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A new bio-inspired model is proposed in this paper. This model mimetizes the simple cells of the mammalian visual processing system in order to recognize low-level geometric structures such as oriented lines, edges and other constructed with these. It takes advantage of geometric algebra in order to represent structures and symmetric operators by estimating the relation between geometric entities and encoding it. This geometric model uses symmetric relations in which exist a invariance under some transformation according to biological models. It is based on a Quaternionic Atomic Function and its phase information to detect oriented lines, edges and geometric structures defined by lines. Also, it uses a geometric neural network to encode the transformation between lines and then for classifying of geometric structures.