Recursive Motion and Structure Estimation with Complete Error Characterization

We present an algorithm that perfom recursive estimation of ego-motion andambient structure from a stream of monocular Perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measurements computed by a 2-perspective-views step. Key features of our filter are (I) global observability of the model, (2) complete on-line characterization of the uncertainty of the measurements provided by the two-views step. The filter is thus guaranteed to be well-behaved regardless of the particular motion undergone by the observel: Regions of motion space that do not allow recovery of structure (e.g. pure rotation) may be crossed while maintaining good estimates of structure and motion; whenever reliable measurements are available they are exploited. The algorithm works well for arbitrary motions with minimal smoothness assumptions and no ad hoc tuning. Simulations are presented that illustrate these characteristics

Accurate 3D maps from depth images and motion sensors via nonlinear Kalman filtering

This paper investigates the use of depth images as localisation sensors for 3D map building. The localisation information is derived from the 3D data thanks to the ICP (Iterative Closest Point) algorithm. The covariance of the ICP, and thus of the localization error, is analysed, and described by a Fisher Information Matrix. It is advocated this error can be much reduced if the data is fused with measurements from other motion sensors, or even with prior knowledge on the motion. The data fusion is performed by a recently introduced specific extended Kalman filter, the so-called Invariant EKF, and is directly based on the estimated covariance of the ICP. The resulting filter is very natural, and is proved to possess strong properties. Experiments with a Kinect sensor and a three-axis gyroscope prove clear improvement in the accuracy of the localization, and thus in the accuracy of the built 3D map.Comment: Submitted to IROS 2012. 8 page

Dynamic Estimation of Rigid Motion from Perspective Views via Recursive Identification of Exterior Differential Systems with Parameters on a Topological Manifold

We formulate the problem of estimating the motion of a rigid object viewed under perspective projection as the identification of a dynamic model in Exterior Differential form with parameters on a topological manifold. We first describe a general method for recursive identification of nonlinear implicit systems using prediction error criteria. The parameters are allowed to move slowly on some topological (not necessarily smooth) manifold. The basic recursion is solved in two different ways: one is based on a simple extension of the traditional Kalman Filter to nonlinear and implicit measurement constraints, the other may be regarded as a generalized "Gauss-Newton" iteration, akin to traditional Recursive Prediction Error Method techniques in linear identification. A derivation of the "Implicit Extended Kalman Filter" (IEKF) is reported in the appendix. The ID framework is then applied to solving the visual motion problem: it indeed is possible to characterize it in terms of identification of an Exterior Differential System with parameters living on a C0 topological manifold, called the "essential manifold". We consider two alternative estimation paradigms. The first is in the local coordinates of the essential manifold: we estimate the state of a nonlinear implicit model on a linear space. The second is obtained by a linear update on the (linear) embedding space followed by a projection onto the essential manifold. These schemes proved successful in performing the motion estimation task, as we show in experiments on real and noisy synthetic image sequences

Reducing "Structure From Motion": a General Framework for Dynamic Vision - Part 2: Experimental Evaluation

A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Although all methods may be derived from a "natural" dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the specific applications and the goals one is targeting. Which one is the winning strategy? In this paper we analyze the properties of the dynamical models that originate from each strategy under a variety of experimental conditions. For each model we assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate

Reducing “Structure from Motion”: a general framework for dynamic vision. 2. Implementation and experimental assessment

For pt.1 see ibid., p.933-42 (1998). A number of methods have been proposed in the literature for estimating scene-structure and ego-motion from a sequence of images using dynamical models. Despite the fact that all methods may be derived from a “natural” dynamical model within a unified framework, from an engineering perspective there are a number of trade-offs that lead to different strategies depending upon the applications and the goals one is targeting. We want to characterize and compare the properties of each model such that the engineer may choose the one best suited to the specific application. We analyze the properties of filters derived from each dynamical model under a variety of experimental conditions, assess the accuracy of the estimates, their robustness to measurement noise, sensitivity to initial conditions and visual angle, effects of the bas-relief ambiguity and occlusions, dependence upon the number of image measurements and their sampling rate

A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating

An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this purpose, the choice of the process noise covariance is generally unclear. In this chapter, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise covariance on the states and parameters, as given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering technique by updating the process noise covariance at each time step based on estimates. We compare the performance of this framework with different fixed values of process noise covariance in biomolecular system models, including an oscillator model, as well as in experimentally measured data for a negative transcriptional feedback circuit. We find that the Extended Kalman Filter with such process noise covariance update is closer to the optimality condition in the sense that the innovation sequence becomes white and in achieving a balance between the mean square estimation error and parameter convergence time. The results of this chapter may help in the use of Extended Kalman Filters for systems where process noise covariance depends on states and/or parameters.Comment: 23 pages, 9 figure