A principled representation of elongated structures using heatmaps
Abstract The detection of elongated structures like lines or edges is an essential component in semantic image analysis. Classical approaches that rely on significant image gradients quickly reach their limits when the structure is context-dependent, amorphous, or not directly visible. This study in...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-09-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-41221-2 |
| _version_ | 1797560028344877056 |
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| author | Florian Kordon Michael Stiglmayr Andreas Maier Celia Martín Vicario Tobias Pertlwieser Holger Kunze |
| author_facet | Florian Kordon Michael Stiglmayr Andreas Maier Celia Martín Vicario Tobias Pertlwieser Holger Kunze |
| author_sort | Florian Kordon |
| collection | DOAJ |
| description | Abstract The detection of elongated structures like lines or edges is an essential component in semantic image analysis. Classical approaches that rely on significant image gradients quickly reach their limits when the structure is context-dependent, amorphous, or not directly visible. This study introduces a principled mathematical description of elongated structures with various origins and shapes. Among others, it serves as an expressive operational description of target functions that can be well approximated by Convolutional Neural Networks. The nominal position of a curve and its positional uncertainty are encoded as a heatmap by convolving the curve distribution with a filter function. We propose a low-error approximation to the expensive numerical integration by evaluating a distance-dependent function, enabling a lightweight implementation with linear time complexity. We analyze the method’s numerical approximation error and behavior for different curve types and signal-to-noise levels. Application to surgical 2D and 3D data, semantic boundary detection, skeletonization, and other related tasks demonstrate the method’s versatility at low errors. |
| first_indexed | 2024-03-10T17:53:37Z |
| format | Article |
| id | doaj.art-337d457635e047d8b4241937143376dd |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-10T17:53:37Z |
| publishDate | 2023-09-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-337d457635e047d8b4241937143376dd2023-11-20T09:15:34ZengNature PortfolioScientific Reports2045-23222023-09-0113111910.1038/s41598-023-41221-2A principled representation of elongated structures using heatmapsFlorian Kordon0Michael Stiglmayr1Andreas Maier2Celia Martín Vicario3Tobias Pertlwieser4Holger Kunze5Pattern Recognition Lab, Friedrich-Alexander Universität Erlangen-NürnbergOptimization Group, Institute of Mathematical Modelling, Analysis and Computational Mathematics, University of WuppertalPattern Recognition Lab, Friedrich-Alexander Universität Erlangen-NürnbergPattern Recognition Lab, Friedrich-Alexander Universität Erlangen-NürnbergPattern Recognition Lab, Friedrich-Alexander Universität Erlangen-NürnbergPattern Recognition Lab, Friedrich-Alexander Universität Erlangen-NürnbergAbstract The detection of elongated structures like lines or edges is an essential component in semantic image analysis. Classical approaches that rely on significant image gradients quickly reach their limits when the structure is context-dependent, amorphous, or not directly visible. This study introduces a principled mathematical description of elongated structures with various origins and shapes. Among others, it serves as an expressive operational description of target functions that can be well approximated by Convolutional Neural Networks. The nominal position of a curve and its positional uncertainty are encoded as a heatmap by convolving the curve distribution with a filter function. We propose a low-error approximation to the expensive numerical integration by evaluating a distance-dependent function, enabling a lightweight implementation with linear time complexity. We analyze the method’s numerical approximation error and behavior for different curve types and signal-to-noise levels. Application to surgical 2D and 3D data, semantic boundary detection, skeletonization, and other related tasks demonstrate the method’s versatility at low errors.https://doi.org/10.1038/s41598-023-41221-2 |
| spellingShingle | Florian Kordon Michael Stiglmayr Andreas Maier Celia Martín Vicario Tobias Pertlwieser Holger Kunze A principled representation of elongated structures using heatmaps Scientific Reports |
| title | A principled representation of elongated structures using heatmaps |
| title_full | A principled representation of elongated structures using heatmaps |
| title_fullStr | A principled representation of elongated structures using heatmaps |
| title_full_unstemmed | A principled representation of elongated structures using heatmaps |
| title_short | A principled representation of elongated structures using heatmaps |
| title_sort | principled representation of elongated structures using heatmaps |
| url | https://doi.org/10.1038/s41598-023-41221-2 |
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