A Multiresolution Image Completion Algorithm for Compressing Digital Color Images

Algorithm 3

Pseudocode of proposed framework with PDEs inpainting algorithm based on 𝑝 Laplacian operator.

(1) Obtain a noisy image as input

             𝑧(𝑥)=𝑓(𝑥)+𝑛(𝑥)

(2) Smooth the noisy image using

             𝜕𝑧𝑔𝜕𝑥=div(‖∇𝑧‖)⋅∇𝑧

(3) Analyze the smoothed image by extracting edges through

         ∇𝑧𝑥,𝑦=𝜕_𝑥𝑧𝑥,𝑦²+𝜕_𝑦𝑧𝑥,𝑦²

           𝜕𝜃=arctan^𝑦𝑧(𝑥,𝑦)𝜕_𝑦𝑧(𝑥,𝑦)

(4) Identify the structural and textural regions based on the extracted edges.

(5) Skip the regions that are not selected as necessary information instead fill

  the DC value and create a DC filled image

(6) Perform ANN Compression and Decompression using

         compⁱⁿ=∑^𝑁_𝑖=1𝑉_𝑖,𝑗𝑧_𝑖,1≤𝑗≤𝐾

         𝑧ⁱⁿ_𝑗=∑^𝑁_𝑖=1𝑊_𝑖,𝑗compⁱⁿ,1≤𝑗≤𝑁

       where 𝑉_𝑖𝑗 & 𝑊_𝑖𝑗 are weights of compressor and decompressor respectively.

(7) Start the inpainting process with initial guess 𝜍^new_{𝑗,𝑙,𝑘}=𝛼_{𝑗,𝑙,𝑘}𝜒_{𝑗,𝑙,𝑘}.

Set 𝜍^old_{𝑗,𝑙,𝑘}=0 and the initial error 𝐸=𝜍^new−𝜍^old₂

   Where 𝜒_{𝑗,𝑙,𝑘}=10𝑗,𝑙,𝑘∈𝐼𝑗,𝑙,𝑘∉𝐼 and 𝐼 is the inpainting region.

(8) While 𝑖≤𝑁 or 𝐸≤𝛿,𝑑𝑜

(a) Set 𝜍^old=𝜍^new

(b) Calculate SH_curv using (12)–(15)

(c) For all 𝑗,𝑙,𝑘 update

       𝜍^new_{𝑗,𝑙,𝑘}=𝜍^old_{𝑗,𝑙,𝑘}+Δ_𝑡Δ_𝑥SH_curv−𝜆_{𝑗,𝑙,𝑘}𝜍_{𝑗,𝑙,𝑘}−𝛼_{𝑗,𝑙,𝑘},

        where Δ_𝑡 is the time step size & Δ_𝑥 is the space grid size

(d) Compute error 𝐸=𝜍^new−𝜍^old₂

(e) End the while loop