A rectilinear Gaussian model for estimating straight-line parameters

• A defocused edge can be represented by the rectilinear Gaussian model.
• Straight-line parameters can be estimated by both spatial and gray-scale information.
• Four parameters of straight line in an image can be estimated simultaneously.
• The presented approach outperforms the traditional one.

For characterizing straight lines in defocused images, a rectilinear Gaussian model (RGM) is proposed. Based on this model, a novel method for estimating the parameters of straight lines is presented. This method, called gray-scale least square (GLS) method, directly deals with gray-scale image data without requiring any preprocessing and hence no additional noise is introduced. Furthermore, the method is able to simultaneously estimate four parameters of straight lines by performing the algorithm only once, while two parameters can be typically estimated by traditional method. Besides this, all parameters are given in closed-form solution. In order to illustrate the effectiveness of RGM and the GLS method, the experiments are performed on a set of artificial images and natural images. The experimental results show that the GLS method outperforms the traditional method from the point of view of sensitivity to noise and accuracy of parameter estimation.