The major factor in determining the quality of an image which has been automatically retargeted is "intention". Does the new image convey the same intention as as the original image? It is practically impossible to determine an intent computationally, and in may cases different people will see different intentions in the same image.
A possible way to give the user some control on image retargeting is by executing the shift-map program using several different parameters. Each set of parameters will give a different result, and the user could select the result he likes most.
For image reduction we have designed the following four fixed sets of parameters, each giving a different result:
(1) Use Border: The output image is constrained to include the borders of the original image. The shift-map is only in the x direction, and image gradients are used as a saliency map for the data term.
(2) Allow crop: The shift-map is in the x direction, and image gradient is used as a saliency map. Preference to the use of image boundaries is given only as a soft constraint.
(3) Scale + Shift-Map: Use (2) on an image that was uniformly scaled to half of the final reduction size.
(4) Use Border+Y-Shift: Shift-map in both x and y directions. No saliency map is used, and the output must include the image boundaries.
We run shift-map with the four parameters above on a dataset provided by Miki Rubinstein and Ariel Shamir for retargeting images to 4 different sizes (reduction to 50%, 75%, expansion to 125%, 150%). In each case we got four results corresponding to the four parameters sets above, and selected the result that looked best for us. Results are here.
Examples for the 4 sets of parameters that provided different "flavors" of shift-map* (20 examples of 4 runs, all on reduction in 50%) are here.
In cases where no saliency map is used and the only constrain is to use the image boundaries, the algorithm is aiming for best possible retargeting, taking in consideration only the smoothness term (e.g. best possible stitching). This can lead to unexpected and interesting results, some even with artistic value by their own. Several of those results are here and here .