Image resampling problems

In practical computer vision systems resampling is commonplace. Format conversion, rectification, and warping are all operations that involve resampling. Therefore there is considerable interest in developing resampling schemes that operate with any scaling factor without user intervention. Most resampling methods assume that the original intensity distribution is correctly sampled and construct new images by linear filtering followed by resampling. It is the design of the filter that is usually the subject for discussion since one seeks to remove the aliases due to sampling in some mathematically tractable fashion. If a quantitative quality measure is given for an interpolation technique it is usually obtained by contracting then expanding the image back to its original size and computing the error between it and the original. For example, in a recent paper [ 12 ], images are contracted and expanded by a factor and compared quantitatively on the basis of signal-to-error ratios. However, several studies [ 15 , 6 ] have concluded that both signal-to-error ratio (SER) [ 4 ], and gradient-weighted error [ 16 ], are unsatisfactory measures of perceived image similarity. In Figure  1 , for example, images have been corrupted with additive noise, with different spatial correlation functions, but with identical signal-to-error ratios of 20 dB. At normal viewing distance readers with normal eyesight will find the left-hand image in Figure  1 considerably more disturbing than the right.

   
Figure: Images corrupted with additive Gaussian noise with a centre wavenumber of 8 radians per degree (left) and 32 radians per degree (right). Correct viewing distance is 51 cm.

In the absence of quantitative models of the human vision system a crude approach based on signal-to-error ratios is understandable. However, recently, simple models of the human vision system have become available ([ 15 , 18 , 17 ] for example). In this paper we adapt such a model, originally developed for examining coding errors, and test its effectiveness with resampled images.