We investigate 2-tape weighted finite automata called weighted finite
transducers (WFT) and their applications to image processing. We show
that probabilistic mutually recursive function systems (PMRFS) can be
simulated by iterative weighted finite transductions. We conjecture th
at iterative WFT are stronger than PMRFS and give examples of WFT that
support this conjecture. We also show that the family of images defin
ed by iterative WFT is closed under continuous invertible WFT relation
s which include invertible affine transformations as a special case. W
e give examples of iterative WFT which can compute mathematical functi
ons given by a Taylor series with ''regular'' coefficients which canno
t be computed by WFA. We discuss the implementation of an efficient im
age manipulation system which includes the implementation of efficient
algorithms for the application of a WFT to an image in either pixel o
r WFA representation and for composition of WFT. The system also inclu
des the Culik-Kari recursive WFA inference algorithm as a conversion f
rom pixel representation to WFA representation.