<ul data-eligibleForWebStory="true"><li>Density-equalizing map (DEM) is a valuable technique for shape deformations based on underlying density function.</li><li>Traditional DEM methods rely on numerical solvers or optimization-based approaches, leading to accuracy limitations and other challenges.</li><li>A new approach, called learning-based density-equalizing mapping (LDEM), using deep neural networks is proposed.</li><li>LDEM introduces a loss function ensuring density uniformity and geometric regularity and utilizes a hierarchical prediction approach.</li><li>The method shows superior properties for density-equalizing and bijectivity compared to previous methods across various density distributions.</li><li>LDEM can be easily extended from 2D to 3D without altering the model architecture or loss formulation.</li><li>The technique opens up new possibilities for efficient and reliable computation of density-equalizing maps.</li><li>LDEM can be applied to tasks like surface remeshing with different effects.</li><li>The paper is available on arXiv with the identifier: 2506.10027v1.</li></ul>

Learning-based density-equalizing map

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