On the detection of feature on the line segment by using cross correlation

We can regard the planer figure as the complex valued function. We analyze a line figure by analyzing the complex function instead of processing it directly. The complex function is assumed to be periodic in this theory. We report the method in which the function that represents a non-closed line segment is made to be periodic. We describe of similarity of line segment and feature detection method by using the cross correlation of the complex valued functions which represent the line figures. The similarity is invariant to the size and rotation. This feature detection method can extract the various features from fine level to coarse level. This method is discussed theoretically and the experiment is reported. In the experiment, the similarities of figures are calculated and the local feature of the objective line figure are detected. We analyzed the contour figure by the features in various level.