UC Santa Cruz
Global Image Filtering
- Author(s): Talebi, Hossein
- Advisor(s): Milanfar, Peyman
- et al.
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
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).