arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1901.00616cs.LGcs.CVstat.ML
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体积卷积:单位球中的自动表示学习

Volumetric Convolution: Automatic Representation Learning in Unit Ball

Australian National University(澳大利亚国立大学)

Sameera Ramasinghe, Salman Khan, Nick Barnes

摘要:

卷积是一种在深度网络中使用分层获得抽象特征表示的有效技术。虽然在欧几里得几何中执行卷积相当简单,但将其扩展到其他拓扑空间--例如球体($\mathbb{S}^2$)或单位球($\mathbb{B}^3$)--需要独特的挑战。在这项工作中,我们提出了一种新的“\emph{volumetric convolution}”操作,可以有效地卷积任意函数在$\mathbb{B}^3$。我们基于Zernike多项式为\emph{volumetric convolution}开发了一个理论框架,并将其有效地实现为深度网络的可微分和易于插入的层。此外,我们的配方导致推导出一个新的公式来衡量一个函数的对称性在$\mathbb{B}^3$围绕任意轴,这是有用的三维形状分析任务。我们在一个可能的用例上证明了所提出的体积卷积操作的有效性,即,3D物体识别任务。

英文摘要:

Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere ($\mathbb{S}^2$) or a unit ball ($\mathbb{B}^3$)---entails unique challenges. In this work, we propose a novel `\emph{volumetric convolution}' operation that can effectively convolve arbitrary functions in $\mathbb{B}^3$. We develop a theoretical framework for \emph{volumetric convolution} based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer for deep networks. Furthermore, our formulation leads to derivation of a novel formula to measure the symmetry of a function in $\mathbb{B}^3$ around an arbitrary axis, that is useful in 3D shape analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on a possible use-case i.e., 3D object recognition task.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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