However, its geometric analysis is based on quantities that are difficult to interpret and are not amenable to statistical analysis. In this paper we provide a refined geometric analysis and a new statistical analysis that show that DPCP can tolerate as many outliers as the square of the number of inliers, thus improving upon other provably correct robust PCA methods. We also propose a scalable Projected Sub-Gradient Method (DPCP-PSGM) for solving the DPCP problem and show that it achieves linear convergence even though the underlying optimization problem is non-convex and non-smooth. Experiments on road plane detection from 3D point cloud data demonstrate that DPCP-PSGM can be more efficient than the traditional RANSAC algorithm, which is one of the most popular methods for such computer vision applications.

This introduces challenges for learning-based approaches, as 3D object annotations are scarce in real images. Previous work chose to train on synthetic data with ground truth 3D information, but suffered from domain adaptation when tested on real data. In this work, we propose MarrNet, an end-to-end trainable model that sequentially estimates 2.5D sketches and 3D object shape. Our disentangled, two-step formulation has three advantages. First, compared to full 3D shape, 2.5D sketches are much easier to be recovered from a 2D image; models that recover 2.5D sketches are also more likely to transfer from synthetic to real data. Second, for 3D reconstruction from 2.5D sketches, systems can learn purely from synthetic data. This is because we can easily render realistic 2.5D sketches without modeling object appearance variations in real images, including lighting, texture, etc.

However, its geometric analysis is based on quantities that are difficult to interpret and are not amenable to statistical analysis. In this paper we provide a refined geometric analysis and a new statistical analysis that show that DPCP can tolerate as many outliers as the square of the number of inliers, thus improving upon other provably correct robust PCA methods. We also propose a scalable Projected Sub-Gradient Method (DPCP-PSGM) for solving the DPCP problem and show that it achieves linear convergence even though the underlying optimization problem is non-convex and non-smooth. Experiments on road plane detection from 3D point cloud data demonstrate that DPCP-PSGM can be more efficient than the traditional RANSAC algorithm, which is one of the most popular methods for such computer vision applications.

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