Encoding cost in the subspace spanned by the filters.
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A Cost as a function of rotation angle for response noise models with scaled additive and constant additive noise. With scaled additive noise, the optimal filters (lower solid curve) provide a unique encoding up to a sign flip (i.e. rotation angle = 180°). Orthogonal filters with scaled additive noise that span the same subspace (lower dashed curve) provide an encoding that is periodic on 90°. For comparison, cost as a function of rotation angle for filters with constant additive noise and matched noise power is also shown (see text). (Note that the original, optimal filters (c.f. Fig 6A) have a cosine similarity (i.e. correlation) of ρ = -0.22, corresponding to an angle difference of 103°.) B Cost landscape for scaled additive noise within the subspace spanned by filters 1 and 2 for all possible rotation angles and angle differences (i.e. correlations). The curves in A show vertical slices through this space. Arrow marks optimal filters. C Cost landscape with additive noise. D Filters as a function of rotation angle in the subspace.