loomis,
last updated *1 November 2013 *