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利用几何代数进行线段模型匹配和运动估计

黄良明,彭立中,程民德(北京大学数学科学学院,北京 100871)

摘 要
首先探讨了Clifford代数(几何代数)在计算机视觉中的应用,并得到了2D与3D旋转的统一表达公式,进而探讨了该公式在直线模型匹配和运动估计中的应用;在改进2D多角弧匹配算法的基础上,提出了一个同时进行线段模型的匹配和运动估计的算法。该算法通过最小化模型线段与被检测线段间的距离(距离函数定义为对应点间欧氏距离的积分)而求得的最佳运动估计中的旋转,可由一个矩阵的奇异值分解来表示,从而为首次同时解决这两个问题,进行了初步尝,且该算法不受维数限制。最后的模拟实验结果表明,该算法效果良好。
关键词
Matching and Estimating Motion of Line Model Using Geometric Algebra

HUANG Liang ming,PENG Li zhong,CHENG Min de()

Abstract
Matching and estimating motion are basic problem of computer vision. Classical methods are first to find the matching point (or line etc.) and then estimating motion. This paper discussed the application of Clifford algebra (Geometric algebra) in the area of computer vision, presented the uniform formula of 2D and 3D rotation and their application in matching and estimation motion of the line segments model. Based on improving the algorithm of matching 2D polygonal arcs in reference [4], this paper provides an algorithm solve both of matching and estimating motion simultaneously using Clifford algebra. Via minimizing the distance between the model and the detected characteristic (the distance measure is defined as the integral of the Euclidean distance between corresponding points), The algorithm results with that the rotation of the best estimation can be represented by the SVD of a matrix. To our knowledge, this paper is the first investigation to solve both of them. And the algorithm is free from the dimension of the line segment model. Synthetic data has been used to test the algorithm, and excellent result has been obtained.
Keywords
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