text: Abstract There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3) techniques often suffer from reproducibility issue. This study contributes in two ways. First, we propose a novel convolutional neural network (CNN) for mesh segmentation. It uses 1D data, filters and a multi-branch architecture for separate training of multi-scale features. Together with a novel way of computing conformal factor (CF), our technique clearly out-performs existing work. Secondly, we publicly provide implementations of several deep learning techniques, namely, neural networks (NNs), autoencoders (AEs) and CNNs, whose architectures are at least two layers deep. The significance of this study is that it proposes a robust form of CF, offers a novel and accurate CNN technique, and a comprehensive study of several deep learning techniques for baseline comparison.
  @cite_15: We present a new 3D shape descriptor based on conformal geometry. Our descriptor is invariant under non-rigid quasi-isometric transformations, such as pose changes of articulated models, and is both compact and efficient to compute. We demonstrate the performance of our descriptor on a database of watertight models, and show it is comparable with state-of-the-art descriptors.
  @cite_2: This article presents a novel approach for 3D mesh labeling by using deep Convolutional Neural Networks (CNNs). Many previous methods on 3D mesh labeling achieve impressive performances by using predefined geometric features. However, the generalization abilities of such low-level features, which are heuristically designed to process specific meshes, are often insufficient to handle all types of meshes. To address this problem, we propose to learn a robust mesh representation that can adapt to various 3D meshes by using CNNs. In our approach, CNNs are first trained in a supervised manner by using a large pool of classical geometric features. In the training process, these low-level features are nonlinearly combined and hierarchically compressed to generate a compact and effective representation for each triangle on the mesh. Based on the trained CNNs and the mesh representations, a label vector is initialized for each triangle to indicate its probabilities of belonging to various object parts. Eventually, a graph-based mesh-labeling algorithm is adopted to optimize the labels of triangles by considering the label consistencies. Experimental results on several public benchmarks show that the proposed approach is robust for various 3D meshes, and outperforms state-of-the-art approaches as well as classic learning algorithms in recognizing mesh labels.
summary: @cite_15 , CF after one stage of Laplacian-smoothing, combination of CF0 and CF1, combination of all smoothed CF features, and combination of all CF (including CF0). The chart shows that the new smoothed CF features improve upon the original in most cases, and also further improves when they are combined with the original CF . In this paper, we show that by using multi-scale features, treating them as separate 1D vectors per scale, and applying multi-branch 1D CNN filters through the network, we avoid the parameter tuning problem of reshaping a 2D matrix. Our method clearly out-performs existing work @cite_2 in accuracy. Further, we provide comprehensive evaluation of various deep learning techniques, and show how CNN , though more complex, can improve performance over simpler architectures ( NN , AE ). It is worth noting that we have found existing methods lack reproducibility. Some existing work have not provided any or complete experimental code. Despite using the exact architecture and settings stated, some high performing results are hard to reproduce.