The state-of-the-art digital photography has made great progress over the past decades;

however, imaging still suffers from distortions such as noise and blur. The result is an increased demand for more efficient and effective computational photography algorithms. In this dissertation a new data-dependent image filtering scheme is proposed. More specifically, various image enhancement applications from denoising to image editing are thoroughly explained. The proposed filters exploit the existing self-similarity of images to introduce a new set of basis functions capable of efficiently describing image components.

First, by focusing on the local similarities of images, measured by pixel affinities, a spatially adapted filtering strategy capable of improving performance of the existing local filters is introduced. The filter’s strength is tuned by estimating the local signal-to-noise ratio (SNR), such that high SNR image patches are filtered more aggressively and low SNR patches are treated conservatively.

Second, we explore the global similarity of images and introduce a new image filtering scheme based on the spectrum of global affinities. The global filter is derived from a fully connected graph representing the image, and can be approximated using the Nystrom extension. Using this, we drive an approximation to the spectral (principal) components of the global filter, which can be implemented efficiently by sampling a fairly small percentage of the pixels in the image. These orthonormal eigenfunctions are highly expressive of the coarse and fine details in the underlying image, where each eigenvector can be interpreted as one scale of a data-dependent multiscale image

decomposition. In this filtering scheme, each eigenvalue can boost or suppress the

corresponding signal component in each scale. Experiments illustrate that the mapping

of the eigenvalues by an appropriate polynomial function endows the filter with a number

of important capabilities, such as edge-aware sharpening, denoising, tone manipulation

and abstraction.

Lastly, asymptotic performance of the global denoising filter is analyzed to show that its performance always improves as a function of image size, regardless of image content. The rate of this improvement is estimated as an upper bound on the mean-squared-error (MSE).