Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting
Abstract
:1. Introduction
- (1)
- Compared with existing methods, our proposed method is able to address the nonlinear data model problem faced by the traditional MC methods. It is also able to address the global structure problem in existing deep learning-based MC methods.
- (2)
- The proposed method can be pre-trained to learn the global image structure and underlying relationship between input matrix data with missing elements and the recovered output data. Once successfully trained, the network does not need to be optimized again in the subsequent image in-painting tasks, thereby providing a high-performance and easy-to-deploy nonlinear matrix completion solution.
- (3)
- To improve the performance of the proposed method, a new algorithm for pre-filling the missing elements of the image is proposed. This new padding method performs global analysis of the matrix data to predict the missing elements as their initial values, which improves the performance of matrix completion and image in-painting.
2. Related Work
3. The Proposed Method
3.1. Mathematical Model of the DMFCNet Method
3.1.1. and Updating Modules
3.1.2. Updating Module
3.2. Pre-Filling
Algorithm 1 DMFCNet-1 |
|
Algorithm 2 DMFCNet-2 |
|
3.3. Loss Function
3.4. Training
4. Experiments
4.1. Datasets
4.2. Experimental Settings
4.3. Image In-Painting
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Missing Rate | Images NO. | PSNR/SSIM | |||
---|---|---|---|---|---|
DMFCNet-1 | DMFCNet-2 | ||||
30% | 1 | 29.89/0.904 | 33.29/0.956 | 31.11/0.952 | 34.68/0.971 |
2 | 27.63/0.915 | 30.59/0.958 | 28.08/0.953 | 31.94/0.974 | |
3 | 30.80/0.908 | 33.44/0.959 | 32.21/0.963 | 35.29/0.973 | |
4 | 30.10/0.902 | 32.56/0.946 | 31.92/0.946 | 33.70/0.960 | |
5 | 32.52/0.875 | 36.47/0.956 | 35.59/0.968 | 38.32/0.976 | |
Average | 30.19/0.901 | 33.27/0.955 | 31.78/0.956 | 34.78/0.971 | |
50% | 1 | 27.46/0.847 | 30.04/0.914 | 27.24/0.879 | 30.30/0.929 |
2 | 23.98/0.863 | 27.23/0.929 | 23.24/0.856 | 27.74/0.939 | |
3 | 27.97/0.852 | 30.19/0.921 | 27.77/0.896 | 31.00/0.938 | |
4 | 27.56/0.831 | 29.73/0.898 | 28.18/0.873 | 30.04/0.908 | |
5 | 29.85/0.804 | 33.54/0.919 | 31.58/0.923 | 34.39/0.947 | |
Average | 27.37/0.840 | 30.14/0.916 | 27.60/0.885 | 30.69/0.932 | |
70% | 1 | 24.92/0.763 | 26.23/0.834 | 23.79/0.729 | 26.12/0.829 |
2 | 21.65/0.781 | 23.43/0.860 | 19.12/0.665 | 22.29/0.810 | |
