Pre-processing for approximate Bayesian computation in image analysis

Most of the existing algorithms for approximate Bayesian computation (ABC) assume that it is feasible to simulate pseudo-data from the model at each iteration. However, the computational cost of these simulations can be prohibitive for high dimensional data. An important example is the Potts model, which is commonly used in image analysis. Images encountered in real world applications can have millions of pixels, therefore scalability is a major concern. We apply ABC with a synthetic likelihood to the hidden Potts model with additive Gaussian noise. Using a pre-processing step, we fit a binding function to model the relationship between the model parameters and the synthetic likelihood parameters. Our numerical experiments demonstrate that the precomputed binding function dramatically improves the scalability of ABC, reducing the average runtime required for model fitting from 71 hours to only 7 minutes. We also illustrate the method by estimating the smoothing parameter for remotely sensed satellite imagery. Without precomputation, Bayesian inference is impractical for datasets of that scale.

Scalable Bayesian Computation for intractable likelihoods in image analysis

The inverse temperature hyperparameter of the hidden Potts model governs the strength of spatial cohesion and therefore has a substantial influence over the resulting model fit. The difficulty arises from the dependence of an intractable normalising constant on the value of the inverse temperature, thus there is no closed form solution for sampling from the distribution directly. We review three computational approaches for addressing this issue, namely pseudolikelihood, path sampling, and the approximate exchange algorithm. We compare the accuracy and scalability of these methods using a simulation study.

Improved simultaneous computation of motion detection and optical flow for object tracking

Object tracking systems require accurate segmentation of the objects from the background for effective tracking. Motion segmentation or optical flow can be used to segment incoming images. Whilst optical flow allows multiple moving targets to be separated based on their individual velocities, optical flow techniques are prone to errors caused by changing lighting and occlusions, both common in a surveillance environment. Motion segmentation techniques are more robust to fluctuating lighting and occlusions, but don't provide information on the direction of the motion. In this paper we propose a combined motion segmentation/optical flow algorithm for use in object tracking. The proposed algorithm uses the motion segmentation results to inform the optical flow calculations and ensure that optical flow is only calculated in regions of motion, and improve the performance of the optical flow around the edge of moving objects. Optical flow is calculated at pixel resolution and tracking of flow vectors is employed to improve performance and detect discontinuities, which can indicate the location of overlaps between objects. The algorithm is evaluated by attempting to extract a moving target within the flow images, given expected horizontal and vertical movement (i.e. the algorithms intended use for object tracking). Results show that the proposed algorithm outperforms other widely used optical flow techniques for this surveillance application.

Tracking road edges in the panospheric image plane

This paper presents a technique for tracking road edges in a panoramic image sequence. The major contribution is that instead of unwarping the image to find parallel lines representing the road edges, we choose to warp the parallel groundplane lines into the image plane of the equiangular panospheric camera. Updating the parameters of the line thus involves searching a very small number of pixels in the panoramic image, requiring considerably less computation than unwarping. Results using real-world images, including shadows, intersections and curves, are presented.

Particulate texture image analysis with applications

Texture analysis and textural cues have been applied for image classification, segmentation and pattern recognition. Dominant texture descriptors include directionality, coarseness, line-likeness etc. In this dissertation a class of textures known as particulate textures are defined, which are predominantly coarse or blob-like. The set of features that characterise particulate textures are different from those that characterise classical textures. These features are micro-texture, macro-texture, size, shape and compaction. Classical texture analysis techniques do not adequately capture particulate texture features. This gap is identified and new methods for analysing particulate textures are proposed. The levels of complexity in particulate textures are also presented ranging from the simplest images where blob-like particles are easily isolated from their back- ground to the more complex images where the particles and the background are not easily separable or the particles are occluded. Simple particulate images can be analysed for particle shapes and sizes. Complex particulate texture images, on the other hand, often permit only the estimation of particle dimensions. Real life applications of particulate textures are reviewed, including applications to sedimentology, granulometry and road surface texture analysis. A new framework for computation of particulate shape is proposed. A granulometric approach for particle size estimation based on edge detection is developed which can be adapted to the gray level of the images by varying its parameters. This study binds visual texture analysis and road surface macrotexture in a theoretical framework, thus making it possible to apply monocular imaging techniques to road surface texture analysis. Results from the application of the developed algorithm to road surface macro-texture, are compared with results based on Fourier spectra, the auto- correlation function and wavelet decomposition, indicating the superior performance of the proposed technique. The influence of image acquisition conditions such as illumination and camera angle on the results was systematically analysed. Experimental data was collected from over 5km of road in Brisbane and the estimated coarseness along the road was compared with laser profilometer measurements. Coefficient of determination R2 exceeding 0.9 was obtained when correlating the proposed imaging technique with the state of the art Sensor Measured Texture Depth (SMTD) obtained using laser profilometers.

Practical improvements to simultaneous computation of multi-view geometry and radial lens distortion

This paper discusses practical issues related to the use of the division model for lens distortion in multi-view geometry computation. A data normalisation strategy is presented, which has been absent from previous discussions on the topic. The convergence properties of the Rectangular Quadric Eigenvalue Problem solution for computing division model distortion are examined. It is shown that the existing method can require more than 1000 iterations when dealing with severe distortion. A method is presented for accelerating convergence to less than 10 iterations for any amount of distortion. The new method is shown to produce equivalent or better results than the existing method with up to two orders of magnitude reduction in iterations. Through detailed simulation it is found that the number of data points used to compute geometry and lens distortion has a strong influence on convergence speed and solution accuracy. It is recommended that more than the minimal number of data points be used when computing geometry using a robust estimator such as RANSAC. Adding two to four extra samples improves the convergence rate and accuracy sufficiently to compensate for the increased number of samples required by the RANSAC process.

Hessian-based affine adaptation of salient local image features

Affine covariant local image features are a powerful tool for many applications, including matching and calibrating wide baseline images. Local feature extractors that use a saliency map to locate features require adaptation processes in order to extract affine covariant features. The most effective extractors make use of the second moment matrix (SMM) to iteratively estimate the affine shape of local image regions. This paper shows that the Hessian matrix can be used to estimate local affine shape in a similar fashion to the SMM. The Hessian matrix requires significantly less computation effort than the SMM, allowing more efficient affine adaptation. Experimental results indicate that using the Hessian matrix in conjunction with a feature extractor that selects features in regions with high second order gradients delivers equivalent quality correspondences in less than 17% of the processing time, compared to the same extractor using the SMM.

Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.