Error Analysis of Geometric Ellipse Detection Methods Due to Quantization

Abstract

Many geometric methods have been used extensively for detection of ellipses in images. Though the geometric methods have rigorous mathematical framework, the effect of quantization appears in various forms and introduces errors in the implementation of such models. This unexplored aspect of geometric methods is studied in this paper. We identify the various sources that can affect the accuracy of the geometric methods. Our results show that the choice of points used in geometric methods is a very crucial factor in the accuracy. If the curvature covered by the chosen points is low, then the error may be significantly high. We also show that if numerically computed tangents are used in the geometric methods, the accuracy of the methods is sensitive to the error in the computation of the tangents. Our analysis is used to propose a probability density function for the relative error of the geometric methods. Such distribution can be an important tool for determining practical parameters like the size of bins or clusters in the Hough transform. It can also be used to compare various methods and choose a more suitable method.