An efficient texture modelling framework based on Topological Attribute Patterns (TAP) is presented considering topology related attributes calculated from Local Binary Patterns (LBP). Our main contribution is to introduce new efficient mapping mechanisms that improve some typical mappings for LBP-based operators in texture classification such as rotation invariant patterns (ri), rotation invariant uniform patterns (riu2), and Local Binary Count (LBC). Like them, the proposed approach allows contrast and rotation invariant image description using more compact descriptors by projecting binary patterns to a reduced feature space. However, its expressiveness, and then its discrimination capability, is higher, since it includes additional information, related to the connected components of the binary patterns. The proposed mapping, evaluated and compared with different popular mappings, validates the interest of our approach. We then develop Complemented Patterns of Topological Attributes (CTAP) that generalise TAP model and exploit complemented information to further enhance its discrimination capability, and evaluate it on different texture datasets.