【摘要】 基于二种典型边缘的尺度空间边缘检测结果，分析实际计算过程中数字信号的最小分辨率对尺度因子进化的约束，导出了尺度因子对给定边缘和最小分辨率的关系不等式。该结果从实际计算的角度解释了尺度定理的产生原因，同时为多尺度边缘检测中尺度因子进化步长的选择提供了依据。更多还原

【Abstract】 Considering the edge detection results of two typical edges in scale space, we derived the limitation of the minimum resolution of a digital image to the scale factor. The extreme of the zero crossing monotonically decreases with the increase of the scale factor. The inequality, which must be satisfied by the minimum resolution and the scale factor for a given image, is given. The causality of the scale theorem generated in the multiscale analysis is explained in the practical calculation, which provides a theoretical basis for scale evolution selection in multiscale edge detection.更多还原