3 | 25.02/0.770 | 26.62/0.861 | 23.94/0.744 | 26.66/0.853 | |
4 | 24.93/0.721 | 26.47/0.801 | 24.95/0.739 | 26.62/0.808 | |
5 | 27.70/0.746 | 29.82/0.859 | 28.14/0.832 | 31.47/0.884 | |
Average | 24.84/0.756 | 26.51/0.843 | 23.99/0.742 | 26.63/0.837 |
Missing Rate | Images NO. | PSNR/SSIM | |||||||
---|---|---|---|---|---|---|---|---|---|
MF [21] | NNM [16] | TNNM [8] | DLMC [28] | NC-MC [41] | LNOP [42] | DMFCNet-1 | DMFCNet-2 | ||
20% | 1 | 29.72/0.890 | 32.06/0.929 | 32.30/0.935 | 31.22/0.913 | 32.05/0.939 | 32.55/0.934 | 35.60/0.972 | 37.57/0.984 |
2 | 26.10/0.831 | 29.24/0.896 | 29.60/0.904 | 29.09/0.888 | 29.85/0.912 | 30.12/0.906 | 33.35/0.972 | 35.03/0.985 | |
3 | 30.90/0.901 | 33.26/0.939 | 33.54/0.943 | 32.70/0.933 | 33.37/0.948 | 33.92/0.945 | 35.77/0.973 | 37.69/0.984 | |
4 | 31.99/0.938 | 33.39/0.951 | 33.63/0.954 | 32.26/0.938 | 33.73/0.959 | 33.81/0.955 | 34.97/0.969 | 36.20/0.978 | |
5 | 35.71/0.939 | 37.31/0.959 | 37.71/0.961 | 36.92/0.955 | 37.55/0.967 | 37.87/0.962 | 39.04/0.972 | 41.08/0.986 | |
Average | 30.88/0.900 | 33.05/0.935 | 33.36/0.940 | 32.44/0.926 | 33.31/0.945 | 33.65/0.940 | 35.75/0.972 | 37.51/0.983 | |
30% | 1 | 27.42/0.822 | 29.37/0.873 | 29.68/0.883 | 29.35/0.867 | 29.69/0.893 | 29.82/0.881 | 33.29/0.956 | 34.68/0.971 |
2 | 23.91/0.762 | 25.80/0.916 | 26.14/0.827 | 26.46/0.825 | 26.70/0.842 | 26.54/0.827 | 30.59/0.958 | 31.94/0.974 | |
3 | 28.63/0.845 | 30.29/0.885 | 30.68/0.894 | 30.35/0.891 | 30.88/0.909 | 31.02/0.896 | 33.44/0.959 | 35.29/0.973 | |
4 | 29.54/0.895 | 30.72/0.913 | 31.07/0.919 | 30.34/0.903 | 31.31/0.927 | 31.15/0.920 | 32.56/0.946 | 33.70/0.960 | |
5 | 33.32/0.904 | 34.48/0.931 | 34.87/0.932 | 34.68/0.931 | 35.03/0.944 | 35.05/0.934 | 36.47/0.956 | 38.32/0.976 | |
Average | 28.56/0.846 | 30.13/0.904 | 30.49/0.891 | 30.24/0.883 | 30.72/0.903 | 30.72/0.892 | 33.27/0.955 | 34.78/0.971 | |
40% | 1 | 25.84/0.771 | 27.13/0.804 | 27.43/0.818 | 27.40/0.799 | 27.70/0.836 | 27.56/0.812 | 31.00/0.932 | 32.10/0.952 |
2 | 21.04/0.655 | 23.16/0.718 | 23.44/0.732 | 23.93/0.730 | 23.96/0.740 | 23.87/0.732 | 28.68/0.937 | 29.17/0.953 | |
3 | 26.17/0.777 | 27.65/0.816 | 28.07/0.828 | 28.36/0.839 | 28.56/0.854 | 28.38/0.829 | 31.60/0.939 | 32.50/0.956 | |
4 | 27.36/0.842 | 28.69/0.865 | 29.04/0.874 | 28.79/0.863 | 29.42/0.889 | 29.14/0.874 | 30.57/0.916 | 31.81/0.940 | |
5 | 30.72/0.852 | 32.07/0.889 | 32.51/0.893 | 33.02/0.900 | 32.80/0.911 | 32.63/0.895 | 34.23/0.930 | 36.12/0.962 | |
