mlsanityData to 14 Oct 2026

Rate-optimal neural boundary detection from unlabeled noisy images

arXiv 2606.00715 ↗First posted 30 May 2026stat.ME stat.MLcited by 0

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Abstract (arXiv)

We study boundary detection for unlabeled noisy images from a statistical perspective. The aim is to recover an unknown object region from raw intensity observations without pixel-wise annotating labels or a parametric model for the intensity distributions. Motivated by robust Gibbs posterior approaches based on thresholded misclassification losses, we propose a continuous hinge-type surrogate loss for boundary detection. The proposed loss is amenable to gradient-based optimization and can be combined with deep neural networks to represent complex object boundaries. We prove that the proposed loss function is Fisher consistent under a mild separation assumption and obtain a calibration inequality linking excess surrogate risk to the symmetric difference error of the estimated region. Under a piecewise smooth boundary model, we prove that the resulting deep neural network estimator achieves the minimax-optimal boundary recovery rate, up to logarithmic factors. The piecewise smooth formulation accommodates boundaries with corners and kinks, thereby extending beyond globally smooth boundary models. Numerical experiments demonstrate that the proposed method accurately and stably recovers object boundaries across a range of noise levels and shape configurations, and compares favorably with existing unsupervised boundary detection methods.

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References · 20

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8 more
  1. 2022Adaptive deep learning for nonlinear time series modelscited by 11
  2. 2023Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inferencecited by 9
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  8. 2025Optimal Convergence Rates of Deep Neural Network Classifierscited by 1

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