Edge/Structure-Preserving Texture Filter via Relative Bilateral Filtering with a Conditional Constraint

Image texture filtering plays an essential role in computer vision tasks. However, it remains challenging in determining the tradeoff between over-smoothing in weak large-scale textures (with low-amplitude gradients) and under-smoothing in strong small-scale textures (with high-amplitude gradients) for images with complex patterns. Inspired by scale-space theory and intensive experiments, a relative bilateral filter with a conditional constraint (RBFC) is presented to address the issue. This filter utilizes the relative bilateral filter (RBF) as one local regularization to capture and suppress weak large-scale textures from the prominent edges/structures. Meanwhile, a conditional sparse constraint is responsible for discovering and suppressing strong small-scale textures in the gradient domain. To solve the nonconvex problem in RBFC, a numerical approximation to the optimization is derived and a novel solution by decomposing into two subproblems is proposed. Qualitative and quantitative experiments show that the proposed method is effective and superior to the state-of-the-art methods in preserving image smoothness.