A computational model for face feature extraction and recognition capable of achieving a high degree of invariance to illumination and pose is presented. Similar to the complex V1 cells, the model uses a sparse binary code to represent an edge orientation. The binary code represents the face features for recognition. This paper investigates the geometrical structure of the linear space of face representation vectors. For this study the Yale Face Database B is used. It is shown that the biologically inspired procedure provides the face representation of a good quality: vectors representing the faces of the same person under different poses and illumination conditions are grouped together in the vector space. This code enables a very high recognition rate for both the illumination invariance and pose invariance settings.