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This paper proposes a representational model for image pairs such asconsecutive video frames that are related by local pixel displacements, in thehope that the model may shed light on motion perception in primary visualcortex (V1). The model couples the following two components: (1) the vectorrepresentations of local contents of images and (2) the matrix representationsof local pixel displacements caused by the relative motions between the agentand the objects in the 3D scene. When the image frame undergoes changes due tolocal pixel displacements, the vectors are multiplied by the matrices thatrepresent the local displacements. Thus the vector representation isequivariant as it varies according to the local displacements. Our experimentsshow that our model can learn Gabor-like filter pairs of quadrature phases. Theprofiles of the learned filters match those of simple cells in Macaque V1.Moreover, we demonstrate that the model can learn to infer local motions ineither a supervised or unsupervised manner. With such a simple model, weachieve competitive results on optical flow estimation.

Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion