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arXiv · 2609.30955

Flow-TAG: Flow-based conditional latent transport for accurate spline approximation and data compression

Roman Pavelkin·Luis A. Zavala-Mondragon·Fons van der Sommen
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Abstract

Robust curve fitting is essential in computer-aided design for transforming noisy, discrete data into accurate geometric models that ensure numerical stability across engineering workflows. B-spline models have become the industry standard for this task, offering a flexible and reliable framework characterized by local control and smooth shape representation. This paper presents flow-TAG--a data-driven framework based on a generative flow model with a 1D U-Net backbone capable of mapping the geometry of a curve to the optimal parametrization for cubic B-splines. By leveraging learned geometric patterns, flow-TAG exhibits superior parameterization performance, robustness to noise in the input data, and strong generalization capability to previously unseen 2D and 3D curves drawn from distinct data distributions. Flow-TAG yields fitted curves that achieve the lower root-mean-square error (55% lower on average) and Hausdorff distance (52% lower on average) relative to state-of-the-art data-driven methods. In addition, we investigate the practical applicability of our generative framework in the compression of ECG signals for wearable devices. The proposed compression setup provides a compression ratio of 13 with the signal distortion of around 5%, which is acceptable in the field.

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Roman Pavelkin, Luis A. Zavala-Mondragon, Fons van der Sommen. 2026-09-25. Flow-TAG: Flow-based conditional latent transport for accurate spline approximation and data compression. https://arxiv.org/abs/2609.30955

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