On the linear transform technique for generating rough surfaces

Abstract The linear filtering model is widely adopted because it can effectively control the areal autocorrelation function (AACF). However, these methods either constrain only half of the AACF or add the assumption of symmetry along one coordinate axis, which leads to a limited scope of applicability of the model. In this paper, a new AACF constraint for all spatial information is present. The new constraint function can provide objectives for all AACFs, and thus both isotropic rough surfaces, anisotropic surfaces of arbitrary orientation, and cross-textured surfaces can be reconstructed. The numerical experimental results show that the AACF fits well for isotropic as well as arbitrarily oriented anisotropic surfaces. For cross-textures surfaces, the errors are significant, indicating that the linear filtering model still has potential for improvement.

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