Adaptive Image Resizing Based on Continuous-Domain Stochastic Modeling
H. Kirshner, A. Bourquard, J.P. Ward, M. Porat, M. Unser
IEEE Transactions on Image Processing, vol. 23, no. 1, pp. 413-423, January 2014.
We introduce an adaptive continuous-domain modeling approach to texture and natural images. The continuous-domain image is assumed to be a smooth function, and we embed it in a parameterized Sobolev space. We point out a link between Sobolev spaces and stochastic auto-regressive models, and exploit it for optimally choosing Sobolev parameters from available pixel values. To this aim, we use exact continuous-to-discrete mapping of the auto-regressive model that is based on symmetric exponential splines. The mapping is computationally efficient, and we exploit it for maximizing an approximated Gaussian likelihood function. We account for non-Gaussian Lévy-type processes by deriving a more robust estimator that is based on the sample auto-correlation sequence. Both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria. Experimental image resizing results indicate that the auto-correlation criterion can cope better with non-Gaussian processes and model mismatch. Our work demonstrates the importance of the auto-correlation function in adaptive image interpolation and image modeling tasks, and we believe it is instrumental in other image processing tasks as well.
@ARTICLE(http://bigwww.epfl.ch/publications/kirshner1401.html,
AUTHOR="Kirshner, H. and Bourquard, A. and Ward, J.P. and Porat, M. and
Unser, M.",
TITLE="Adaptive Image Resizing Based on Continuous-Domain Stochastic
Modeling",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2014",
volume="23",
number="1",
pages="413--423",
month="January",
note="")