Before revision:   To derive the proposed representation, Varadhan's formula is exploited to approximate the non-linear Eikonal partial differential equation (PDE) of the Euclidean distance field~(EDF ) by the logarithm of the screen Poisson equation that is linear .
After revision:  To derive the proposed representation, Varadhan's formula is exploited to approximate the non-linear Eikonal partial differential equation (PDE) of the Euclidean distance field~(EDF ) by the logarithm of a linear PDE .