V. N. Smelyansky, P. Cheeseman, D. A. Maluf and R. D. Morris
To appear in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, Hilton Head Island, June 2000.
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.
R. D. Morris
In Proceedings of the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, York, July 1999.
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.
R. D. Morris, P. Cheeseman, V. N. Smelyanskiy and D. A. Maluf
In Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, Caesarea, June 1999.
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 results 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.
R. D. Morris, X. Descombes and J. Zerubia
In Proceedings of IEEE International Conference on Image Processing, Santa Barbara, October 1997.
Developments in Markov Chain Monte Carlo procedures have made it possible to perform fully Bayesian image segmentation. By this we mean that all the parameters are treated identically, be they the segmentation labels, the class parameters or the Markov Random Field prior parameters. We perform the analysis by sampling from the posterior distribution of all the parameters. Sampling from the MRF parameters has traditionally been considered if not intractable then at least computationally prohibitive. In the statistics literature there are descriptions of experiments showing that the MRF parameters may be sampled by approximating the partition function. These experiments are all, however, on `toy' problems -- for the typical size of image encountered in engineering applications phase transition behaviour of the models becomes a major limiting factor in the estimation of the partition function. Nevertheless, we show that, with some care, fully Bayesian segmentation can be performed on realistic sized images. We also compare the fully Bayesian approach with the approximate pseudolikelihood method.
X. Descombes, R. D. Morris, J. Zerubia and M. Berthod
In Proceedings of the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, Venice, 1997.
Recent developments in statistics now allow maximum like-lihood estimators for the parameters of Markov Random Fields to be constructed. We detail the theory required, and present an algorithm which is easily implemented and practical in terms of computation time. We demonstrate this algorithm on three MRF models, the standard Potts model, an inhomogeneous variation of the Potts model and a long-range interaction model, better adapted to modelling real-world images. We estimate the parameters from a synthetic and a real image, and then resynthesise the models to demonstrate which features of the image have been captured by the model.
R. D. Morris, X. Descombes and J. Zerubia
In Proceedings of IEEE Digital Signal Processing Workshop, Loen, Norway, September 1996
The Ising and Potts models have been used since the earliest work on MRF based image segmentation as the underlying model for the region labels, and continue to be used for this task. Recently, however, advances in Markov chain Monte Carlo techniques have highlighted the shortcomings of these models as models of region labels. In this paper we present a demonstration of why these models are unsuitable for segmentation. We hope this will help motivate the search for better models.
R. D. Morris, W. J. Fitzgerald and A. C. Kokaram
In proceedings of IEEE International Conference on Image Processing, Lausanne, Switzerland, September 1996
We address the problem of detecting, and subsequently removing, 'line scratch' distortion in motion picture frames (see figure []). A model for the lines' interaction with the image data is constructed. A sampling based algorithm based on the Reversible Jump Markov chain Monte Carlo framework is developed which enables automatic determination of both the unknown number of lines present, together with the lines' parameters. Previous work has not attempted to automatically determine the number of lines present. Our approach is widely applicable in many object recognition problems, where the number of objects is unknown.
R. D. Morris and W. J. Fitzgerald
In Proceedings of the International Conference for Young Computer Scientists (ICYCS '95), Beijing, China, July 1995
Pixel matching motion estimation algorithms are commonly used in image sequence processing tasks. The importance of regularising the estimated displacement field to obtain a solution close to the true motion is well known. In this paper we use a Markov Random Field (MRF) prior on the displacement field, and formulate the MRF to correspond to the translational motion of rigid bodies. We then extend this framework to include estimation of the occluded areas in a unified manner.
R. D. Morris and W. J. Fitzgerald
In Proceedings of International Workshop on Image Processing, Budapest, Hungary, June 1994
In this paper we apply stochastic methods (Gibbs sampling and simulated annealing) and deterministic (mean field) approximations to the problem of detecting and interpolating 'dirt and sparkle' or `blotches' in archived motion pictures.
R. D. Morris and W. J. Fitzgerald
In Proceedings of ICASSP 94, Adelaide, Australia, April 1994
Many archived motion pictures suffer from what we term replacement noise, that is various degradations such as dirt, scratches, fingerprints etc, where the original picture is replaced by some unrelated information. In this paper we use markov random field based motion field segmentation to detect these areas, and then interpolate into the gaps using a motion-compensated interpolation scheme to restore the frame.
R. D. Morris and W. J. Fitzgerald
In Proceedings of International Conference on Image Processing: Theory and Applications (IPTA '93), San Remo, Italy, June 1993
We describe a method for restoring image sequences degraded by speckle. We model the sequence as a 3D Markov Random Field, using a motion-compensated temporal neighbourhood. The conditional probability assigned to each pixel by the model is used to detect speckle. The flagged pixels are then restored by replacing them with the grey scale value with the highest conditional probability.