Predefined images were used as the input images for NASA G.Projector 3. The resolution of the predefined images was W = 20,000 pixels and H = 10,000 pixels. Parameter P = 200 was used for the predefined latitude and longitude images. Moreover, the accuracy of our proposed metrics was evaluated. These map projections were evaluated by the proposed metrics. In this study, the NASA G.Projector 3 software was employed to generate images for approximately 200 map projections. There are several mapping software programs, such as NASA’s G.Projector, Mapthematics LLC’s Geocart, and Esri’s ArcGIS. To improve the accuracy of the image-based method, a surface fitting-based noise reduction was accordingly introduced. The proposed method uses distorted images generated by mapping software as input and calculates distortion metrics based on the distorted images. The proposed metric is an improvement method of the previous GCA-based metrics, but it is not explicitly dependent on forward or inverse equations of map projections. In this study, we proposed an image-based metric to measure the distortion of map projections. Additionally, GCA-based metrics are explicitly dependent on inverse equations of map projections for transforming sample points. GCA-based and FWD–GCA-based metrics are explicitly dependent on the forward equations (orange lines in Figure 1) of map projections for transforming sample points. Furthermore, some common image filtering approaches (e.g., median filter and Gaussian filter) were applied to the proposed metric to further improve the visual or numerical results of our method. As there are large errors in ordinary image-based approaches, surface fitting-based noise reduction was introduced to reduce errors in image-based metrics. The use of mapping software avoids the explicit forward formulae of map projections. Mapping software was adopted in our approach to generate distorted images. Predefined images with known patterns were employed in our image-based approach to represent the relationship between colors and latitude (or longitude) coordinates. In this study, we exploited the characteristic of image in map projections and the characteristic of differential independence of GCA-based indicators to establish a novel image-based metric and to evaluate the distortions in map projections. Map projections are generally imagery forms to depict natural or social features. Image-based approaches are widely used in different domains. Experimental results demonstrated that the proposed image-based approach and surface fitting-based noise reduction are feasible and practical for the evaluation of the angular distortion of map projections. In the experiment, the NASA G.Projector was employed as the mapping software for evaluating more than 200 map projections. Sufficient experiments were made to validate the proposed image-based metric and the accompanying noise reduction approach. We established and solved systems of linear equations based on bivariate polynomial functions in the process of noise reduction. To reduce the error, we introduced surface-fitting-based noise reduction in our approach. However, there were fairly large computation errors in the ordinary image-based approach without special correction. Therefore, there was no direct explicit dependence on the forward equations of the map projections in our proposed metric. The mapping software performed the underlying transformation of map projections. The generated distorted images with known patterns were then exploited to calculate the proposed angular distortion metric. Images with predefined patterns were used to generate distorted images using mapping software. In this study, we introduced a novel image-based angular distortion metric based on the previous spherical great circle arcs-based metric. Measuring, analyzing, reducing, and optimizing distortions in map projections is important in cartography.
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