  We present a new method to estimate the rate-distortion-perception function
in the perfect realism regime (PR-RDPF), for multivariate continuous sources
subject to a single-letter average distortion constraint. The proposed approach
is not only able to solve the specific problem but also two related problems:
the entropic optimal transport (EOT) and the output-constrained rate-distortion
function (OC-RDF), of which the PR-RDPF represents a special case. Using copula
distributions, we show that the OC-RDF can be cast as an I-projection problem
on a convex set, based on which we develop a parametric solution of the optimal
projection proving that its parameters can be estimated, up to an arbitrary
precision, via the solution of a convex program. Subsequently, we propose an
iterative scheme via gradient methods to estimate the convex program. Lastly,
we characterize a Shannon lower bound (SLB) for the PR-RDPF under a mean
squared error (MSE) distortion constraint. We support our theoretical findings
with numerical examples by assessing the estimation performance of our
iterative scheme using the PR-RDPF with the obtained SLB for various sources.
