Dose 2016

Convolution integral

A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function .

C-S Chui and R Mohan, Med Phy 15(2), 1988

1D kernel function

step function

The steps to convolve these two functions are: 1. Folding 2. Displacement 3. Multiplication 4. Integration

∫ ∫ ∞ ∞− yxg f ∞ =

[

] ( ) ,

(

) (

)

' dy dx y yx xgyxf

⊗

' ,'

,'

− −

'

'

2D definition

∞−