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The 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 a 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 computation simplification method is presented to reduce the computational cost. The method presents a reduced set of parameters that 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 to other more complex approaches.