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="")