Document Zbl 1547.68681

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Math. Imaging Vis.</a> <a href="/?q=in%3A516647" title="Articles in this Issue">66, No. 3, 246-270 (2024)</a>. </div> <div class="abstract">Summary: Scale invariance of an algorithm refers to its ability to treat objects equally independently of their size. For neural networks, scale invariance is typically achieved by data augmentation. However, when presented with a scale far outside the range covered by the training set, neural networks may fail to generalize. Here, we introduce the Riesz network, a novel scale- invariant neural network. Instead of standard 2d or 3d convolutions for combining spatial information, the Riesz network is based on the Riesz transform which is a scale-equivariant operation. As a consequence, this network naturally generalizes to unseen or even arbitrary scales in a single forward pass. As an application example, we consider detecting and segmenting cracks in tomographic images of concrete. In this context, ‘scale’ refers to the crack thickness which may vary strongly even within the same sample. To prove its scale invariance, the Riesz network is trained on one fixed crack width. We then validate its performance in segmenting simulated and real tomographic images featuring a wide range of crack widths. An additional experiment is carried out on the MNIST Large Scale data set.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7904655">Cited in <strong>2</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T07" title="MSC2020">68T07</a> </td> <td class="space"> Artificial neural networks and deep learning </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B20" title="MSC2020">42B20</a> </td> <td class="space"> Singular and oscillatory integrals (Calderón-Zygmund, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A44A15" title="MSC2020">44A15</a> </td> <td class="space"> Special integral transforms (Legendre, Hilbert, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T45" title="MSC2020">68T45</a> </td> <td class="space"> Machine vision and scene understanding </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ascale+invariance">scale invariance</a>; <a href="/?q=ut%3ARiesz+transform">Riesz transform</a>; <a href="/?q=ut%3Aneural+networks">neural networks</a>; <a href="/?q=ut%3Acrack+segmentation">crack segmentation</a>; <a href="/?q=ut%3Ageneralization+to+unseen+scales">generalization to unseen scales</a>; <a href="/?q=ut%3Acomputed+tomography">computed tomography</a>; <a href="/?q=ut%3Acracks+in+tomographic+images+of+concrete">cracks in tomographic images of concrete</a></div> <div class="software"> <h3>Software:</h3><a href="/software/33176">U-Net</a>; <a href="/software/33901">RFSIM</a>; <a href="/software/22205">Adam</a>; <a href="/software/27075">ScatNet</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1547.68681" data-ciurl="/ci/07904655" data-biburl="/bibtex/07904655.bib" data-amsurl="/amsrefs/07904655.bib" data-xmlurl="/xml/07904655.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07904655.pdf" title="Zbl 1547.68681 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s10851-024-01171-4" aria-label="DOI for “Riesz networks: scale-invariant neural networks in a single forward pass”" title="10.1007/s10851-024-01171-4">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2305.04665"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Lindeberg, T., Feature detection with automatic scale selection, Int. 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