Non-maximum suppression is an edge thinning technique.
Given estimates of the image gradients, a search is carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction. In some implementations, the algorithm categorizes the continuous gradient directions into a small set of discrete directions, and then moves a 3x3 filter over the output of the previous step (that is, the edge strength and gradient directions). At every pixel, it suppresses the edge strength of the center pixel (by setting its value to 0) if its magnitude is not greater than the magnitude of the two neighbors in the gradient direction. For example,
- if the rounded gradient angle is zero degrees (i.e. the edge is in the north–south direction) the point will be considered to be on the edge if its gradient magnitude is greater than the magnitudes at pixels in the east and west directions,
- if the rounded gradient angle is 90 degrees (i.e. the edge is in the east–west direction) the point will be considered to be on the edge if its gradient magnitude is greater than the magnitudes at pixels in the north and south directions,
- if the rounded gradient angle is 135 degrees (i.e. the edge is in the northeast–southwest direction) the point will be considered to be on the edge if its gradient magnitude is greater than the magnitudes at pixels in the north west and south east directions,
- if the rounded gradient angle is 45 degrees (i.e. the edge is in the north west–south east direction) the point will be considered to be on the edge if its gradient magnitude is greater than the magnitudes at pixels in the north east and south west directions.
In more accurate implementations, linear interpolation is used between the two neighbouring pixels that straddle the gradient direction. For example, if the gradient angle is between 45 degrees and 90 degrees, interpolation between gradients at the north and north east pixels will give one interpolated value, and interpolation between thesouth and south west pixels will give the other (using the conventions of last paragraph). The gradient magnitude at the central pixel must be greater than both of these for it to be marked as an edge.
Note that the sign of the direction is irrelevant, i.e. north–south is the same as south–north and so on.