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Register a new userAWCD: An Efficient Point Cloud Processing Approach via Wasserstein Curvature
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Added by
Yihao Luo
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In this paper, we introduce the adaptive Wasserstein curvature denoising (AWCD), an original processing approach for point cloud data. By collecting curvatures information from Wasserstein distance, AWCD consider more precise structures of data and preserves stability and effectiveness even for data with noise in high density. This paper contains some theoretical analysis about the Wasserstein curvature and the complete algorithm of AWCD. In addition, we design digital experiments to show the denoising effect of AWCD. According to comparison results, we present the advantages of AWCD against traditional algorithms.
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Given restrictions on the availability of data, active learning is the process of training a model with limited labeled data by selecting a core subset of an unlabeled data pool to label. Although selecting the most useful points for training is an optimization problem, the scale of deep learning data sets forces most selection strategies to employ efficient heuristics. Instead, we propose a new integer optimization problem for selecting a core set that minimizes the discrete Wasserstein distance from the unlabeled pool. We demonstrate that this problem can be tractably solved with a Generalized Benders Decomposition algorithm. Our strategy requires high-quality latent features which we obtain by unsupervised learning on the unlabeled pool. Numerical results on several data sets show that our optimization approach is competitive with baselines and particularly outperforms them in the low budget regime where less than one percent of the data set is labeled.
We present a new versatile building block for deep point cloud processing architectures that is equally suited for diverse tasks. This building block combines the ideas of spatial transformers and multi-view convolutional networks with the efficiency of standard convolutional layers in two and three-dimensional dense grids. The new block operates via multiple parallel heads, whereas each head differentiably rasterizes feature representations of individual points into a low-dimensional space, and then uses dense convolution to propagate information across points. The results of the processing of individual heads are then combined together resulting in the update of point features. Using the new block, we build architectures for both discriminative (point cloud segmentation, point cloud classification) and generative (point cloud inpainting and image-based point cloud reconstruction) tasks. The resulting architectures achieve state-of-the-art performance for these tasks, demonstrating the versatility and universality of the new block for point cloud processing.
Most audio processing pipelines involve transformations that act on fixed-dimensional input representations of audio. For example, when using the Short Time Fourier Transform (STFT) the DFT size specifies a fixed dimension for the input representation. As a consequence, most audio machine learning models are designed to process fixed-size vector inputs which often prohibits the repurposing of learned models on audio with different sampling rates or alternative representations. We note, however, that the intrinsic spectral information in the audio signal is invariant to the choice of the input representation or the sampling rate. Motivated by this, we introduce a novel way of processing audio signals by treating them as a collection of points in feature space, and we use point cloud machine learning models that give us invariance to the choice of representation parameters, such as DFT size or the sampling rate. Additionally, we observe that these methods result in smaller models, and allow us to significantly subsample the input representation with minimal effects to a trained model performance.
Point cloud processing is very challenging, as the diverse shapes formed by irregular points are often indistinguishable. A thorough grasp of the elusive shape requires sufficiently contextual semantic information, yet few works devote to this. Here we propose DensePoint, a general architecture to learn densely contextual representation for point cloud processing. Technically, it extends regular grid CNN to irregular point configuration by generalizing a convolution operator, which holds the permutation invariance of points, and achieves efficient inductive learning of local patterns. Architecturally, it finds inspiration from dense connection mode, to repeatedly aggregate multi-level and multi-scale semantics in a deep hierarchy. As a result, densely contextual information along with rich semantics, can be acquired by DensePoint in an organic manner, making it highly effective. Extensive experiments on challenging benchmarks across four tasks, as well as thorough model analysis, verify DensePoint achieves the state of the arts.
State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the geometry of the classification landscape and decision boundaries. We show in particular that adversarial training leads to a significant decrease in the curvature of the loss surface with respect to inputs, leading to a drastically more linear behaviour of the network. Using a locally quadratic approximation, we provide theoretical evidence on the existence of a strong relation between large robustness and small curvature. To further show the importance of reduced curvature for improving the robustness, we propose a new regularizer that directly minimizes curvature of the loss surface, and leads to adversarial robustness that is on par with adversarial training. Besides being a more efficient and principled alternative to adversarial training, the proposed regularizer confirms our claims on the importance of exhibiting quasi-linear behavior in the vicinity of data points in order to achieve robustness.
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