Potts Model - The Potts Model in Signal and Image Processing

The Potts Model in Signal and Image Processing

The Potts model has applications in signal reconstruction. Assume that we are given noisy observation of a piecewise constant signal To recover from the noisy observation vector, on seeks a minimizer of the corresponding inverse problem, the -Potts functional which is defined by

$P_\gamma(u) = \gamma \| \nabla u \|_0 + \| u-f\|_p^p = \gamma \# \{ i : u_i \neq u_{i+1} \} + \sum_{i=1}^n |u_i - f_i|^p$

The jump penalty forces piecewise constant solutions and the data term couples the minimizing candidate to the data The parameter controls the tradeoff between regularity and data fidelity. There are fast algorithms for the exact minimization of the L^1 and the L^2-Potts functional (Friedrich, Kempe, Liebscher, Winkler, 2008).

In image processing, the Potts functional is related to the segmentation problem. However, in two dimensions the problem is NP-hard (Boykov, Veksler, Zabih, 2001).

Famous quotes containing the words model, signal and/or image:

“She represents the unavowed aspiration of the male human being, his potential infidelity—and infidelity of a very special kind, which would lead him to the opposite of his wife, to the “woman of wax” whom he could model at will, make and unmake in any way he wished, even unto death.”
—Marguerite Duras (b. 1914)

“Mistakes, scandals, and failures no longer signal catastrophe. The crucial thing is that they be made credible, and that the public be made aware of the efforts being expended in that direction. The “marketing” immunity of governments is similar to that of the major brands of washing powder.”
—Jean Baudrillard (b. 1929)

“I passed a little further on and heard a lotus talk:
Who made the world and ruleth it, He hangeth on a stalk,
For I am in His image made, and all this tinkling tide
Is but a sliding drop of rain between His petals wide.”
—William Butler Yeats (1865–1939)