# Per-Pixel Manifold-Based Color Calibration Technique
## 8 Summary  
In the paper, we have presented a new formulation of the per-pixel color calibration between images. The presented method can be applied to images with an arbitrary number of channels due to the flexibility and generalization provided by our derivation. The proposed algorithm is based on per-pixel manifold color transformation estimation. The proposed algorithm estimated a smooth manifold of color transformations across the whole image, even in the case when not all pixels have correspondence. The method allows for color profile mapping in difficult areas, like occluded regions of images, in shadows, and in the presence of reflections and a non-uniform lighting. The proposed method provides a gain in objective quality measure PSNR of 1.10 dB on average over seven different test sequences. The proposed method provided improvement for all tested sequences; the quality increase was in the range from 2.83 dB to 0.15 dB. The explanation of the differences may be attributed qualitatively to the different lighting conditions. Smaller improvements were observed for outdoor sequences recorded during a cloudy day, with no bright sun, and for sequences with uniform ambient lighting. For sequences with artificial light, the improvement was significantly larger. The subjective quality increase is also significant, as presented by the images in Figures 1 and 4.  
Much more improvement due to the use of the proposed method is observed when SSD between the virtual view synthesized from the left view is compared to the view synthesized from the right view. Here, when compared to the no color correction scenario, the reduction was more than 20-fold, with a maximum of 87-fold SSD reduction. When compared to a scenario where a competing method [33] is used, the SSD reduction is from 19.8-fold to 79.9-fold.  
Figure 4: Results of the proposed method for images with different lighting conditions. From the left: image with flash, no-flash image, result of our color-correction of the image with flash.  
The presented method is envisaged to be applied as a preprocessing step in a post-production phase, since the computational complexity is significant, the most time-consuming part being the large sparse matrix inversion. While real-time image processing was beyond the scope of this work, it is worth noting that faster matrix inversion methods exist, which would reduce the computational complexity of our method.  
The method significantly improves the quality of the virtual view synthesized from the multi-camera setups by applying color correction to all original views. It can be used in immersive video applications, where it can greatly reduce the color mismatch between camera views. It is also useful for single images in the scenario, flash-no flash images, as evidenced in the experiments.  
Conceptualization, K.W. and T.G.; methodology, S.G.; software, K.W.; validation, S.G., T.G. and K.K.; formal analysis, S.G.; investigation, T.G. and K.K.; writing--original draft preparation, K.W.; writing--review and editing, T.G. and K.K. All authors have read and agreed to the published version of the manuscript.  
Project funded by The National Centre for Research and Development in the LIDER Programme (LIDER/34/0177/L-8/16/NCBR/2017). The work was supported by the Ministry of Science and Higher Education, Poland.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Mucha sp. z o.o. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.