arXiv:2511.19706eess.IVcs.CV2025-11被引 1

提出一种旋转不变的图像描述符,兼具信息完整与计算高效。

Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor

  • 基于频域构造复数向量,保留图像除方向外全部信息
  • 理论证明其可逆性及对噪声的鲁棒性,数值近似精度有保障
  • 适合需要旋转不变性的图像识别与重建任务

旋转不变性是计算机视觉中的基本需求。传统方法依赖手工设计的旋转不变表示,虽简洁可解释但表达能力有限;近年深度模型通过学习实现旋转不变性,虽性能强但效率低、难解释。本文提出选择性盘形双谱(SDB),一种复值旋转不变向量,保留图像除方向外的所有信息。主要贡献包括:提出SDB及其逆变换、降低空间与计算复杂度(相比全盘双谱)、推导其在噪声下的期望与方差;同时提出数值近似算法,并提供精度与旋转不变性的理论保证。实验验证了SDB在分类任务中对旋转的不变性及抗噪能力,并应用于旋转图像的多参考对齐重建。

原文摘要 · Abstract (English)

Rotation invariance is a fundamental requirement across many computer vision tasks. Historically, this inductive bias has been encoded through hand-crafted rotation-invariant representations. These are compact, interpretable, and fast to compute, but they come at the cost of descriptive power. More recently, architectures achieve inductive bias through learned representations. These are highly descriptive and achieve strong empirical performance, at the cost of efficiency and interpretability. In this work, we propose an alternative at the intersection of both paradigms. We introduce the selective disk bispectrum (SDB), a complex-valued rotation-invariant vector that preserves all information about the image except its orientation. Our key theoretical contributions are the selective disk bispectrum, its inversion, its (reduced) spatial and computational complexities (compared to the full disk bispectrum), and its expectation and variance under noise. Furthermore, we propose a numerical SDB approximation and provide theoretical guarantees for its accuracy and rotation invariance. Empirically, we validate SDB's invariance and robustness to noise classification tasks. We test our reconstruction algorithm on multi-reference alignment of rotated images.

图像描述符旋转不变性频域特征复数表示

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