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_40: Many shape co-segmentation methods employ multiple descriptors to measure the similarities between parts of a set of shapes in a descriptor space. Different shape descriptors characterize a shape in different aspects. Simply concatenating them into a single vector might greatly degrade the performance of the co-analysis in the presence of irrelevant and redundant information. In this paper, we propose an approach to fuse multiple descriptors for unsupervised co-segmentation of a set of shapes from the same family. Starting from the over-segmentations of shapes, our approach generates the consistent segmentation by performing the spectral clustering in a fused space of shape descriptors. The core of our approach is to seek for an optimal combination of affinity matrices of different descriptors so as to alleviate the impact of unreliable and irrelevant features. More specially, we introduce a local similarity based affinity aggregation spectral clustering algorithm, which assumes the local similarities are more reliable than far-away ones. Experimental results show the efficiency of our approach and improvements over the state-of-the-art algorithms on the benchmark datasets.
  @cite_27: We introduce an algorithm for unsupervised co-segmentation of a set of shapes so as to reveal the semantic shape parts and establish their correspondence across the set. The input set may exhibit significant shape variability where the shapes do not admit proper spatial alignment and the corresponding parts in any pair of shapes may be geometrically dissimilar. Our algorithm can handle such challenging input sets since, first, we perform co-analysis in a descriptor space, where a combination of shape descriptors relates the parts independently of their pose, location, and cardinality. Secondly, we exploit a key enabling feature of the input set, namely, dissimilar parts may be "linked" through third-parties present in the set. The links are derived from the pairwise similarities between the parts' descriptors. To reveal such linkages, which may manifest themselves as anisotropic and non-linear structures in the descriptor space, we perform spectral clustering with the aid of diffusion maps. We show that with our approach, we are able to co-segment sets of shapes that possess significant variability, achieving results that are close to those of a supervised approach.
  @cite_1: This paper presents a data-driven approach to simultaneous segmentation and labeling of parts in 3D meshes. An objective function is formulated as a Conditional Random Field model, with terms assessing the consistency of faces with labels, and terms between labels of neighboring faces. The objective function is learned from a collection of labeled training meshes. The algorithm uses hundreds of geometric and contextual label features and learns different types of segmentations for different tasks, without requiring manual parameter tuning. Our algorithm achieves a significant improvement in results over the state-of-the-art when evaluated on the Princeton Segmentation Benchmark, often producing segmentations and labelings comparable to those produced by humans.
summary: From the literature, we have two further observations. First, existing feature driven techniques use local features developed by the influential work @cite_1 . These features are mostly defined per face (a few are normalized by different geodesic radii for smoothing purposes), as such, there is no spatial scale information included in the architecture. To the best of our knowledge, a feature-based deep learning network architecture that considers multi-scale geometric features derived from a set of local faces has not been fully explored in supervised mesh segmentation. We hypothesise that multi-scale features would be useful because face-based @cite_27 and patch-based techniques @cite_40 have both shown good performance in co-segmentation. Second, whilst deep learning is useful, there is not much analysis as how CNN perform compared to other techniques in the deep learning family.