Functional maps representation on product manifolds

We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices

TVL₁ Planarity Regularization for 3D Shape Approximation

The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within. This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy

Procedural Modeling and Physically Based Rendering for Synthetic Data Generation in Automotive Applications

We present an overview and evaluation of a new, systematic approach for generation of highly realistic, annotated synthetic data for training of deep neural networks in computer vision tasks. The main contribution is a procedural world modeling approach enabling high variability coupled with physically accurate image synthesis, and is a departure from the hand-modeled virtual worlds and approximate image synthesis methods used in real-time applications. The benefits of our approach include flexible, physically accurate and scalable image synthesis, implicit wide coverage of classes and features, and complete data introspection for annotations, which all contribute to quality and cost efficiency. To evaluate our approach and the efficacy of the resulting data, we use semantic segmentation for autonomous vehicles and robotic navigation as the main application, and we train multiple deep learning architectures using synthetic data with and without fine tuning on organic (i.e. real-world) data. The evaluation shows that our approach improves the neural network's performance and that even modest implementation efforts produce state-of-the-art results.Comment: The project web page at http://vcl.itn.liu.se/publications/2017/TKWU17/ contains a version of the paper with high-resolution images as well as additional materia

A Joint 3D-2D based Method for Free Space Detection on Roads

In this paper, we address the problem of road segmentation and free space detection in the context of autonomous driving. Traditional methods either use 3-dimensional (3D) cues such as point clouds obtained from LIDAR, RADAR or stereo cameras or 2-dimensional (2D) cues such as lane markings, road boundaries and object detection. Typical 3D point clouds do not have enough resolution to detect fine differences in heights such as between road and pavement. Image based 2D cues fail when encountering uneven road textures such as due to shadows, potholes, lane markings or road restoration. We propose a novel free road space detection technique combining both 2D and 3D cues. In particular, we use CNN based road segmentation from 2D images and plane/box fitting on sparse depth data obtained from SLAM as priors to formulate an energy minimization using conditional random field (CRF), for road pixels classification. While the CNN learns the road texture and is unaffected by depth boundaries, the 3D information helps in overcoming texture based classification failures. Finally, we use the obtained road segmentation with the 3D depth data from monocular SLAM to detect the free space for the navigation purposes. Our experiments on KITTI odometry dataset, Camvid dataset, as well as videos captured by us, validate the superiority of the proposed approach over the state of the art.Comment: Accepted for publication at IEEE WACV 201