1. Haze removal using dark channel prior

2. Preface Guided Image Filter Pros: fast, high-quality Cons: halos,strokes

3. Preface Single image haze removal using dark channel prior. Step 2: Soft Matting Pros: high-quality Cons: time-consuming e.g..: L:

4. Definition I: guidance image ωk ： window p: input image μk: mean σ2:variance(of I in ωk) q: output image |ω|: the number of pixels in I ε: regularization parameter

5. Definition The key assumption of the guided filter is a local linear model between the guidance I and the filter output q. To determine the coefficients: pk: mean of p in ωk

6. Definition: Computing ak,bk for all ωk

7. Edge-preserving Filtering When I=p, ε=0,ak=1,bk=0 。  Case 1: ”Flat patch”. If the image I is constant in ωk, ak = 0 and bk = pk;  Case 2: ”High variance”. If the image I changes a lot within ωk, ak becomes close to 1 while bk is close to 0.  we have that if a pixel is in the middle of a ”high variance” area, then its value is unchanged, whereas if it is in the middle of a ”flat patch” area, its value becomes the average of the pixels nearby.

8. Gradient Preserving Filtering Bilateral filter cons: Gaussian weighted average Guided filter pros:

9. Relation to the Matting Laplacian Matrix One Jacobi iteration

10. Time complexity O(N),independent of r. For RGB color guidance images: 0(N). 0.3s VS 10s (bilateral filter) for 1M pixel image. 0.1s VS >10s (soft matting) for 600*400 color image VS 10s