This paper tackles the recurrent problem of disparity estimation since the mapping from disparity to depth is well understood while the automatic disparity extraction is still subject to errors. We propose to use the image derivatives with the phase-based approach to overcome the tuning problem of the filter. Moreover, we propose a quadratic model for the singularities neighborhood detection. The approach is characterized by the simplicity of its implementation. It also provides dense and accurate disparity maps. A numerical error analysis shows that the results are very satisfactory.