Robin D. Morris

Bayesian super-resolved surface reconstruction from images

Bayesian inference has been used successfully for many problems where the aim is to infer the parameters of a model of interest. In this paper we formulate the three dimensional reconstruction problem as the problem of inferring the parameters of a surface model from image data, and show how Bayesian methods can be used to estimate the parameters of this model given the image data. Thus we recover the three dimensional description of the scene. This approach also gives great flexibility. We can specify the geometrical properties of the model to suit our purpose, and can also use different models for how the surface reflects the light incident upon it. In common with other Bayesian inference problems, the estimation methodology requires that we can simulate the data that would have been recorded for any values of the model parameters. In this application this means that if we have image data we must be able to render the surface model. However it also means that we can infer the parameters of a model whose resolution can be chosen irrespective of the resolution of the images, and may be super-resolved. We present results of the inference of surface models from simulated aerial photographs for the case of super-resolution, where many surface elements project into a single pixel in the low-resolution images.

A Bayesian approach to high resolution 3D surface reconstruction from multiple images

We present a radically different approach to the recovery of the three dimensional geometric and reflectance properties of a surface from image data. We pose the problem in a Bayesian framework, and proceed to infer the parameters of the model describing the surface. This allows great flexibility in the specification of the model, in terms of how both the geometrical properties and surface reflectance are specified. In the usual manner for Bayesian approaches it requires that we can simulate the data that would have been recorded for any state of the model in order to infer the model. The theoretical aspects are thus very general. We present rules for one type of surface geometry (the triangular mesh) and for the Lambertian model of light scattering. Our framework also allows the easy incorporation of data from multiple sensing modalities.

Quantum Adiabatic Optimization and Combinatorial Landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of the satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma=M/N . We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (instead of only energy) is used, and are able to show the existence of a dynamic threshold gamma= gamma(d) starting with some value of K -the number of variables in each clause. Beyond the dynamic threshold, the algorithm should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on the satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.

Dramatic Improvements to Feature Based Stereo

The camera registration extracted from feature based stereo is usually considered sufficient to accurately localize the 3D points. However, for natural scenes the feature localization is not as precise as in man-made environments. This results in small camera registration errors. We show that even very small registration errors result in large errors in dense surface reconstruction.We describe a method for registering entire images to the inaccurate surface model. This gives small, but crucially important improvements to the camera parameters. The new registration gives dramatically better dense surface reconstruction.

Matching Images to Models - Camera Calibration for 3-D Surface Reconstruction

In a previous paper we described a system which recursively recovers a super-resolved three dimensional surface model from a set of images of the surface. In that paper we assumed that the camera calibration for each image was known. In this paper we solve two problems. Firstly, if an estimate of the surface is already known, the problem is to calibrate a new image relative to the existing surface model. Secondly, if no surface estimate is available, the relative camera calibration between the images in the set must be estimated. This will allow an initial surface model to be estimated. Results of both types of estimation are given.

Auxiliary Variables for Markov Random Fields with Higher Order Interactions

Markov Random Fields are widely used in many image processing applications. Recently the shortcomings of some of the simpler forms of these models have become apparent, and models based on larger neighbourhoods have been developed. When single-site updating methods are used with these models, a large number of iterations are required for convergence. The Swendsen-Wang algorithm and Partial Decoupling have been shown to give potentially enormous speed-up to computation with the simple Ising and Potts models. In this paper we show how the same ideas can be used with binary Markov Random Fields with essentially any support to construct auxiliary variable algorithms. However, because of the complexity and certain characteristics of the models, the computational gains are limited.

A parameterization invariant approach to the statistical estimation of the CKM phase α

In contrast to previous analyses, we demonstrate a Bayesian approach to the estimation of the CKM phase {alpha} that is invariant to parameterization. We also show that in addition to computing the marginal posterior in a Bayesian manner, the distribution must also be interpreted from a subjective Bayesian viewpoint. Doing so gives a very natural interpretation to the distribution. We also comment on the effect of removing information about {beta}{sup 00}.

An Analysis Methodology for the Gamma-ray Large Area Space Telescope

The Large Area Telescope (LAT) instrument on the Gamma Ray Large Area Space Telescope (GLAST) has been designed to detect high‐energy gamma rays and determine their direction of incidence and energy. We propose a reconstruction algorithm based on recent advances in statistical methodology. This method, alternative to the standard event analysis inherited from high energy collider physics experiments, incorporates more accurately the physical processes occurring in the detector, and makes full use of the statistical information available. It could thus provide a better estimate of the direction and energy of the primary photon.

Parameter and Structure Inference for Nonlinear Dynamical Systems

A great many systems can be modeled in the nonlinear dynamical systems framework, as ẋ = f(x) + ξ(t), where f() is the potential function for the system, and ξ is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We use the Bayesian Information Criteria (BIC) to rank models, together with the beam search to search the space of models. We show that we can accurately determine the structure of simple nonlinear dynamical system models, and the structure of the coupling between nonlinear dynamical systems where the individual systems are known. This last case has important ecological applications.