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_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.
  @cite_6: We propose a fast method for 3D shape segmentation and labeling via Extreme Learning Machine (ELM). Given a set of example shapes with labeled segmentation, we train an ELM classifier and use it to produce initial segmentation for test shapes. Based on the initial segmentation, we compute the final smooth segmentation through a graph-cut optimization constrained by the super-face boundaries obtained by over-segmentation and the active contours computed from ELM segmentation. Experimental results show that our method achieves comparable results against the state-of-the-arts, but reduces the training time by approximately two orders of magnitude, both for face-level and super-face-level, making it scale well for large datasets. Based on such notable improvement, we demonstrate the application of our method for fast online sequential learning for 3D shape segmentation at face level, as well as realtime sequential learning at super-face level.
  @cite_50: This paper presents a 3D-mesh segmentation algorithm based on a learning approach. A large database of manually segmented 3D-meshes is used to learn a boundary edge function. The function is learned using a classifier which automatically selects from a pool of geometric features the most relevant ones to detect candidate boundary edges. We propose a processing pipeline that produces smooth closed boundaries using this edge function. This pipeline successively selects a set of candidate boundary contours, closes them and optimizes them using a snake movement. Our algorithm was evaluated quantitatively using two different segmentation benchmarks and was shown to outperform most recent algorithms from the state-of-the-art.
  @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.
  @cite_10: Feature learning for 3D shapes is challenging due to the lack of natural paramterization for 3D surface models. We adopt the multi-view depth image representation and propose Multi-View Deep Extreme Learning Machine MVD-ELM to achieve fast and quality projective feature learning for 3D shapes. In contrast to existing multi-view learning approaches, our method ensures the feature maps learned for different views are mutually dependent via shared weights and in each layer, their unprojections together form a valid 3D reconstruction of the input 3D shape through using normalized convolution kernels. These lead to a more accurate 3D feature learning as shown by the encouraging results in several applications. Moreover, the 3D reconstruction property enables clear visualization of the learned features, which further demonstrates the meaningfulness of our feature learning.
summary: Existing supervised techniques rely on local features. The work by @cite_1 proposed a method for mesh segmentation where a large pool of geometric features are ranked using JointBoost so that the best features are used to describe specific segments. Similarly, the work by @cite_50 ranks a large pool of features in order to detect the optimal segment boundaries for a given mesh, and an extreme learning machine was trained to classify labels using one @cite_6 and two layers @cite_10 . However, supervised methods can perform poorly on very complex meshes, due to insufficient training data or large variations within label classes @cite_6 @cite_2 .