A general texture description model is proposed, using topol-ogy related attributes calculated from Local Binary Patterns (LBP). The proposed framework extends and generalises existing LBP-based descrip-tors like LBP-rotation invariant uniform patterns (LBP riu2), and Local Binary Count (LBC). Like them, it allows contrast and rotation invari-ant image description using more compact descriptors than classic LBP. However, its expressiveness, and then its discrimination capability, is higher, since it includes additional information, including the number of connected components. The impact of the different attributes on texture classification performance is assessed through a systematic comparative evaluation, performed on three texture datasets. The results validate the interest of the proposed approach, by showing that some combinations of attributes outperform state-of-the-art LBP-based texture descriptors.