Learning Efficient Point Cloud Generation for Dense 3D Object Reconstruction

Conventional methods of 3D object generative modeling learn volumetric predictions using deep networks with 3D convolutional operations, which are direct analogies to classical 2D ones. However, these methods are computationally wasteful in attempt to predict 3D shapes, where information is rich only on the surfaces. In this paper, we propose a novel 3D generative modeling framework to efficiently generate object shapes in the form of dense point clouds. We use 2D convolutional operations to predict the 3D structure from multiple viewpoints and jointly apply geometric reasoning with 2D projection optimization. We introduce the pseudo-renderer, a differentiable module to approximate the true rendering operation, to synthesize novel depth maps for optimization. Experimental results for single-image 3D object reconstruction tasks show that we outperforms state-of-the-art methods in terms of shape similarity and prediction density

Deep-LK for Efficient Adaptive Object Tracking

In this paper we present a new approach for efficient regression based object tracking which we refer to as Deep- LK. Our approach is closely related to the Generic Object Tracking Using Regression Networks (GOTURN) framework of Held et al. We make the following contributions. First, we demonstrate that there is a theoretical relationship between siamese regression networks like GOTURN and the classical Inverse-Compositional Lucas & Kanade (IC-LK) algorithm. Further, we demonstrate that unlike GOTURN IC-LK adapts its regressor to the appearance of the currently tracked frame. We argue that this missing property in GOTURN can be attributed to its poor performance on unseen objects and/or viewpoints. Second, we propose a novel framework for object tracking - which we refer to as Deep-LK - that is inspired by the IC-LK framework. Finally, we show impressive results demonstrating that Deep-LK substantially outperforms GOTURN. Additionally, we demonstrate comparable tracking performance to current state of the art deep-trackers whilst being an order of magnitude (i.e. 100 FPS) computationally efficient

ST-GAN: Spatial Transformer Generative Adversarial Networks for Image Compositing

We address the problem of finding realistic geometric corrections to a foreground object such that it appears natural when composited into a background image. To achieve this, we propose a novel Generative Adversarial Network (GAN) architecture that utilizes Spatial Transformer Networks (STNs) as the generator, which we call Spatial Transformer GANs (ST-GANs). ST-GANs seek image realism by operating in the geometric warp parameter space. In particular, we exploit an iterative STN warping scheme and propose a sequential training strategy that achieves better results compared to naive training of a single generator. One of the key advantages of ST-GAN is its applicability to high-resolution images indirectly since the predicted warp parameters are transferable between reference frames. We demonstrate our approach in two applications: (1) visualizing how indoor furniture (e.g. from product images) might be perceived in a room, (2) hallucinating how accessories like glasses would look when matched with real portraits.Comment: Accepted to CVPR 2018 (website & code: https://chenhsuanlin.bitbucket.io/spatial-transformer-GAN/

Topological Field Theory with Haagerup Symmetry

We construct a (1+1)$d$ topological field theory (TFT) whose topological defect lines (TDLs) realize the transparent Haagerup $\mathcal{H}_3$ fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data, including the three-point coefficients and lasso diagrams, are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. While many of the constraints we derive are not limited to the this particular TFT with six vacua, we leave open the construction of TFTs with two or four vacua. Finally, TFTs realizing the Haagerup $\mathcal{H}_1$ and $\mathcal{H}_2$ fusion categories can be obtained by gauging algebra objects. This note makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.Comment: 41+11 pages, 1 figure, 3 tables; v2: corrected statements about the literature, revised Appendix

The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)

The notion of a transparent fusion category is defined. For the Haagerup-Izumi fusion rings with G=Z_(2n+1) (the Z_3 case is the Haagerup H_3 fusion ring), the transparent property reduces the number of independent F-symbols from order O(n6) to O(n^2), rendering the pentagon identity practically solvable. Transparent fusion categories are constructed up to Z_(15), and the explicit F-symbols are compactly presented. The potential construction of categories for new families of fusion rings is discussed

The F-Symbols for Transparent Haagerup-Izumi Categories with G = Z_(2n+1)

The notion of a transparent fusion category is defined. For the Haagerup-Izumi fusion rings with G=Z_(2n+1) (the Z_3 case is the Haagerup H_3 fusion ring), the transparent property reduces the number of independent F-symbols from order O(n6) to O(n^2), rendering the pentagon identity practically solvable. Transparent fusion categories are constructed up to Z_(15), and the explicit F-symbols are compactly presented. The potential construction of categories for new families of fusion rings is discussed