Average | 26.23/0.779 | 27.74/0.818 | 28.10/0.830 | 28.30/0.826 | 28.49/0.846 | 28.32/0.828 | 31.21/0.931 | 32.34/0.953 | |
50% | 1 | 24.01/0.685 | 25.07/0.717 | 25.37/0.731 | 25.10/0.703 | 25.54/0.746 | 25.42/0.722 | 30.04/0.914 | 30.30/0.929 |
2 | 19.65/0.588 | 20.95/0.626 | 21.27/0.635 | 21.75/0.639 | 21.56/0.634 | 21.57/0.632 | 27.23/0.929 | 27.74/0.939 | |
3 | 24.60/0.713 | 25.40/0.733 | 25.96/0.757 | 26.42/0.772 | 26.50/0.790 | 26.12/0.751 | 30.19/0.921 | 31.00/0.938 | |
4 | 25.69/0.784 | 26.82/0.805 | 27.26/0.819 | 27.08/0.812 | 27.63/0.837 | 27.29/0.816 | 29.73/0.898 | 30.04/0.908 | |
5 | 29.26/0.798 | 29.92/0.839 | 30.54/0.842 | 31.19/0.858 | 31.06/0.867 | 30.60/0.844 | 33.54/0.919 | 34.39/0.947 | |
Average | 24.64/0.714 | 25.63/0.744 | 26.08/0.757 | 26.31/0.757 | 26.46/0.775 | 26.20/0.753 | 30.14/0.916 | 30.69/0.932 | |
60% | 1 | 22.27/0.618 | 23.21/0.624 | 23.50/0.642 | 23.31/0.623 | 23.53/0.643 | 23.52/0.631 | 28.17/0.889 | 28.27/0.893 |
2 | 16.75/0.468 | 18.81/0.518 | 19.04/0.527 | 19.36/0.530 | 18.39/0.481 | 19.28/0.524 | 25.48/0.907 | 25.34/0.901 | |
3 | 21.99/0.607 | 23.49/0.641 | 24.11/0.666 | 24.43/0.684 | 24.34/0.673 | 24.22/0.654 | 28.94/0.904 | 29.05/0.907 | |
4 | 24.04/0.704 | 24.94/0.722 | 25.33/0.739 | 25.37/0.735 | 25.55/0.754 | 25.41/0.736 | 28.23/0.862 | 28.45/0.868 | |
5 | 26.44/0.692 | 28.15/0.770 | 28.71/0.869 | 29.54/0.810 | 29.17/0.796 | 28.83/0.773 | 32.08/0.901 | 32.88/0.924 | |
Average | 22.30/0.618 | 23.72/0.655 | 24.14/0.689 | 24.40/0.676 | 24.20/0.669 | 24.25/0.724 | 28.58/0.893 | 28.80/0.900 | |
70% | 1 | 21.04/0.520 | 21.41/0.515 | 21.82/0.532 | 21.50/0.494 | 21.17/0.476 | 21.85/0.518 | 26.23/0.834 | 26.12/0.829 |
2 | 15.50/0.384 | 16.77/0.404 | 16.84/0.405 | 17.04/0.406 | 15.10/0.312 | 17.25/0.412 | 23.43/0.860 | 22.29/0.810 | |
3 | 20.80/0.520 | 21.32/0.515 | 21.99/0.539 | 22.19/0.549 | 21.17/0.481 | 22.09/0.531 | 26.62/0.861 | 26.66/0.853 | |
4 | 22.59/0.617 | 23.16/0.623 | 23.38/0.636 | 23.50/0.642 | 23.12/0.620 | 23.57/0.634 | 26.47/0.801 | 26.62/0.808 | |
5 | 24.86/0.614 | 25.78/0.683 | 26.12/0.664 | 27.06/0.719 | 26.09/0.663 | 26.53/0.680 | 29.82/0.859 | 31.47/0.884 | |
Average | 21.00/0.531 | 21.69/0.548 | 22.03/0.555 | 22.26/0.562 | 21.33/0.510 | 22.26/0.555 | 26.51/0.843 | 26.63/0.837 |
Image Size | Missing Rate | MF | NNM | TNNM | DLMC | NC-MC | LNOP | DMFCNet-1 | DMFCNet-2 |
---|---|---|---|---|---|---|---|---|---|
