Local Readjustment for High-Resolution 3D Reconstruction: Supplementary Material Siyu Zhu 1, Tian Fang 2, Jianxiong Xiao 3, and Long Quan 4 1,2,4 The Hong Kong University of Science and Technology 3 Princeton University 1. Introduction Owing to space constraints, the formal paper provides parts of our experimental results. This document presents more results of real datasets without ground truth, real datasets with ground truth, and synthetic datasets to both quantitatively and qualitatively demonstrate that our method significantly reduces severe propagated errors and estimation biases caused by the initial global adjustment, and helps to recover the detailed geometry. 2. Real Datasets without Ground Truth 2.1. The Results of the Casa Milla Dataset Figure 1. Sample images of the Casa Milla dataset. 1
Dense Reconstruction Figure 2. The comparison between mesh models with and without readjustment (RA) for the Casa Milla dataset. We should note that some serious artifacts in the dense reconstruction (marked by purple rectangles) are caused by the Non-Lambertian surface and cannot be resolved by our method. Dense Reconstruction Figure 3. The comparison between mesh models with and without readjustment (RA) for the Casa Milla dataset. 2
Dense Reconstruction Figure 4. The comparison between mesh models with and without readjustment (RA) for the Casa Milla dataset. Dense Reconstruction Figure 5. The comparison between mesh models with and without readjustment (RA) for the Casa Milla dataset. 3
2.2. The Results of the Station Dataset Figure 6. Sample images of the Station dataset. Dense Reconstruction Figure 7. The comparison between mesh models with and without readjustment (RA) for the Station dataset. 4
Dense Reconstruction Figure 8. The comparison between mesh models with and without readjustment (RA) for the Station dataset. Dense Reconstruction Figure 9. The comparison between mesh models with and without readjustment (RA) for the Station dataset. 5
2.3. The Results of the Louvre Dataset Figure 10. Sample images of the Louvre dataset. Dense Reconstruction Figure 11. The comparison between mesh models with and without readjustment (RA) for the Louvre dataset. 6
Dense Reconstruction Figure 12. The comparison between mesh models with and without readjustment (RA) for the Louvre dataset. 7
2.4. The Results of the Castle Dataset Figure 13. Sample images of the Castle dataset. Dense Reconstruction Figure 14. The comparison between mesh models with and without readjustment (RA) for the Castle dataset. 8
Dense Reconstruction With RA Wit RA With RA With RA With RA Figure 15. The comparison between mesh models with and without readjustment (RA) for the Castle dataset. 9
3. Real Datasets with Ground Truth 3.1. Histograms and Curves The well-known dense multi-view stereo benchmark [1] contains six datasets, namely fountain-p11, Herz-Jesu-P8, entry- P10, castle-p19, Herz-Jesu-P25, and castle-p30. Because of the lack of space, we have shown the experimental results of the Herz-Jesu-P8, entry-p10, and castle-p19 datasets in our formal paper. Here, the relative error histograms and cumulative relative error curves of the other three datasets are provided. occupancy 25 20 15 10 5 fountain P11 occupancy 30 20 10 Herz Jesu P25 occupancy 30 20 10 castle P30 0 1 2 3 4 5 6 7 8 9 10 11 sigma 0 1 2 3 4 5 6 7 8 9 10 11 sigma 0 1 2 3 4 5 6 7 8 9 10 11 sigma 1 fountain P11 1 Herz Jesu P25 1 castle P30 cumulative 0.8 0.6 0.4 0.2 0 0 5 10 sigma cumulative 0.8 0.6 0.4 0.2 0 0 5 10 sigma cumulative 0.8 0.6 0.4 0.2 0 0 5 10 sigma Figure 16. Relative error histograms and cumulative relative error curves of the real datasets with ground truth, namely fountain-p11, Herz-Jesu-P25, and castle-p30. 3.2. Visual Comparisons Dense Reconstruction Figure 17. The comparison between mesh models with and without readjustment (RA) for the castle-p30 dataset. 10
