arXiv:2503.04507v2 Announce Type: replace-cross Abstract: The geometry of an object plays a vital role in modulating its interactions with the physical world. It nevertheless remains difficult to describe geometric information numerically for the purposes of statistical inference or classification tasks. Here, we introduce a new topological transform which leverages directional piecewise-linear Morse theory to quantify the geometry of an embedded object by cataloguing critical points across multiple height-functions. The output of this Morse transform records both the heights and the local top
The paper was published on arXiv, indicating ongoing research and development in computational AI and geometric analysis, leveraging recent advancements in topological data analysis.
This research introduces a novel method for numerically describing geometric information, which is crucial for statistical inference and classification tasks, potentially enhancing AI's understanding of physical objects.
The Morse transform offers a new tool for quantifying object geometry, which could improve the performance and robustness of AI systems in fields like computer vision, robotics, and scientific modeling.
- · AI researchers
- · Robotics companies
- · Computer vision developers
- · Materials science
Improved geometric understanding in AI models, leading to more accurate object recognition and manipulation.
Enhanced capabilities for AI in design, manufacturing, and autonomous systems requiring precise physical interaction.
Accelerated development of AI for complex scientific simulations and drug discovery where molecular geometry is paramount.
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Read at arXiv cs.LG