Abstract: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.

The authors propose a method that describes line structures in given 3D medical images by estimating the values of model parameters: A Gaussian function is employed as the model function and the values of the parameters are estimated by means of a weighted integral method, in which you can estimate the parameter values by solving a system of linear equations of parameters which are derived from differential equations that are satisfied by the Gaussian model function. Different from many other model-based methods for the description, the proposed method requires no parameter sweep and hence can estimate the parameter values efficiently. Once you estimate the parameter values, you can describe the location, the orientation and the scale of line structures in given 3D images. Experimental results with artificial 3D images and with clinical X-ray CT ones demonstrate the estimation performance of the proposed method.