Multipoint Filtering with Local Polynomial Approximation and Range Guidance

This paper presents a novel guided image filtering method using multipoint local polynomial approximation (LPA) with range guidance. In our method, the LPA is extended from a pointwise model into a multipoint model for reliable filtering and better preserving image spatial variation which usually contains the essential information in the input image. In addition, we develop a scheme with constant computational complexity (invariant to the size of filtering kernel) for generating a spatial adaptive support region around a point. By using the hybrid of the local polynomial model and color/intensity based range guidance, the proposed method not only preserves edges but also does a much better job in preserving spatial variation than existing popular filtering methods. Our method proves to be effective in a number of applications: depth image upsampling, joint image denoising, details enhancement, and image abstraction. Experimental results show that our method produces better results than state-of-the-art methods and it is also computationally efficient.