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.