67,324 research outputs found
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
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
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
Parameter estimation by implicit sampling
Implicit sampling is a weighted sampling method that is used in data
assimilation, where one sequentially updates estimates of the state of a
stochastic model based on a stream of noisy or incomplete data. Here we
describe how to use implicit sampling in parameter estimation problems, where
the goal is to find parameters of a numerical model, e.g.~a partial
differential equation (PDE), such that the output of the numerical model is
compatible with (noisy) data. We use the Bayesian approach to parameter
estimation, in which a posterior probability density describes the probability
of the parameter conditioned on data and compute an empirical estimate of this
posterior with implicit sampling. Our approach generates independent samples,
so that some of the practical difficulties one encounters with Markov Chain
Monte Carlo methods, e.g.~burn-in time or correlations among dependent samples,
are avoided. We describe a new implementation of implicit sampling for
parameter estimation problems that makes use of multiple grids (coarse to fine)
and BFGS optimization coupled to adjoint equations for the required gradient
calculations. The implementation is "dimension independent", in the sense that
a well-defined finite dimensional subspace is sampled as the mesh used for
discretization of the PDE is refined. We illustrate the algorithm with an
example where we estimate a diffusion coefficient in an elliptic equation from
sparse and noisy pressure measurements. In the example, dimension\slash
mesh-independence is achieved via Karhunen-Lo\`{e}ve expansions
- …