Many areas of biomedical engineering involve the modelling of biological systems, often using data from medical scanning techniques such as computed microtomography (μCT), and the prediction of the mechanical properties of these systems via finite element models. These models, and also those produced from remodelling simulations on idealized bone structures, are inherently highly pixelated and therefore have a high degree of surface roughness. The purpose of this paper is to demonstrate that this surface roughness need not necessarily have an influence on the predicted properties of the object under examination. To demonstrate this, two-dimensional idealized models of cancellous bone structures were used that were initially depleted and then rebuilt stochastically. A hysteresis effect was observed such that a significant amount of rebuilding beyond the original density was required to regain the initial intact stiffness. To ensure that this effect was not an artefact of the high degree of surface roughness of the rebuilt structures, a two-stage smoothing procedure was applied to assess if this had any effect on the stiffness of the structures. The superpixelation of the structures appeared to have a more profound effect than the smoothing procedures, although the smoothed structures still had stiffness and density values similar to those of the original structures, with a hysteresis effect still evident. This proves that the pixelization of the structures does not have a significant effect on the predicted mechanical properties of the structures. This work has important implications for other models that exhibit a high degree of surface roughness.