Linear Systems
- Any linear and translation invariant image operator must satisfy the following:
- They can be implemented by the convolution
- where h is the kernel (also called Point Spread Function - PSF) of the convolution, which characterizes any linear translation invariant operator
Morphological Dilation and Erosion
- Dilation is any operator that commutes with union (max):
- Erosion is any operator that commutes with intersection (min):
- Structural dilation is any translation invariant dilation:
- Structural erosion is any translation invariant erosion:
- The structural dilation and erosion are characterized by the structuring element b
Convolution x Dilation/Erosion
Compositions of Operators
- Composing linearly two convolutions can be replaced by a single convolution
- Composing dilation, erosion, union, intersection and negation:
- can generate any digital image operator
- More complicated morphological operators can be designed by the composition of the 5 primitive operators above.