Ordering relations
Two images are equal if all their corresponding pixels are equal.
An image is less or equal another if this relationship is true for every pixel.
It is possible to extent this relationship to image operators. An operator is less or equal another if the relationship is valid for any image that is applied to the operators.
Image operators properties
There are many interesting properties of image to image transformation which are very useful to characterise morphological operators.
- Translation invariance
- Rotation invariance (isotropic operator)
- Local knowledge The operator is characterized by a window.
- Idempotence Further applications of the operator does not change the result.
- Extensivity The output image is larger or equal than the input image.
- Anti-extensivity The output image is smaller or equal than the input image.
- Increasingness The operator preserves the order of the images. If the image 1 is smaller or equal than image 2, the application of the filter will not change the order of the results.
- Duality Two operators are dual with respect with the complement, if
- Auto-duality An operator is auto-dual if the application of the operator to the image or to its complement gives the same result.
- Homotopy The operator does not change the topology of the image.
