###### Abstract
The modified curvature-based method [18] was initially used to identify relief candidate segments from mesh partitions. The relief candidates include actual reliefs and relief-like noise. From each candidate segment, 79-dimensional geometrical features were extracted, which consist of the appearance, quadratic approximation for cross section, and local extrema of the candidate segments. The geometrical information was learned by the SVM to determine whether the candidate is relief or not. While this machine learning method outperformed the height estimation [8] and curvature-based methods [7; 18], the superior performance of the SVM-based method [24] is largely dependent on the local surface features that were identified on the 3D mesh and the conditions for the removal of degraded region. In this paper, we consider the spin image (SI) as features to describe the local surface of 3D mesh. SI is widely used in computer vision and computer-aided design because of its efficient shape representation of 3D objects which was posed as surface matching problem [25]. The effectiveness of SI for describing the surface of steels had been promisingly demonstrated [26]. The main contribution of this paper is the training of a machine learning classifier based on the SI descriptions that are extracted from the 3D mesh of very rough stele. In order to effectively distinguish the relief region from the background surface, we enhance the representation of the SI description by structurally configuring multiple SIs. Considering the canal-like shape of the reliefs, the minimal curvature direction, \(\mathbf{t}_{min}\) follows the canal at a position within the relief, while the maximal curvature direction, \(\mathbf{t}_{max}\) climbs up the canal along the cross section. As a result, the locations apart with a certain distance along \(\mathbf{t}_{min}\) from the given relief position tend to belong to the identical relief, while the locations apart along \(\mathbf{t}_{max}\) would be the background. Using the principal curvature directions at a particular vertex with reference, four relative surface points are identified on the 3D mesh. We refer to the aggregation of the SIs of these five points including the reference and its four relative points as cross spin image (CSI). In the proposed approach, the CSIs are extracted as features per vertex to train a three-class label random forest (RF) model. The class labels of the surface points include the relief, background, and the degraded region. The \(k\)-nearest neighbors (\(k\)-NN) algorithm is used to refine the classification results. The degraded region is identified and re-labeled to background region. As such, the proposed method classifies the surface points as relief or non-relief region. In contrast with the SVM-based method which classifies relief using candidate segment [24], the classification of the proposed machine learning-based method is done per vertex. The remaining sections of the paper are divided as follows: Studies relevant to the proposed method are discussed in Section 2. We present the proposed approach in Section 3. Various parameters used in the proposed method are determined and the performance of the proposed method is compared with existing techniques based on intuitive geometrical features in Section 4. Finally, we conclude our findings in Section 5.