Global image editing using the spectrum of affinity matrices

In this work we introduce a new image editing tool, based on the spectrum of a global filter computed from image affinities. Recently, we have shown that the global filter derived from a fully connected graph representing the image, can be approximated using the Nyström extension [1]. This filter is computed by approximating the leading eigenvectors of the filter. 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. Our analysis shows 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 and tone manipulation.