{"paper":{"title":"Volumetric Convolution: Automatic Representation Learning in Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Nick Barnes, Salman Khan, Sameera Ramasinghe","submitted_at":"2019-01-03T05:53:25Z","abstract_excerpt":"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 efficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.00616","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}