2013 Volume 5 Pages 70-74
We propose a new method that efficiently and accurately estimates the parameters of the Gaussian function that describes the given local image profiles. The Gaussian function is non-linear with respect to the parameters to be estimated, and this non-linearity makes their efficient and accurate estimation difficult. In our proposed method, the weighted integral method is introduced to linearize the parameter estimation problem: A system of differential equations is firstly derived that is satisfied by the Gaussian function and that is linear with respect to the parameters. The system is then converted to that of integral equations. Given a local sub-window of the image, one can obtain the system of integral equations and estimate the parameters of the Gaussian that describe the appearance in the sub-window by solving the linear system of the parameters. Experimental results showed that our proposed method estimates the parameters more efficiently and accurately than existing state-of-the-art methods.