A Revisit to the Normalized Eight-Point Algorithm and A Self-Supervised Deep Solution

The Normalized Eight-Point algorithm has been widely viewed as the cornerstone in two-view geometry computation, where the seminal Hartley's normalization greatly improves the performance of the direct linear transformation (DLT) algorithm. A natural question is, whether there exists and how to find other normalization methods that may further improve the performance as per each input sample. In this paper, we provide a novel perspective and make two contributions towards this fundamental problem: 1) We revisit the normalized eight-point algorithm and make a theoretical contribution by showing the existence of different and better normalization algorithms; 2) We present a deep convolutional neural network with a self-supervised learning strategy to the normalization. Given eight pairs of correspondences, our network directly predicts the normalization matrices, thus learning to normalize each input sample. Our learning-based normalization module could be integrated with both traditional (e.g., RANSAC) and deep learning framework (affording good interpretability) with minimal efforts. Extensive experiments on both synthetic and real images show the effectiveness of our proposed approach.Comment: 12 pages, 7 figures, A preliminary versio

Seg2pix: Few Shot Training Line Art Colorization with Segmented Image Data

There are various challenging issues in automating line art colorization. In this paper, we propose a GAN approach incorporating semantic segmentation image data. Our GAN-based method, named Seg2pix, can automatically generate high quality colorized images, aiming at computerizing one of the most tedious and repetitive jobs performed by coloring workers in the webtoon industry. The network structure of Seg2pix is mostly a modification of the architecture of Pix2pix, which is a convolution-based generative adversarial network for image-to-image translation. Through this method, we can generate high quality colorized images of a particular character with only a few training data. Seg2pix is designed to reproduce a segmented image, which becomes the suggestion data for line art colorization. The segmented image is automatically generated through a generative network with a line art image and a segmentation ground truth. In the next step, this generative network creates a colorized image from the line art and segmented image, which is generated from the former step of the generative network. To summarize, only one line art image is required for testing the generative model, and an original colorized image and segmented image are additionally required as the ground truth for training the model. These generations of the segmented image and colorized image proceed by an end-to-end method sharing the same loss functions. By using this method, we produce better qualitative results for automatic colorization of a particular character’s line art. This improvement can also be measured by quantitative results with Learned Perceptual Image Patch Similarity (LPIPS) comparison. We believe this may help artists exercise their creative expertise mainly in the area where computerization is not yet capable

2008: Verifying global minima for L2 minimization problems

We consider the least-squares (L2) triangulation problem and structure-and-motion with known rotatation, or known plane. Although optimal algorithms have been given for these algorithms under an L-infinity cost function, finding optimal least-squares (L2) solutions to these problems is difficult, since the cost functions are not convex, and in the worst case can have multiple minima. Iterative methods can usually be used to find a good solution, but this may be a local minimum. This paper provides a method for verifying whether a local-minimum solution is globally optimal, by providing a simple and rapid test involving the Hessian of the cost function. In tests of a data set involving 277,000 independent triangulation problems, it is shown that the test verifies the global optimality of an iterative solution in over 99.9 % of the cases. 1

A Fast Method to Minimize L! Error Norm for Geometric Vision Problems

Minimizing L∞ error norm for some geometric vision problems provides global optimization using the well-developed algorithm called SOCP (second order cone programming). Because the error norm belongs to quasi-convex functions, bisection method is utili