Probability Density Function Transfer in High Dimensional Spaces and its Application to Colour Transfer
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This thesis addresses the topic of example-based colour transfer from the domain of image processing. Colour transfer is often recast as a distribution transfer problem in which the actual probability density function of a given target colour samples is transferred to the input colour samples. Existing colour transformations rely on solving the problem only in colour space and do not scale well to high-dimensional spaces due to the increase in the computational complexity associated with the increase of the data dimensionality. This poses a challenging problem to current colour transfer methods and limits the potential of encoding and fusing different types of relevant information that could enhance image descriptors and guide the transfer process.
The aim of this thesis is to propose transfer functions that are scalable to high-dimensional spaces and suitable to parallel computation. We extend the colour problem space to high-dimensional space by constructing pixel descriptors that encode colour, spatial and local structure information to guide and enhance the performance of the transfer function. We propose to solve the high-dimensional distribution transfer problem in 1D space using an iterative projection approach with three statistical methods: Optimal Transport, L2 inference, and Kernel Regression, taking into
account available information about correspondences between the input and the target distributions. Our high-dimensional construction implies a new reconstruction step since each recoloured pixel benefits from the contribution of several estimated candidates using an averaging solution that allows denoising and artifact removal as well as colour transfer. The extensive experiments and analysis conducted in this thesis show quantitative and qualitative competitive results compared with the leading state of the art methods of colour transfer.