Name
Abstract | ||
|---|---|---|
We consider a class of convex functionals that can be seen as smooth approximations of the a"" (1)-TV model. The minimizers of such functionals were shown to exhibit a qualitatively different behavior compared to the nonsmooth a"" (1)-TV model (Nikolova et al. in Exact histogram specification for digital images using a variational approach, 2012). Here we focus on the way the parameters involved in these functionals determine the features of the minimizers . We give explicit relationships between the minimizers and these parameters. Given an input digital image f, we prove that the error obeys where b is a constant independent of the input image. Further we can set the parameters so that epsilon > 0 is arbitrarily close to zero. More precisely, we exhibit explicit formulae relating the model parameters, the input image f and the values b and epsilon. Conversely, we can fix the parameter values so that the error meets some prescribed b,epsilon. All theoretical results are confirmed using numerical tests on natural digital images of different sizes with disparate content and quality. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10851-013-0420-0 | JOURNAL OF MATHEMATICAL IMAGING AND VISION |
Keywords | Field | DocType |
Parameter estimation for smoothed l(1)-TV model,Histogram specification,Quantisation noise,l(infinity) error,Convex optimization | Histogram,Numerical tests,Mathematical optimization,Explicit formulae,Approximations of π,Digital image,Regular polygon,Convex optimization,Mathematics | Journal |
Volume | Issue | ISSN |
48 | SP2 | 0924-9907 |
Citations | PageRank | References |
3 | 0.49 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| F. Baus | 1 | 3 | 0.49 |
| Mila Nikolova | 2 | 1792 | 105.71 |
| gabriele steidl | 3 | 896 | 84.29 |