离散图象的Pascal三角形：定义、性质及其在形状分析中的应用
The Pascal Triangle of a Discrete Image: Definition, Properties and Application to Shape Analysis
摘要：
我们定义的帕斯卡三角形的离散（灰度）图像作为一个金字塔的安排复值的时刻，我们探讨其几何意义。特别是，我们表明，该三角形的行k的条目对应于图像的Radon变换的k阶矩的傅立叶级数系数。平面上的群作用可以自然地延拓到帕斯卡三角形的入口上。我们研究了一些常见的群作用，如旋转和反射的延伸，我们提出了简单的测试，检测这些群作用下的等价性和自等价性。这项工作的激励应用是表征图像上对象的几何形状的问题，例如通过检测近似对称性。
英文摘要：
We define the Pascal triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal triangle. We study the prolongation of some common group actions, such as rotations and reflections, and we propose simple tests for detecting equivalences and self-equivalences under these group actions. The motivating application of this work is the problem of characterizing the geometry of objects on images, for example by detecting approximate symmetries.
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