Joint multiregion segmentation and parametric estimation of image motion by basis function representation and level set evolution

The purpose of this study is to investigate a variational method for joint segmentation and parametric estimation of image motion by basis function representation of motion and level set evolution. The functional contains three terms. One term is of classic regularization to bias the solution toward a segmentation with smooth boundaries. A second term biases the solution toward a segmentation with boundaries which coincide with motion discontinuities, following a description of motion discontinuities by a function of the image spatio-temporal variations. The third term refers to region information and measures conformity of the parametric representation of the motion of each region of segmentation to the image spatio-temporal variations. The components of motion in each region of segmentation are represented as functions in a space generated by a set of basis functions. The coefficients of the motion components considered combinations of the basis functions are the parameters of representation. The necessary conditions for a minimum of the functional, which are derived taking into consideration the dependence of the motion parameters on segmentation, lead to an algorithm which condenses to concurrent curve evolution, implemented via level sets, and estimation of the parameters by least squares within each region of segmentation. The algorithm and its implementation are verified on synthetic and real images using a basis of cosine transforms.