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This paper presents a new efficient and fast approach to texture characterization for high-speed Web inspection applications (mainly focused on textured material grading and fault detection). 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 cost. Feasibility and reliability of the method is evaluated by means of a comparative study including other algorithms widely used in inspection applications. The results show a similar or superior performance to other approaches but with a reduced computational cost.