Let \(X=\{X(t)\in \mathbb{R}^{d},t\in \mathbb{R}^{N}\}\) be a centered anisotropic Gaussian random field with stationary increments. Under certain conditions, we present the exact Hausdorff-type measures ϕ−mΛ for the image set X([0, 1]N) and the graph set GrX([0,1]N), where ϕ is a Hausdorff measure function and Λ is an infinitely increasing sequence of positive integers. Moreover, we derive a necessary and sufficient condition on the sequence A such that the general Hausdorff measure functions for X([0,1]N) and GrX([0,1]N) are always the correct measure functions. Our results generalize the corresponding results of Xiao(1998) for fractional Brownian motion and Chen and Liu(2005) for isotropic Gaussian random fields to anisotropic Gaussian random fields.
