A method for calculating a focal stack associated with an object space from the discrete plenoptic function thereof, f(s,t,j,k), which comprises evaluating the photographic formation integral as a sum along the length of planes in a 4D hypercube, said evaluation of the photographic formation integral in turn comprising the following steps:
- at the start of the computation, making the captured data, f(s,t,j,k), be equal to the transformed data up to step 0,
- f
- ~
- 0
-
- (
- r
- ,
- s
- ,
- t
- ,
- j
- ,
- k
- )
- ,
- i
- .
- e
- .
- :
-
- j
- x
- 0
-
- (
- r
- ,
- s
- ,
- t
- ,
- j
- ,
- k
- )
- =
- f
- (
- s
- ,
- t
-
- 2
-
-
- n
- ,
- j
- ,
- k
- )
- ;
- and then applying n=log2 N times the following partial transformation:
- f
- ~
- m
- +
- 1
- (
- r
- 0
- ,
- …
-
- ,
- r
- m
- -
- 1
-
- ρ
- :
- m
-
-
- bits
-
- r
- :
- m
- +
- 1
-
-
- bits
- ,
- r
- m
- ,
- s
- m
- +
- 1
- ,
- …
-
-
- s
- n
- -
- 1
-
- s
- :
- n
- -
- m
- -
- 1
-
-
- bits
- ,
- t
- m
- +
- 1
- ,
- …
-
- ,
- t
- n
- -
- 1
-
- t
- :
- n
- -
- m
- -
- 1
-
-
- bits
-
- 2
-
-
- n
- -
- m
- -
- 1
-
-
- bits
- ,
- j
- ,
- k
- )
- =
- f
- ~
- m
-
- (
- ρ
- ,
- 0
- ,
- s
- ,
- 0
- ,
- t
- ,
- j
- ,
- k
- )
- +
- f
- ~
- m
-
- (
- ρ
- ,
- 1
- ,
- s
- ,
- 0
- ,
- t
- ,
- j
- +
- r
- m
- +
- λ
-
- (
- ρ
- )
- ,
- k
- )
- +
- f
- ~
- m
-
- (
- ρ
- ,
- 0
- ,
- s
- ,
- 1
- ,
- t
- ,
- j
- ,
- k
- +
- r
- m
- +
- λ
-
- (
- ρ
- )
- )
- +
- f
- ~
- m
-
- (
- ρ
- ,
- 1
- ,
- s
- ,
- 1
- ,
- t
- ,
- j
- +
- r
- m
- +
- λ
-
- (
- ρ
- )
- ,
- k
- +
- r
- m
- +
- λ
-
- (
- ρ
- )
- )