The Kirsch operator or Kirsch compass kernel is a non-linear edge detector that finds the maximum edge strength in a few predetermined directions. It is named after the computer scientist Russell Kirsch.

Mathematical description[edit]

The operator takes a single kernel mask and rotates it in 45 degree increments through all 8 compass directions: N, NW, W, SW, S, SE, E, and NE. The edge magnitude of the Kirsch operator is calculated as the maximum magnitude across all directions:

where z enumerates the compass direction kernels g:

and so on.

The edge direction is defined by the mask that produces the maximum edge magnitude.

Example images[edit]

• 
  Original
• 
  Maximum gradient in the 8 directions

• 
  Image filtered with g⁽¹⁾
• 
  Image filtered with g⁽²⁾
• 
  Image filtered with g⁽³⁾
• 
  Image filtered with g⁽⁴⁾

• 
  Image filtered with g⁽⁵⁾
• 
  Image filtered with g⁽⁶⁾
• 
  Image filtered with g⁽⁷⁾
• 
  Image filtered with g⁽⁸⁾

References[edit]

• Kirsch, R. (1971). "Computer determination of the constituent structure of biological images". Computers and Biomedical Research. 4 (3): 315–328. CiteSeerX 10.1.1.161.956. doi:10.1016/0010-4809(71)90034-6.