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A study of local smoothness-informed convolutional neural network models for image inpainting

Fulian Li

Fulian Li

Department of Applied Mathematics, University of Science and Technology BeijingBeijing, China
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Li, Fulian
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Ping Lin

Ping Lin

Division of Mathematics, University of DundeeScotland, United Kingdom
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Lin, Ping
  
14 apr 2022
A study of local smoothness-informed convolutional neural network models for image inpainting's Cover Image
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Pubblicato online: 14 apr 2022
Pagine: 897 - 908
Ricevuto: 25 dic 2021
Accettato: 10 apr 2022
DOI: https://doi.org/10.2478/amns.2022.1.00013
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© 2023 Fulian Li et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

A damaged image. Ω1 is the undetectable domain, Ω2 is the detectable domain.
A damaged image. Ω1 is the undetectable domain, Ω2 is the detectable domain.

Fig. 2

Computational Framework. The 0th layer is the input (damaged image), the 39 hidden layers contain the kernels and biases, each hidden layer has 16 neurons, the last layer outputs the estimation of the real image. W × W denotes the size of the image. The upper backward line means each output back to the input layer for next training. At the first training, g0 = f. Each formula denotes the gray value of each point of the image after convolution and activation, *denotes the convolution symbol.
Computational Framework. The 0th layer is the input (damaged image), the 39 hidden layers contain the kernels and biases, each hidden layer has 16 neurons, the last layer outputs the estimation of the real image. W × W denotes the size of the image. The upper backward line means each output back to the input layer for next training. At the first training, g0 = f. Each formula denotes the gray value of each point of the image after convolution and activation, *denotes the convolution symbol.

Fig. 3

Images captured by the authors. (a) denotes the complete images, (b) denotes the damaged images.
Images captured by the authors. (a) denotes the complete images, (b) denotes the damaged images.

Fig. 4

The left image is from [16], the right one is the damaged image.
The left image is from [16], the right one is the damaged image.

Fig. 5

Inpainting results. (a) column is the complete local image, (b) column is the damaged local image, (c)–(g) columns are the outputs of the CNN trained with Ld, Leu(λ = 0.001, n = 100), Lcs(λ = 0.001, n = 100), LD(H1, β = 0.001), LD(H2, β = 0.001).
Inpainting results. (a) column is the complete local image, (b) column is the damaged local image, (c)–(g) columns are the outputs of the CNN trained with Ld, Leu(λ = 0.001, n = 100), Lcs(λ = 0.001, n = 100), LD(H1, β = 0.001), LD(H2, β = 0.001).

Fig. 6

Inpainting results. (a) column is the complete local image, (b) column is the damaged local image, (c)–(g) columns are the outputs of the CNN trained with Ld, Leu(λ = 0.001, n = 100), Lcs(λ = 0.001, n = 100), LD(H1, β = 10, 100, 10, 100, 100 orderly from the first row to the last row), LD(H2,β = 0.001, 0.001, 0.001, 0.1, 1 orderly from the first row to the last row).
Inpainting results. (a) column is the complete local image, (b) column is the damaged local image, (c)–(g) columns are the outputs of the CNN trained with Ld, Leu(λ = 0.001, n = 100), Lcs(λ = 0.001, n = 100), LD(H1, β = 10, 100, 10, 100, 100 orderly from the first row to the last row), LD(H2,β = 0.001, 0.001, 0.001, 0.1, 1 orderly from the first row to the last row).
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