A Numerical Imaging Approach to Comparative Visualization

Numerical simulation is now an acceptable mode of inquiry into a wide range of physical phenomena. As computational methods and hardware continue to advance, it is often the case that older, legacy applications no longer implement the best technology for solving a problem and must be updated. Once modified, these applications need to be extensively studied to ensure that they retain the important characteristics of the original application (accuracy, convergence, etc.). Furthermore, as experimental techniques continue to advance, it is possible to extensively validate existing numerical simulation applications with more accurate physical measurements. Side-by-side comparison and juxtaposition facilitate visual verification of verisimilitude. However in many applications the datasets are too large and complex, and visualization techniques too complex or ill-understood, to rely solely on visual verification. In the present work a quantitative, computable metric is proposed which incorporates both quantitative measures and a visual comparison element to highlight the differences between two datasets. The comparison metric is multi-part and captures the spatial spread of the differences, and can also highlight the differences in regions of high and low transitions.The metric can be applied to both datasets and images alike. We demonstrate the effectiveness of the proposed metric on a variety of examples. These proposed method can not only be used for examples from the computational sciences, but can also be applied towards the comparison of datasets and images from other domains including medical.