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This paper presents a solution to the Projective Structure from Motion (PSfM) problem able to deal efficiently with missing data, outliers and, for the first time, large scale 3D reconstruction scenarios. By embedding the projective depths into the projective parameters of the points and views, we decrease the number of unknowns to estimate and improve computational speed by optimizing standard linear Least Squares systems instead of homogeneous ones. In order to do so, we show that an extension of the linear constraints from the Generalized Projective Reconstruction Theorem can be transferred to the projective parameters, ensuring also a valid projective reconstruction in the process. We use an incremental approach that, starting from a solvable sub-problem, incrementally adds views and points until completion with a robust, outliers free, procedure. Experiments with simulated data shows that our approach is performing well, both in term of the quality of the reconstruction and the capacity to handle missing data and outliers with a reduced computational time. Finally, results on real datasets shows the ability of the method to be used in medium and large scale 3D reconstruction scenarios with high ratios of missing data (up to 98\%).

Optical colonoscopy is the gold standard procedure to detect colorectal cancer, the fourth most common cancer in the United Kingdom. Up to 22%–28% of polyps can be missed during the procedure that is associated with interval cancer. A vision-based autonomous soft endorobot for colonoscopy can drastically improve the accuracy of the procedure by inspecting the colon more systematically with reduced discomfort. A three-dimensional understanding of the environment is essential for robot navigation and can also improve the adenoma detection rate. Monocular depth estimation with deep learning methods has progressed substantially, but collecting ground-truth depth maps remains a challenge as no 3D camera can be fitted to a standard colonoscope. This work addresses this issue by using a self-supervised monocular depth estimation model that directly learns depth from video sequences with view synthesis. In addition, our model accommodates wide field-of-view cameras typically used in colonoscopy and specific challenges such as deformable surfaces, specular lighting, non-Lambertian surfaces, and high occlusion. We performed qualitative analysis on a synthetic data set, a quantitative examination of the colonoscopy training model, and real colonoscopy videos in near real-time.