Fused Lasso and rotation invariant autoregressive models for texture classification

• Autoregressive random fields are established texture analysis models.
• Rotational invariant autoregressive random field estimation is an ill-conditioned problem.
• Fused Lasso framework can perform estimation on ill-conditioned problems by introducing ℓ1ℓ1 and total variation (TV) constraints.
• The ℓ1ℓ1-norm performs variable selection; the TV seminorm promotes parsimony.
• Fused Lasso parameter estimation outperforms least squares for texture classification on a previously studied Brodatz data set.

Anisotropic, rotation invariant, autoregressive random fields, realised by considering local radial sampling, are flexible models which have been considered for texture classification. Unfortunately, owing to the strong correlations present in the neighbourhood covariate matrix, parameter estimation is complicated by the dichotomy between ill-conditionedness and rotation invariance. Exploiting the Fused Lasso framework, we here propose a compromise which incorporates two regularisers. The ℓ1ℓ1-norm induces stability and performs variable selection amongst strongly correlated radial samples; the total variation seminorm encourages clustering and promotes parsimony. Experiments confirm the potential utility. Parallels are drawn within the texture classification literature and beyond.