Optimal O(1) Bilateral Filter with Arbitrary Spatial and Range Kernels Using Sparse Approximation

Figure 2

Barbara: a demonstration of the visual quality of the approximation results. First column: results obtained using the proposed method, where 𝑁=5. Second column: the color-coded absolute error maps corresponding to the images in the first column. Third column: results obtained using Porikli’s single-box bilateral filter with optimal spatial parameter. Fourth column: the color-coded absolute error maps corresponding to the images in the third column. Fifth column: results obtained using Gunturk’s bilateral filter, where 𝑀=5. Last column: the color-coded absolute error maps corresponding to the images in the fifth column. First row: images are obtained with 𝜎_𝑠=1.2. Second row: images are obtained with 𝜎_𝑠=1.8. Third row: images are obtained with 𝜎_𝑠=3.0. Fourth row: images are obtained with 𝜎_𝑠=6.0. For all these results, 𝜎_𝑟=50 and 𝑃=16. The ranges of the color-coded maps are uniformly limited to [0,50] to facilitate visual comparison.