This paper presents a new efficient approach to texture analysis based on distributions of simple spatial and tonal relationships. The texture description proposed makes use of semicover concept over binary planes derived from grey images. A measure of the local semicover tendency based on joint occurrences of elementary semicover patterns is described, and a simplification method of computation is presented to reduce the computational cost. The method presents a reduced set of parameters what facilitates its optimization in different types of application. The performance of the method is evaluated by means of a comparative study including other algorithms widely used in texture analysis. The results show a similar or superior performance than other more complex approaches.