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      Journal: International Journal of Computer Vision
      Publisher: Springer Nature

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          Sparse coding with an overcomplete basis set: A strategy employed by V1?

          Bruno Olshausen, David J Field (1997)
          Article 0 comments Cited 437 times – based on 0 reviews     Review now
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            Stable recovery of sparse overcomplete representations in the presence of noise

            D.L. Donoho, M Elad, V.N. Temlyakov (2006)
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              What energy functions can be minimized via graph cuts?

              Vladimir Kolmogorov, Ramin Zabih (2004)
              In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.
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                Author and article information

                Journal
                Title: International Journal of Computer Vision
                Abbreviated Title: Int J Comput Vis
                Publisher: Springer Nature
                ISSN (Print): 0920-5691
                ISSN (Electronic): 1573-1405
                Publication date Created: April 2009
                Publication date (Print): January 2009
                Volume: 82
                Issue: 2
                Pages: 205-229
                Article
                DOI: 10.1007/s11263-008-0197-6
                SO-VID: 65e075f5-8e6c-4f9b-b099-095ba68ba774
                Copyright © © 2009
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