On robust estimation of the location parameter

IEEE Transactions on Pattern Analysis and Machine Intelligence

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The Foundations Of Differential Geometry

We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N x N pixel grid, the subspace of all integrable gradient fields is of dimension N 2 - 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter a allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.

What Is the Range of Surface Reconstructions from a Gradient Field

European conference on computer vision (ECCV)

The scene rigidity assumption, also known as the static world assumption, is common in SLAM algorithms. Most existing algorithms operating in complex dynamic environments simplify the problem by removing moving objects from consideration or tracking them separately. Such strong assumptions limit the deployment of autonomous mobile robotic systems in a wide range of important real world applications involving highly dynamic and unstructured environments. This paper presents VDO-SLAM, a robust object-aware dynamic SLAM system that exploits semantic information to enable motion estimation of rigid objects in the scene without any prior knowledge of the objects shape or motion models. The proposed approach integrates dynamic and static structures in the environment into a unified estimation framework resulting in accurate robot pose and spatio-temporal map estimation. We provide a way to extract velocity estimates from object pose change of moving objects in the scene providing an important functionality for navigation in complex dynamic environments. We demonstrate the performance of the proposed system on a number of real indoor and outdoor datasets. Results show consistent and substantial improvements over state-of-the-art algorithms. An open-source version of the source code is available.

VDO-SLAM: A Visual Dynamic Object-aware SLAM System

The static world assumption is standard in most simultaneous localisation and mapping (SLAM) algorithms. Increased deployment of autonomous systems to unstructured dynamic environments is driving a need to identify moving objects and estimate their velocity in real-time. Most existing SLAM based approaches rely on a database of 3D models of objects or impose significant motion constraints. In this paper, we propose a new feature-based, model-free, object-aware dynamic SLAM algorithm that exploits semantic segmentation to allow estimation of motion of rigid objects in a scene without the need to estimate the object poses or have any prior knowledge of their 3D models. The algorithm generates a map of dynamic and static structure and has the ability to extract velocities of rigid moving objects in the scene. Its performance is demonstrated on simulated, synthetic and real-world datasets.

Dynamic SLAM: The Need For Speed

A wide range of system models in modern robotics and avionics applications admit natural symmetries. Such systems are termed equivariant and the structure provided by the symmetry is a powerful tool in the design of observers. Significant progress has been made in the last ten years in the design of filters and observers for attitude and pose estimation, tracking of homographies, and velocity aided attitude estimation, by exploiting their inherent Lie-group state-space structure. However, little work has been done for systems on homogeneous spaces, that is systems on manifolds on which a Lie-group acts rather than systems on the Lie-group itself. Recent research in robotic vision has discovered symmetries and equivariant structure on homogeneous spaces for a host of problems including the key problems of visual odometry and visual simultaneous localisation and mapping. These discoveries motivate a deeper look at the structure of equivariant systems on homogeneous spaces. This paper provides a comprehensive development of the foundation theory required to undertake observer and filter design for such systems.

Equivariant Systems Theory and Observer Design

Event cameras are ideally suited to capture HDR visual information without blur but perform poorly on static or slowly changing scenes. Conversely, conventional image sensors measure absolute intensity of slowly changing scenes effectively but do poorly on high dynamic range or quickly changing scenes. In this paper, we present an event-based video reconstruction pipeline for High Dynamic Range (HDR) scenarios. The proposed algorithm includes a frame augmentation pre-processing step that deblurs and temporally interpolates frame data using events. The augmented frame and event data are then fused using a novel asynchronous Kalman filter under a unifying uncertainty model for both sensors. Our experimental results are evaluated on both publicly available datasets with challenging lighting conditions and fast motions and our new dataset with HDR reference. The proposed algorithm outperforms state-of-the-art methods in both absolute intensity error (48% reduction) and image similarity indexes (average 11% improvement).

Robert Mahony

Papers

VDO-SLAM: A Visual Dynamic Object-aware SLAM System

Dynamic SLAM: The Need For Speed

Equivariant Systems Theory and Observer Design

An Asynchronous Kalman Filter for Hybrid Event Cameras.

Stable trajectory tracking for biped robots