论文标题
线性对称张量 - 指定建模的分析信号阶段$ n-d $ $ n-d $
Analytic Signal Phase in $N-D$ by Linear Symmetry Tensor--fingerprint modeling
论文作者
论文摘要
我们透露，分析信号阶段及其梯度在$ 2-D $和更高的维度上迄今未研究的不连续性。缺点可能导致严重的人工制品，而问题不存在于$ 1-D $的信号中。直接在计算机视觉和生物识别识别中直接使用Gabor阶段或其梯度，例如在有影响力的研究中所做的\ cite {fleet90，wiskott1997face}可能会产生不需要的结果，除非与我们相似的特殊图像，否则会不会被忽略。我们建议使用线性对称阶段，而不是分析信号阶段，依赖于多组Gabor过滤器，但使用可忽略的计算附加组件作为一种补救措施。与分析信号的梯度大小相比，该阶段的梯度幅度是连续的，而如果线性对称张量替代梯度矢量，则保证该相的梯度方向的连续性。建议的阶段还具有内置的自动比例估计器，可用于通过多尺度处理对模式的强大检测。我们在合成的指纹图像上展示了关键的概念，其中关于瞬时频率，（比例\＆方向）的基础真相，并且相位均以有利的结果。还报道了与基线替代方案的比较。为此，一个新型的多尺度细节模型，其中少细节参数的位置，方向和尺度是可转让的，也没有创建无法控制的细节。这是一个有用的工具，可减少具有可解释行为的细节检测方法的发展时间。一个揭示的结果是，细节方向不是仅由线性相确定，而是彼此之间的确定，并且必须纠正影响以获得可置换性和准确的地面真理。基本结论很容易转移到$ n-d $，以及无关的应用程序，例如立体声中的光流或视差估计。
We reveal that the Analytic Signal phase, and its gradient have a hitherto unstudied discontinuity in $2-D $ and higher dimensions. The shortcoming can result in severe artifacts whereas the problem does not exist in $1-D $ signals. Direct use of Gabor phase, or its gradient, in computer vision and biometric recognition e.g., as done in influential studies \cite{fleet90,wiskott1997face}, may produce undesired results that will go unnoticed unless special images similar to ours reveal them. Instead of the Analytic Signal phase, we suggest the use of Linear Symmetry phase, relying on more than one set of Gabor filters, but with a negligible computational add-on, as a remedy. Gradient magnitudes of this phase are continuous in contrast to that of the analytic signal whereas continuity of the gradient direction of the phase is guaranteed if Linear Symmetry Tensor replaces gradient vector. The suggested phase has also a built-in automatic scale estimator, useful for robust detection of patterns by multi-scale processing. We show crucial concepts on synthesized fingerprint images, where ground truth regarding instantaneous frequency, (scale \& direction), and phase are known with favorable results. A comparison to a baseline alternative is also reported. To that end, a novel multi-scale minutia model where location, direction, and scale of minutia parameters are steerable, without the creation of uncontrollable minutia is also presented. This is a useful tool, to reduce development times of minutia detection methods with explainable behavior. A revealed consequence is that minutia directions are not determined by the linear phase alone, but also by each other and the influence must be corrected to obtain steerability and accurate ground truths. Essential conclusions are readily transferable to $N-D $, and unrelated applications, e.g. optical flow or disparity estimation in stereo.
