Sparse coding has been incorporated in models of the visual cortex for its computational advantages and connection to biology. But how the level of sparsity contributes to performance on visual tasks is not well understood. In this work, sparse coding has been integrated into an existing hierarchical V2 model (Hosoya & Hyvärinen, 2015), but replacing its independent component analysis (ICA) with an explicit sparse coding in which the degree of sparsity can be controlled. After training, the sparse coding basis functions with a higher degree of sparsity resembled qualitatively different structures, such as curves and corners. The contributions of the models were assessed with image classification tasks, specifically tasks associated with mid-level vision including figure-ground classification, texture classification, and angle prediction between two line stimuli. In addition, the models were assessed in comparison with a texture sensitivity measure that has been reported in V2 (Freeman et al., 2013) and a deleted-region inference task. The results from the experiments show that although sparse coding performed worse than ICA at classifying images, only sparse coding was able to better match the texture sensitivity level of V2 and infer deleted image regions, both by increasing the degree of sparsity in sparse coding. Greater degrees of sparsity allowed for inference over larger deleted image regions. The mechanism that allows for this inference capability in sparse coding is described in this article.