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摘 要
摘 要:目的:形状的表示和匹配是计算机视觉和模式识别领域的重要问题。在基于区域的形状表示方法中出现了一批典型的方法,包括Hu不变矩方法(Hu不变矩)、角径向变换方法(ART方法)、通用傅立叶描述子方法(GFD方法)、拉东柱状图方法(HRT方法)和多尺度积分不变量方法(MSII方法)等。由于这些方法出现的时间跨度长且在以往的对比研究中研究维度单一,因此需要对这些方法的综合性能做一个全面的比较分析和研究,为下一步的理论研究和实际应用提供方向和指导。方法:采用三个基准形状库,包括简单几何图形形状库、MPEG-7形状库和汽车商标形状库,从三个维度,包括检索得分、检索稳定性和方法的计算复杂度,使用加权综合评估模型对典型的基于区域的形状表示方法进行比较分析,综合评估各种方法的综合性能指标。结果:在综合性能上GFD方法具有最优的效果,其次是ART方法;由于HRT方法在匹配计算阶段具有较高的时间复杂度,在大规模形状库匹配的场景下性能会下降;Hu不变矩和MSII方法的实验效果均不理想。通过比较研究还发现,将形状正交投影到正交基函数是提取形状视觉特征的有效方式。进一步猜想,将图像正交投影到正交基函数也是提取图像视觉特征的有效方式。因此,未来的研究中,寻找理想的正交基函数是提取形状乃至图像视觉特征的重要研究方向。结论:在五种比较研究的方法中,GFD方法和ART方法在综合效果要好于HRT方法、Hu不变矩方法和MSII方法,并且寻找理想的正交基函数是未来形状表示的重要研究方向。
Comparative study of classic region-based shape descriptors

Wu Shaogen()

Abstract:Objective: Shape representation and shape matching are the basic tasks in computer vision and pattern recognition. Among all the region-based methods, they are a bunch of classic methods, which include Hu moment Invariants method (Hu), angular radial transform method (ART), generic Fourier descriptor method (GFD), histogram of Radon transform method (HRT), and multi-scale integral invariant method (MSII). Because of the long time spans between these methods and only a simple factor used in comparative studies, we need a comprehensive comparative study of all the mentioned methods, which will help us in application engineering and in future studies. Method: Based on three shape databases, including a simple geometry shape database, MPEG-7 shape database, and vehicle trademark shape database, and from three aspects, including the retrieval scores, the standard deviations of retrieval, and computation complexity, we evaluated all the five mentioned methods. A weighted formula, which take all the three factors into consideration is also defined in order to measure their comprehensive performances. Result: The GFD method has the best performance, and ART the next. Because HRT method has higher complexity in matching phase than other methods, it can degrade in such situation with large number of shapes. The performance of Hu method and MSII method are not satisfied in all our experiments. We also find that the visual features of a shape can be captured practically by the method of projecting shape onto a basis of orthogonal base functions. Based on this finding, we also guess that the visual features of image can also be captured practically by the same projection method. Conclusion: Among all the evaluated region-based methods, GFD method and ART method have the best performance. Finding new basis of orthogonal base functions is a fruitful direction in shape visual feature extraction as well as in image visual feature extraction.