Scale-Aware and Structure-Preserving Smoother via Gaussian-exponentiated TV for 2D/3D Vision Tasks

Image structure-preserving smoothers play a vital role in 2D/3D vision scene tasks. However, when processing images with complex patterns, they still face challenges such as large-scale weak edge blurring and insufficient sensitivity to prominent structures. Inspired by scaling theory and exponential nonlinear adjustment, we propose a Gaussian-exponentiated Total Variation (GeTV) smoother to address the above issues. As a local regularization term, this smoother introduces a novel scale-aware Gaussian kernel convolution in the gradient domain and its exponentiated structure-sensitive modulation, enabling the discovery of textures with weak correlation at arbitrary scale from prominent structures with strong correlation. Furthermore, considering the local non-convexity in GeTV, we adopt a numerical approximation to transform it into a solvable global optimization problem. Experimental validation demonstrates that the proposed method achieves superior scale- and structure-aware evaluation metrics compared to state-of-the-art competitive methods and exhibits well-smoothing performance in handling complex patterned textures with intensive noise.