  We propose new parameterizations for the border and skewness functions
appearing in the description of 3D nucleon structure in the language of
Generalized Parton Distributions (GPDs). These parameterizations are
constructed in a way to fulfill the basic properties of GPDs, like their
reduction to Parton Density Functions and Elastic Form Factors. They also rely
on the power behavior of GPDs in the $x \to 1$ limit and the propounded
analyticity property of Mellin moments of GPDs. We evaluate Compton Form
Factors (CFFs), the sub-amplitudes of the Deeply Virtual Compton Scattering
(DVCS) process, at the leading order and leading twist accuracy. We constrain
the restricted number of free parameters of these new parameterizations in a
global CFF analysis of almost all existing proton DVCS measurements. The fit is
performed within the PARTONS framework, being the modern tool for generic GPD
studies. A distinctive feature of this CFF fit is the careful propagation of
uncertainties based on the replica method. The fit results genuinely permit
nucleon tomography and may give some insight into the distribution of forces
acting on partons.
