A computational allegory for V1

This contribution introduces a computational allegory for V1 in the task of static image coding. It can be considered an extrapolation of previous V1 models based on unsupervised learning but envisaging two new objectives. The first is a contribution to the discussion of the quantity of V1 cells. The second is the estimation of the quantity of cells within a V1 hypercolumn needed to present to higher-levels the early coding of the correspondent retinal image portion. It is broadly accepted that the quantity of V1 cells coding the correspondent retinal image must be sparse (low dimension) but avoiding pure sparsity (dimension one). The concrete value of that (mean) dimension is still an open issue. Consequently, it is opportune to study the question: “what is the dimension of V1 coding?”. An important side effect of a possible answer could be a contribution to justify the large relative quantity of center-symmetric and simple V1 cells in comparison with the quantity of LGN cells. The implemented allegory is based on unsupervised learning. During the learning phase, a dictionary of image blocks is built by using unsupervised learning principals - principal component analysis (PCA), symmetric component analysis (SCA) and independent component analysis (ICA) operating on small learning sets. During coding, the previously learned dictionary is used to perform matching pursuit in order to code new incoming image blocks as linear combinations of some dictionary components. The results so far obtained support a first provocative answer: “a dimension around 4?”