Dense Reconstruction Figure 18. The comparison between mesh models with and without readjustment (RA) for the Herz-Jesu-P8 dataset. Dense Reconstruction Figure 19. The comparison between mesh models with and without readjustment (RA) for the fountain-p11 dataset. We observe that, compared with the mesh model without readjustment, there is almost no obvious visual improvement in the mesh model with readjustment. It is primarily because these images are all captured in a well-conditioned environment, and the scale of the dataset is comparatively small, meaning it is not the ideal target for our readjustment approach. Fortunately, the images used for reconstruction, especially those for Internet-scale reconstruction, are generally taken under different conditions of lighting, scale, surface reflection, and weather, using various cameras and lens with different focus, sensor noise and distortion, and the estimation bias cannot be ignored. 11
4. Synthetic Datasets Based on prior textured mesh models, both standard models (Block) and those from the general reconstruction engine (Depot and Tower), we use Maya to set synthetic camera poses and get rendered images for dense reconstruction. In this section, we present some visual comparisons between the synthetic datasets with and without readjustment. Moreover, we provide the average relative error of the dataset with and without readjustment where different types and levels of perturbations are manually introduced (the statistics of the Block dataset is shown in the formal paper). 4.1. The Results of the Block Dataset (a) (b) (c) Figure 20. The demonstration of the synthetic Block dataset. (a) The mesh model used for generating synthetic camera geometry. (b) The synthetic camera geometry. (c) Some samples of the rendered images for dense reconstruction. (a) (a) (b) (c) Figure 21. The visual comparison of the synthetic Block dataset. Note that we add Gaussian noise to the parameters of two specific cameras, which are marked by red dashed rectangles in (a). (b) and (c) are respectively the mesh models without and with readjustment. We can clearly observe that the mesh model in (c) contains less severe propagated errors. 12
4.2. The Results of the Depot Dataset (a) (b) (c) Figure 22. The demonstration of the synthetic Depot dataset. (a) The mesh model used for generating synthetic camera geometry. (b) The synthetic camera geometry. (c) Some samples of the rendered images for dense reconstruction. Dense Reconstruction Figure 23. The comparison between mesh models with and without readjustment (RA) for the synthetic Depot dataset. Error type Uniform error Concentrated error Error level 1 pixel 2 pixels 5 pixels 20 pixels 1 pixel 2 pixels 5 pixels 20 pixels Relative 3.457 6.784 15.451 29.453 3.431 6.175 14.745 28.452 error 3.074 5.147 14.974 27.454 2.457 5.407 8.754 16.741 [sigma] Reduction 11.08% 24.13% 3.09% 6.79% 28.39% 12.44% 40.63% 41.16% Table 1. The average relative error of the synthetic Depot dataset with and without readjustment where different types and levels of perturbations are manually introduced. 13
4.3. The Results of the Tower Dataset (a) (b) (c) Figure 24. The demonstration of the synthetic Tower dataset. (a) The mesh model used for generating synthetic camera geometry. (b) The synthetic camera geometry. (c) Some samples of the rendered images for dense reconstruction. Dense Reconstruction Figure 25. The comparison between mesh models with and without readjustment (RA) for the synthetic Tower dataset. Error type Uniform error Concentrated error Error level 1 pixel 2 pixels 5 pixels 20 pixels 1 pixel 2 pixels 5 pixels 20 pixels Relative 3.784 7.345 17.613 32.154 3.556 7.123 17.234 31.157 error 3.462 6.954 16.489 31.156 2.932 5.998 11.194 16.419 [sigma] Reduction 8.51% 5.32% 6.38% 3.10% 17.55% 15.79% 35.05% 47.30% Table 2. The average relative error of the synthetic Tower dataset with and without readjustment where different types and levels of perturbations are manually introduced. 14
References [1] C. Strecha, W. von Hansen, L. V. Gool, P. Fua, and U. Thoennessen. On benchmarking camera calibration and multi-view stereo for high resolution imagery. In CVPR, 2008. 11 15