The Signal Multi-Vector
The Signal Multi-Vector
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DOI：
10.1007/s10851-010-0197-3
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发表时间：
2010-06
影响因子：
2
通讯作者：
Lennart Wietzke;G. Sommer
中科院分区：
文献类型：
--
作者：
Lennart Wietzke;G. Sommer
这项工作涵盖了基于局部相位的图像分析的一个基本问题：经典一维分析信号的各向同性推广到二维。解析信号可以分析一维信号的局部相位和幅度信息。二维单基因信号可以提取局部相位、幅度和附加的方向信息，但本质上受一维信号的限制。在二维图像信号的情况下，单基因信号能够对线和边缘进行旋转不变性分析。在这项工作中，我们提出了二维解析信号作为解析信号和二维单基因信号的一种新的推广。对于二维图像信号，二维分析信号可以在一个统一的框架内对线、边、角和结点进行各向同性分析。此外，我们表明二维信号被定义在齐次共形空间的三维射影子空间上，这提供了信号的描述性几何解释，为几何和二维图像信号的关系提供了新的见解。最后，我们将引入一种新的代数信号表示，它可以被视为经典矩阵和张量的替代和完全同构表示。我们将展示不需要转向技术的各向同性本质二维图像分析的解决方案。
This work covers a fundamental problem of local phase based image analysis: the isotropic generalization of the classical 1D analytic signal to two dimensions. The analytic signal enables the analysis of local phase and amplitude information of 1D signals. Local phase, amplitude and additional orientation information can be extracted by the 2D monogenic signal with the restriction to intrinsically 1D signals. In case of 2D image signals the monogenic signal enables the rotationally invariant analysis of lines and edges. In this work we present the 2D analytic signal as a novel generalization of both the analytic signal and the 2D monogenic signal. In case of 2D image signals the 2D analytic signal enables the isotropic analysis of lines, edges, corners and junctions in one unified framework. Furthermore, we show that 2D signals are defined on a 3D projective subspace of the homogeneous conformal space which delivers a descriptive geometric interpretation of signals providing new insights on the relation of geometry and 2D image signals. Finally, we will introduce a novel algebraic signal representation, which can be regarded as an alternative and fully isomorphic representation to classical matrices and tensors. We will show the solution of isotropic intrinsically 2D image analysis without the need of steering techniques.