We desgin a novel fully convolutional network architecture for shapes, denoted by Shape Fully Convolutional Networks (SFCN). 3D shapes are represented as graph structures in the SFCN architecture, based on novel graph convolution and pooling operations, which are similar to convolution and pooling operations used on images. Meanwhile, to build our SFCN architecture in the original image segmentation fully convolutional network (FCN) architecture, we also design and implement a generating operation with bridging function. This ensures that the convolution and pooling operation we have designed can be successfully applied in the original FCN architecture. In this paper, we also present a new shape segmentation approach based on SFCN. Furthermore, we allow more general and challenging input, such as mixed datasets of different categories of shapes which can prove the ability of our generalisation. In our approach, SFCNs are trained triangles-to-triangles by using three low-level geometric features as input. Finally, the feature voting-based multi-label graph cuts is adopted to optimise the segmentation results obtained by SFCN prediction. The experiment results show that our method can effectively learn and predict mixed shape datasets of either similar or different characteristics, and achieve excellent segmentation results.
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. 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. Unsupervised co-analysis of a set of shapes is a difficult problem since the geometry of the shapes alone cannot always fully describe the semantics of the shape parts. In this paper, we propose a semi-supervised learning method where the user actively assists in the co-analysis by iteratively providing inputs that progressively constrain the system. We introduce a novel constrained clustering method based on a spring system which embeds elements to better respect their inter-distances in feature space together with the user-given set of constraints. We also present an active learning method that suggests to the user where his input is likely to be the most effective in refining the results. We show that each single pair of constraints affects many relations across the set. Thus, the method requires only a sparse set of constraints to quickly converge toward a consistent and error-free semantic labeling of the set. 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. This paper introduces a deep architecture for segmenting 3D objects into their labeled semantic parts. Our architecture combines image-based Fully Convolutional Networks (FCNs) and surface-based Conditional Random Fields (CRFs) to yield coherent segmentations of 3D shapes. The image-based FCNs are used for efficient view-based reasoning about 3D object parts. Through a special projection layer, FCN outputs are effectively aggregated across multiple views and scales, then are projected onto the 3D object surfaces. Finally, a surface-based CRF combines the projected outputs with geometric consistency cues to yield coherent segmentations. The whole architecture (multi-view FCNs and CRF) is trained end-to-end. Our approach significantly outperforms the existing state-of-the-art methods in the currently largest segmentation benchmark (ShapeNet). Finally, we demonstrate promising segmentation results on noisy 3D shapes acquired from consumer-grade depth cameras. We introduce projective analysis for semantic segmentation and labeling of 3D shapes. The analysis treats an input 3D shape as a collection of 2D projections, labels each projection by transferring knowledge from existing labeled images, and back-projects and fuses the labelings on the 3D shape. The image-space analysis involves matching projected binary images of 3D objects based on a novel bi-class Hausdorff distance. The distance is topology-aware by accounting for internal holes in the 2D figures and it is applied to piecewise-linearly warped object projections to compensate for part scaling and view discrepancies. Projective analysis simplifies the processing task by working in a lower-dimensional space, circumvents the requirement of having complete and well-modeled 3D shapes, and addresses the data challenge for 3D shape analysis by leveraging the massive available image data. A large and dense labeled set ensures that the labeling of a given projected image can be inferred from closely matched labeled images. We demonstrate semantic labeling of imperfect (e.g., incomplete or self-intersecting) 3D models which would be otherwise difficult to analyze without taking the projective analysis approach.