用结构一致的相位估计提升图像特征提取精度，尤其在低信噪比下表现优异。
A Structurally Coherent Spatial Phase Estimate
- 基于结构多向量改进传统相位估计方法，增强方向估计鲁棒性
- 提出局部方向方差质量图，在信噪比≤1时仍保持高精度
- 适用于指纹细粒度配准等需精确相位分析的场景
单生信号（MS）由Felsberg和Sommer提出，也称漩涡算子，是二维图像中调幅调相信号的直接幅度与相位解调工具，但仅适用于内在一维（i1D）信号。Felsberg博士论文引入结构多向量（SMV），可建模内在二维（i2D）结构。尽管MS被广泛应用，但SMV使用较少。本文认为，在标准i1D图像特征提取中，SMV因方向估计更鲁棒而更合适，并扩展了Held等人提出的可旋转小波框架以支持SMV特性。进一步提出基于局部方向方差的质量图，强调结构一致的图像块。由此得到的多尺度相位估计在信噪比≤1时仍表现良好。在多个合成相位估计任务及与二维相位解调相关的细粒度指纹注册任务上进行了评估。
原文摘要 · Abstract (English)
The monogenic signal (MS) was introduced by Felsberg and Sommer, and independently by Larkin under the name vortex operator. It is a two-dimensional (2D) analog of the well-known analytic signal, and allows for direct amplitude and phase demodulation of (amplitude and phase) modulated images so long as the signal is intrinsically one-dimensional (i1D). Felsberg's PhD dissertation also introduced the structure multivector (SMV), a model allowing for intrinsically 2D (i2D) structure. While the monogenic signal has become a well-known tool in the image processing community, the SMV is little used, although even in the case of i1D signals it provides a more robust orientation estimation than the MS. We argue the SMV is more suitable in standard i1D image feature extraction due to the this improvement, and extend the steerable wavelet frames of Held et al. to accommodate the additional features of the SMV. We then propose a novel quality map based on local orientation variance which values structurally coherent patches. This yields a multiscale phase estimate which performs well even when signal to noise ratio (SNR) is $\le$ 1. The performance is evaluated on several synthetic phase estimation tasks as well as on a fine-scale fingerprint registration task related to the 2D phase demodulation problem.
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