1,217 research outputs found
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
Progressive Shape-Distribution-Encoder for 3D Shape Retrieval
Since there are complex geometric variations with 3D shapes, extracting efficient 3D shape features is one of the most challenging tasks in shape matching and retrieval. In this paper, we propose a deep shape descriptor by learning shape distributions at different diffusion time via a progressive shape-distribution-encoder (PSDE). First, we develop a shape distribution representation with the kernel density estimator to characterize the intrinsic geometry structures of 3D shapes. Then, we propose to learn a deep shape feature through an unsupervised PSDE. Specially, the unsupervised PSDE aims at modeling the complex non-linear transform of the estimated shape distributions between consecutive diffusion time. In order to characterize the intrinsic structures of 3D shapes more efficiently, we stack multiple PSDEs to form a network structure. Finally, we concatenate all neurons in the middle hidden layers of the unsupervised PSDE network to form an unsupervised shape descriptor for retrieval. Furthermore, by imposing an additional constraint on the outputs of all hidden layers, we propose a supervised PSDE to form a supervised shape descriptor, where for each hidden layer the similarity between a pair of outputs from the same class is as small as possible and the similarity between a pair of outputs from different classes is as large as possible. The proposed method is evaluated on three benchmark 3D shape datasets with large geometric variations, i.e., McGill, SHREC’10 ShapeGoogle and SHREC’14 Human datasets, and the experimental results demonstrate the superiority of the proposed method to the existing approaches
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