基于结构张量的N维图像总最小二乘最优分析信号
Total Least Square Optimal Analytic Signal by Structure Tensor for N-D images
AI总结：
本文提出基于结构张量的N维图像总最小二乘最优分析信号方法，用于自适应滤波器设计和奇点检测。
摘要：
我们通过结构张量生成分析信号，该方法为局部估计方向和尺度提供了总最小二乘最优向量。这些向量共同代表N维频率成分，确定了自适应的复杂探测滤波器。通过自适应滤波器与图像邻域的标量乘积获得N维分析信号，其包含邻域的方向、尺度、相位和振幅信息。ST分析信号f_A是连续且各向同性的，其扩展到N维是直接的。相位梯度可以表示为向量（瞬时频率）或张量。两者都是连续且各向同性的，而张量还保留了方向的连续性和保留了与向量表示相同的信息。张量表示也可以用于检测奇点。已证明使用已知相位图进行检测在2D中与相关于波物理中的等高线处理，包括光学和指纹测量。为了构建自适应滤波器，我们使用了Gabor滤波器家族成员作为探测函数，但也可以使用其他函数族来采样频谱，例如正交滤波器。还报告了与三种基线替代方案的比较——表示（单基因信号）、增强（单基因信号结合样条小波金字塔）和奇点检测（mindtct，广泛用于众多研究的指纹 minutia 检测器）——使用具有精确已知地面真相的图像进行比较，包括位置、方向、奇点类型（如适用）和波周期。
英文摘要：
We produce the analytic signal by using the Structure Tensor, which provides Total Least Squares optimal vectors for estimating orientation and scale locally. Together, these vectors represent N-D frequency components that determine adaptive, complex probing filters. The N-D analytic signal is obtained through scalar products of adaptive filters with image neighborhoods. It comprises orientation, scale, phase, and amplitude information of the neighborhood. The ST analytic signal $ f_A $ is continuous and isotropic, and its extension to N-D is straightforward. The phase gradient can be represented as a vector (instantaneous frequency) or as a tensor. Both are continuous and isotropic, while the tensor additionally preserves continuity of orientation and retains the same information as the vector representation. The tensor representation can also be used to detect singularities. Detection with known phase portraits has been demonstrated in 2-D with relevance to fringe pattern processing in wave physics, including optics and fingerprint measurements. To construct adaptive filters we have used Gabor filter family members as probing functions, but other function families can also be used to sample the spectrum, e.g., quadrature filters. A comparison to three baseline alternatives-in representation (Monogenic signal), enhancement (Monogenic signal combined with a spline-wavelet pyramid), and singularity detection (mindtct, a fingerprint minutia detector widely used in numerous studies)-is also reported using images with precisely known ground truths for location, orientation, singularity type (where applicable), and wave period.
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