Comparisons between images of 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.
We compare color-coded fracture patterns using new metrics based on image warping where warping aligns misaligned or misshapen features. The warping is done reliably and accurately using space-filling curves to sample the images. A new image-based amplitude metric and a phase distance measure are provided to quantify differences between fracture patterns and these show promise as tools in parameter calibration.
We propose a color map for vectors based on the use of the Lightness-Chroma-hue (L*Ch) color space defined by the International Commission on Illumination (CIE). This color space is designed to be perceptually uniform so that a given numerical change in the color code corresponds to a given perceived change in color. Within the color space, vector magnitude is mapped to the intensity of the color while hue (a periodic quantity) indicates the vector direction (also periodic). Additional information about the vector field can be encoded in the color map by varying the chroma. The L2 norm on the color codes induces a metric on vectors, allowing us to analyze and visualize the differences in vectors through differences in color. An example, analyzing smooth vector fields, is shown in Fig. 1.
We compare fracture patterns utilizing the colormap and image warping. Firstly, the fractures, described by a vector jump in displacement, are visualized using the CIEL*Ch color map. We then use space-filling curves to convert the color-mapped 2D image to a 1D function and perform functional warping to rectify the misalignment between images. The conversion to a function provides a simpler and more reliable numerical solution compared to image warping which is computationally challenging. After optimally aligning images, two measures are defined, (1) the amount of warping needed to align the images and (2) an L2 distance after alignment. These measures quantify the differences between fracture patterns and can be visualized naturally through the color map. We demonstrate the usefulness of the new tools in comparing vector fields from Arctic sea-ice motion data in January 1994 and January 1995 and the potential of applying our new measures in model calibration in a multi-crack experiment.