256 × 256 | 30% | 0.095 | 4.905 | 2.974 | 16.129 | 5.651 | 2.384 | 0.390 | 0.341 |
50% | 0.096 | 4.340 | 3.455 | 17.429 | 3.507 | 2.165 | 0.420 | 0.339 | |
70% | 0.130 | 3.534 | 6.816 | 18.644 | 2.260 | 1.649 | 0.436 | 0.329 | |
512 × 512 | 30% | 0.288 | 23.380 | 12.416 | 59.581 | 48.207 | 9.120 | 1.763 | 1.019 |
50% | 0.199 | 18.998 | 17.128 | 69.528 | 23.970 | 8.302 | 1.661 | 1.015 | |
70% | 0.116 | 16.193 | 18.801 | 78.087 | 12.122 | 7.415 | 1.769 | 1.050 |
Mask Type | Images NO. | PSNR/SSIM | ||||||
---|---|---|---|---|---|---|---|---|
MF | NNM | TNNM | DLMC | NC-MC | LNOP | DMFCNet-2 | ||
Text Mask | 1 | 30.33/0.936 | 32.37/0.950 | 32.52/0.952 | 31.64/0.942 | 32.42/0.953 | 32.65/0.953 | 37.13/0.985 |
2 | 24.80/0.891 | 28.74/0.926 | 28.79/0.929 | 28.47/0.920 | 29.25/0.932 | 29.57/0.934 | 34.63/0.984 | |
3 | 30.27/0.930 | 31.97/0.947 | 32.49/0.956 | 32.27/0.948 | 32.75/0.958 | 32.57/0.955 | 35.17/0.985 | |
4 | 33.18/0.957 | 35.16/0.968 | 35.69/0.971 | 34.35/0.960 | 35.54/0.972 | 35.65/0.971 | 37.44/0.983 | |
5 | 34.30/0.949 | 37.54/0.975 | 38.31/0.975 | 37.96/0.974 | 38.70/0.979 | 38.45/0.977 | 40.82/0.990 | |
Average | 30.58/0.933 | 33.16/0.953 | 33.56/0.957 | 32.94/0.949 | 33.73/0.959 | 33.78/0.958 | 37.04/0.985 | |
Grid Mask | 1 | 29.19/0.899 | 32.95/0.942 | 32.96/0.944 | 33.22/0.928 | 32.62/0.943 | 33.20/0.943 | 37.11/0.983 |
2 | 23.22/0.812 | 29.30/0.914 | 29.52/0.918 | 28.92/0.902 | 29.75/0.917 | 30.11/0.919 | 34.34/0.986 | |
3 | 28.41/0.882 | 33.17/0.946 | 33.57/0.951 | 32.44/0.940 | 33.41/0.954 | 33.89/0.951 | 37.67/0.986 | |
4 | 31.01/0.933 | 34.39/0.962 | 34.59/0.964 | 33.39/0.952 | 34.71/0.966 | 34.72/0.964 | 36.75/0.980 | |
5 | 33.14/0.918 | 37.45/0.966 | 37.88/0.967 | 36.46/0.958 | 37.78/0.972 | 38.01/0.968 | 41.16/0.988 | |
Average | 28.99/0.889 | 33.45/0.946 | 33.70/0.949 | 32.89/0.936 | 33.65/0.950 | 33.99/0.949 | 37.41/0.985 |
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Ma, X.; Li, Z.; Wang, H. Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting. Entropy 2022, 24, 1500. https://doi.org/10.3390/e24101500
Ma X, Li Z, Wang H. Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting. Entropy. 2022; 24(10):1500. https://doi.org/10.3390/e24101500
Chicago/Turabian StyleMa, Xiaoxuan, Zhiwen Li, and Hengyou Wang. 2022. "Deep Matrix Factorization Based on Convolutional Neural Networks for Image Inpainting" Entropy 24, no. 10: 1500. https://doi.org/10.3390/e24101500