2,381 research outputs found
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Well-posedness of a nonlinear integro-differential problem and its rearranged formulation
We study the existence and uniqueness of solutions of a nonlinear
integro-differential problem which we reformulate introducing the notion of the
decreasing rearrangement of the solution. A dimensional reduction of the
problem is obtained and a detailed analysis of the properties of the solutions
of the model is provided. Finally, a fast numerical method is devised and
implemented to show the performance of the model when typical image processing
tasks such as filtering and segmentation are performed.Comment: Final version. To appear in Nolinear Analysis Real World Applications
(2016
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