Polygonal meshes provide an efficient representation for 3D shapes. They explicitly captureboth shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN , a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of MeshCNN on various learning tasks applied to 3D meshes.
We jointly embed shapes and images of three categories (chair, aeroplane and car) into a shared space. Distances between entities in the high-dimensional embedding space reflect object similarities between shapes and images (visualized by t-SNE here).
We present a shape segmentation method for complete and incomplete shapes. The key idea is to directly optimize the decomposition based on a characterization of the expected geometry of a part in a shape. Rather than setting the number of parts in advance, we search for the smallest number of parts that admit the geometric characterization of the parts. The segmentation is based on an intermediate-level analysis, where first the shape is decomposed into approximate convex components, which are then merged into consistent parts based on a nonlocal geometric signature. Our method is designed to handle incomplete shapes, represented by point clouds. We show segmentation results on shapes acquired by a range scanner, and an analysis of the robustness of our method to missing regions. Moreover, our method yields results that are comparable to state-of-the-art techniques evaluated on complete shapes.
We introduce a meta-representation that represents the essence of a family of shapes. The meta-representation learns the configurations of shape parts that are common across the family, and encapsulates this knowledge with a system of geometric distributions that encode relative arrangements of parts. Thus, instead of predefined priors, what characterizes a shape family is directly learned from the set of input shapes. The meta-representation is constructed from a set of co-segmented shapes with known correspondence. It can then be used in several applications where we seek to preserve the identity of the shapes as members of the family. We demonstrate applications of the meta-representation in exploration of shape repositories, where interesting shape configurations can be examined in the set; guided editing, where models can be edited while maintaining their familial traits; and coupled editing, where several shapes can be collectively deformed by directly manipulating the distributions in the meta-representation. We evaluate the efficacy of the proposed representation on a variety of shape collections.
Large datasets of 3D objects require an intuitive way to browse and quickly explore shapes from the collection. We present a dynamic map of shapes where similar shapes are placed next to each other. Similarity between 3D models exists in a high dimensional space which cannot be accurately expressed in a two dimensional map. We solve this discrepancy by providing a local map with pan capabilities and a user interface that resembles an online experience of navigating through geographical maps. As the user navigates through the map, new shapes appear which correspond to the specific navigation tendencies and interests of the user, while maintaining a continuous browsing experience. In contrast with state of the art methods which typically reduce the search space by selecting constraints or employing relevance feedback, our method enables exploration of large sets without constraining the search space, allowing the user greater creativity and serendipity. A user study evaluation showed a strong preference of users for our method over a standard relevance feedback method.
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