A predominant feature of Arctic sea ice is the formation of fractures. Comparisons between images of the modeled and observed ice fractures provide a way to evaluate the performance of a sea ice model. However, direct comparison between patterns of fracture based on point-wise differences is flawed since fractures may be misaligned or misshapen between observations and a simulation. This motivates the need for new metrics to quantify the difference between images of fracture patterns.
This study developed new metrics based on image warping for comparing fracture patterns. Warping two-dimensional images is numerically tricky and analytically less convenient than the similar process of aligning functions. We introduce the idea of sampling a two-dimensional image using a space-filling curve to transform two-dimensional image warping into a more reliable functional alignment problem. The paper shows the results of idealized fractures to demonstrate that image alignment is possible and accurate using space-filling curves. New image-based amplitude metric and phase distance measures are provided to quantify differences between fracture patterns and show promise as tools in parameter calibration.
Sea ice fractures exist on curves within a two-dimensional domain. These discrete localized linear features are not likely to be coincident in both the observation and simulation. Traditional metrics based on point-wise differences, such as root mean squared (RMS) error, are flawed when comparing these features. Models that fail to predict fractures can have a smaller RMS error than models that predict these features but at a somewhat displaced position or altered orientation than observations indicate. Image warping optimally aligns image patterns and provides measures that quantify the amount of warping needed to align the images and an L2 distance after alignment – measures used in place of RMS error. However, warping two-dimensional images is numerically tricky and analytically less convenient than the similar process of aligning functions. We propose the use of space-filling curves to convert the 2D image to a 1D function and perform functional alignment to rectify the misalignment between images. The conversion to a function space provides a simpler and more reliable solution compared to image warping. We demonstrate the potential of applying our new measures in model calibration in a multi-crack experiment. Specifically, we illustrate the use of (i) image warping to align localized features for comparison, (ii) space-filling curves to reduce image warping to the easier problem of functional alignment, (iii) metrics for comparison of image features based on image warping, and (iv) the CIEL*Ch color map to visualize the metrics.