Mashhadi Peyman Sheikholharam, Shoorehdeli Mahdi Aliyari, Teshnehlab Mohammad
J Opt Soc Am A Opt Image Sci Vis. 2013 Sep 1;30(9):1796-805. doi: 10.1364/JOSAA.30.001796.
Many successful methods in various vision tasks rely on statistical analysis of visual patterns. However, we are interested in covering the gap between the underlying mathematical representation of the visual patterns and their statistics. With this general trend, in this paper a relationship between phase structure of a class of patterns and their moments after and before filtering have been considered. First, a general formula between the phase structure and moments of the images is obtained. Second, a theorem is developed that states under which conditions two visual patterns with the same frequencies but different phases have the same moments up to a certain moment. Finally, a theorem is developed that explains, given a set of filters, under which conditions two visual patterns with both different frequencies and different phases have the same subband statistics.
许多在各种视觉任务中成功的方法都依赖于对视觉模式的统计分析。然而，我们感兴趣的是弥补视觉模式的潜在数学表示与其统计之间的差距。基于这一总体趋势，本文考虑了一类模式的相位结构与其滤波前后矩之间的关系。首先，得到了图像的相位结构与矩之间的通用公式。其次，推导出一个定理，该定理指出在哪些条件下，具有相同频率但不同相位的两个视觉模式在某一时刻之前具有相同的矩。最后，推导出一个定理，该定理解释了给定一组滤波器，在哪些条件下，具有不同频率和不同相位的两个视觉模式具有相同的子带统计。
