Isometric Mapping

Isometric mapping focuses on creating lower-dimensional representations of data while preserving distances between points, a crucial task in manifold learning and dimensionality reduction. Current research emphasizes developing neural network-based models and algorithms, such as those incorporating Riemannian geometry or Parzen-Rosenblatt window constraints, to improve the accuracy and robustness of isometric mappings, particularly for high-dimensional and non-uniform data. These advancements find applications in diverse fields, including 3D vision, medical image analysis (e.g., skin pigment decomposition and cancer diagnosis), and drug design, enabling improved data analysis and prediction capabilities. The development of complete and continuous isometry invariants is also a significant area of focus, aiming to improve the reliability of comparing complex shapes and structures.