A modified version of the Cotte. Lions, Morel and Coll theory for image selective smoothing and edge detection is proposed. Comparing with their model, the most important advantage of this modification is that the convolution with Gaussian processes in the filtering process is replaced by solving an initial-boundary value problem for the heat equation, which simplifies the numerical scheme to some extent. Numerical experiments on natural images are presented for this model. A modified version of the Cotte. Lions, Morel and Coll theory for image selective smoothing and edge detection is proposed. Comparing with their model, the most important advantage of this modification is that the convolution with Gaussian processes in the filtering process is replaced by solving an initial-boundary value problem for the heat equation, which simplifies the numerical scheme to some extent. Numerical experiments on natural images are presented for this model.