On Determining Slope and Derivative of Curve Components in a Binary Image

This paper addresses the problem of estimating the slope of tangents to digital curves at interested points in a binary image. This kind of an objective could be otherwise accomplished by locally approximating the curve by a second order function and then differentiating the function, though such an effort has not been made so far due to the complexity of the method. Thinning has to be done as a pre-processing step for thick curves and this adds more complexity. A simple method based on principal components analysis (PCA) is presented, which can be used to find the local slope of curves in digital binary images as well the derivative of the function represented by the curve. The proposed technique could be used innovatively in several applications like pattern recognition, mathematical analysis and reconstruction of images with statistical data, used in research papers etc. Problems in the implementation of the method during intermediate stages are also discussed. The algorithm was implemented and tested using MATLAB 7.1. The experimental results show that the method is reasonably accurate and can be used with curves of varying line widths.