Abstract: The problem of excessive reliance on parameter settings in the weighted least squares image smoothing method can lead to blurring of weak gradient structures, preservation of strong gradient textures, and color shifts during multi-scale image decomposition. To address this issue, a weighted least squares image smoothing method based on directional anisotropy is proposed. Firstly, a multi- directional anisotropy structure measurement method is proposed, which enhances the ability to capture texture/structure information by using the directional derivatives of gradient information along each direction. What’s more, it also combines the gradient amplitude of the original image to achieve attenuation of the structure measurement amplitude, thereby improving the refinement of the structure. Secondly, the adaptive Sobel operator with variable template is utilized to replace the one-dimensional difference operator for computing the first-order partial derivatives and gradient weights of the regular term. This adjustment allows for better perception of gradient changes within the neighborhood range, thus preserving the integrity of edges. Lastly, the structure measurement amplitude is integrated into the gradient weights, enabling the use of small-weight smoothing parameters for structure preservation in structural regions and large-weight smoothing parameters for preserving texture details in texture regions. Additionally, a multi-channel smoothing result fusion operation is employed to solve color shifts and color distortion issues. In terms of visual presentation, the new method effectively eliminates textures while retaining delicate structures. In quantitative terms, the new method achieves a harmonious balance between texture suppression and structure preservation, outperforming mainstream texture smoothing methods.

Key words: image smoothing, texture filter, directional anisotropic structure measurement, weighted least squares