A new cartoon + texture image decomposition model based on the Sobolev space

Semi-Sparsity for Smoothing Filters

“…To ensure a systematic comparison, we elaborate on our semi-sparsity model with its superior performance against a series of image decomposition methods. Specifically, we compare the model with the well-known ROF model [10], TV-L 1 [56], TV-G [3], TV-H [15], TV-G-H [57], BTF [38], RTV [5], TGV-L 1 [27], TGV-H [32], HTV-H [32], which cover most of the structural and textual models listed in Tab. 1 and Tab.…”

“…The notation ∥•∥ 0 is the so-called L 0 quasi-norm denoting the number of non-zero entries of a vector, which provides a simple and easily-grasped measurement of sparsity. [10], (c) TV-L 1 (λ = 0.003, α = 0.0045) [56], (d) TV-G (λ = 0.003, α = 0.0005, γ = 0.0002) [3], (e) TV-H (λ = 0.002, α = 0.005) [15], (f) TV-G-H (λ = 0.004, α = 0.001, γ = 0.002) [57], (g) BTF (σ = 5.0, iter = 4) [23], (h) RTV (λ = 0.01, σ = 3.0) [5], (i) TGV-L 1 (λ = 0.0007, α = 0.0008, β = 0.0008) [27], (j) TGV-H (λ = 0.004, α = 0.01, β = 0.03) [32], (k) HTV-H (λ = 0.003, α = 0.006, β = 0.0015) [32], and (l) Ours (λ = 0.005, α = 0.006, β = 0.001). For fairness, all methods are fine-tuned for a similar level of smoothness.…”

“…Visual results of image structures in case of piece-wise constant/smoothing structures and large oscillating textures. (a) Input, (b) ROF (λ = 0.0035, α = 0.001)[10], (c) TV-L 1 (λ = 0.001, α = 0.002)[56], (d) TV-G (λ = 0.003, α = 0.0007, γ = 0.0002)[3], (e) TV-H (λ = 0.002, α = 0.003)[15], (f) TV-G-H (λ = 0.004, α = 0.008, γ = 0.008)[57], (g) BTF (σ = 5.0, iters = 7)[23], (h) RTV (λ = 0.015, σ = 4.0)[5], (i) TGV-L 1 (λ = 0.001, α = 0.002, β = 0.002)[27], (j) TGV-H (λ = 0.002, α = 0.05, β = 0.04)[32], (k) HTV-H (λ = 0.002, α = 0.0045, β = 0.004)[32], and (l) Ours (λ = 0.004, α = 0.007, β = 0.002). Quantitative results with ST R(C 0 /C 1 ) metrics, (b)∼(j): 18.88(0.1220/0.0158), 18.89(0.0365/0.0204), 18.90(0.1101/0.0259), 18.89(0.0486/0.0429), 18.84(0.0444/0.0500),19.01(0.0373/0.0834), 18.97(0.0539/0.0195), 18.67(0.1003/0.1742), 18.86(0.0320/0.2002), 18.87(0.0431/0.1421), 18.95(0.0292/0.0188).…”

“…TV-L 1[56] (d) TV-G[3] (e) TV-H[15] (f) TV-G-H[57] (g) BTF[23] (h) RTV[5] (i) TGV-L 1 [27] (j) TGV-H[32] (k) HTV-H[32] (l) Ours…”

“…The correlation coefficient of STR metrics C 0 /C 1 between image structure u /∇u (gradient) and image texture v = f −u on the new dataset, and the computation time (s) compared with the state-of-the-art methods. TV-L 1[56] TV-G[3] TV-H −1[15] TV-G-H[57] BTF[38] RTV[5] TGV-L 1[27] TGV-H[32] HTV-H[32] Ours The relationship is more clear when comparing the textures v with the gradient map of structures ∇u as indicated in Fig.8 (c)∼(d). Specifically, we show their overlap regions in Fig.8(e) in Blue, where the former textures v with the gradient map of structures ∇u are shown in Red and Green.…”