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In this paper, we introduce a novel notion of separation surfaces for image decomposition. A surface is embedded in the spectral total-variation (TV) 3D domain and encodes a spatially varying separation scale. The method allows good separation of textures with gradually varying pattern size, pattern contrast, or illumination. The recently proposed TV spectral framework is used to decompose the image into a continuum of textural scales. A desired texture, within a scale range, is found by fitting a surface to the local maximal responses in the spectral domain. A band above and below the surface, referred to as the texture stratum, defines for each pixel the adaptive scale range of the texture. Based on the decomposition, an application is proposed, which can attenuate or enhance textures in the image in a very natural and visually convincing manner.

Separation Surfaces in the Spectral TV Domain for Texture Decomposition