PatchMatch Belief Propagation for Correspondence Field Estimation and its Applications

Correspondence fields estimation is an important process that lies at the core of many different applications. Is it often seen as an energy minimisation problem, which is usually decomposed into the combined minimisation of two energy terms. The first is the unary energy, or data term, which reflects how well the solution agrees with the data. The second is the pairwise energy, or smoothness term, and ensures that the solution displays a certain level of smoothness, which is crucial for many applications. This thesis explores the possibility of combining two well-established algorithms for correspondence field estimation, PatchMatch and Belief Propagation, in order to benefit from the strengths of both and overcome some of their weaknesses. Belief Propagation is a common algorithm that can be used to optimise energies comprising both unary and pairwise terms. It is however computational expensive and thus not adapted to continuous spaces which are often needed in imaging applications. On the other hand, PatchMatch is a simple, yet very efficient method for optimising the unary energy of such problems on continuous and high dimensional spaces. The algorithm has two main components: the update of the solution space by sampling and the use of the spatial neighbourhood to propagate samples. We show how these components are related to the components of a specific form of Belief Propagation, called Particle Belief Propagation (PBP). PatchMatch however suffers from the lack of an explicit smoothness term. We show that unifying the two approaches yields a new algorithm, PMBP, which has improved performance compared to PatchMatch and is orders of magnitude faster than PBP. We apply our new optimiser to two different applications: stereo matching and optical flow. We validate the benefits of PMBP through series of experiments and show that we consistently obtain lower errors than both PatchMatch and Belief Propagation

Monte Carlo Methods in Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography (QPAT) is a hybrid biomedical imaging technique that derives its specificity from the wavelength-dependent absorption of near-infrared/visible laser light, and its sensitivity from ultrasonic waves. This promising technique has the potential to reveal more than just structural information, it can also probe tissue function. Specifically, QPAT has the capability to estimate concentrations of endogenous chromophores, such as the concentrations of oxygenated and deoxygenated haemoglobin (from which blood oxygenation can be calculated), as well as the concentrations of exogenous chromophore, e.g. near-infrared dyes or metallic nanoparticles. This process is complicated by the fact that a photoacoustic image is not directly related to the tissue properties via the absorption coefficient, but is proportional to the wavelength-dependent absorption coefficient times the internal light fluence, which is also wavelength-dependent and is in general unknown. This thesis tackles this issue from two angles; firstly, the question of whether certain experimental conditions allow the impact of the fluence to be neglected by assuming it is constant with wavelength, a `linear inversion', is addressed. It is demonstrated that a linear inversion is appropriate only for certain bands of illumination wavelengths and for limited depth. Where this assumption is not accurate, an alternative approach is proposed, whereby the fluence inside the tissue is modelled using a novel Monte Carlo model of light transport. This model calculates the angle-dependent radiance distribution by storing the field in Fourier harmonics, in 2D, or spherical harmonics, in 3D. This thesis demonstrates that a key advantage of computing the radiance in this way is that it simplifies the computation of functional gradients when the estimation of the absorption and scattering coefficients is cast as a nonlinear least-squares problem. Using this approach, it is demonstrated in 2D that the estimation of the absorption coefficient can be performed to a useful level of accuracy, despite the limited accuracy in reconstruction of the scattering coefficient