Efficient Evaluation of Image Expressions

Hi all,


I have a language used perform map/image algebra calculations using
expressions like the following:


------------------------------------------------------
if isNull(i1) or isNull(i2) or isNull(i3) or isNull(i4) or isNull(i5)
or isNull(i6) or
          isNull(i7) or isNull(i8)
    then null
    else
        (if (-4113.26 + 0.07*i7 - 5.08*i8/100 + 47.89*abs(i1) +
99.72*abs(i2) + 214.96*
              (
                  -2.332 + 2.561*i4 + 0.55*i6
              ) +
              1.57*i3) > 0 then
              -4113.26 + 0.07*i7 - 5.08*i8/100 + 47.89*abs(i1) +
99.72*abs(i2) + 214.96*
              (
                  -2.332 + 2.561*i4 + 0.55*i6
              ) +
              1.57*i3
              else 0
          )/1000
-------------------------------------------------------


This language deals with sub expressions, much like a functional
language. In this example, i1, i2, i3... represent cells of images.
So, the expression above is calculating a new image using for eight
different images (i1 .. i8)


Basically, the expression is parsed and an intermediate structure is
constructed. Then, for each image coordinate, the corresponding cells
of the eight images are scanned, presented to expression, and the
expression evaluated, much like a pixel shader does.


The problem is how to represent the expression so that the execution
becomes more efficient.


Currently I have a base Expression class and subclasses representing
the possible operators (+, -, abs, if-then-else, isNull etc). This
expressions are linked forming a tree. The evaluation process walk on
this tree evaluating sub-expression by expression and passing the
resulting values to the dependent ones, until I get a final result
representing the overall expression value.


Simple expressions, like the one above, have good performance, but if
the expression gets more complicated, the evaluation process becomes
painfully slow. Any advice?


Thank you.


Hermann

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