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Explore the world of topological descriptors and scalar field comparison in this comprehensive lecture by Vijay Natarajan from the Indian Institute of Science, Bengaluru. Delve into the challenges posed by complex data from high-fidelity computational simulations and high-resolution imaging devices. Discover how topological descriptors, particularly merge trees, provide abstract representations of data features that are succinct and suitable for visual analysis. Learn about tree edit distance-based measures for comparing merge trees, their mathematical properties, and efficient computation methods. Gain insights into the application of these techniques for intuitive feature-driven analysis and visualization of CFD and 3D cryo-electron microscopy data. Enhance your understanding of advanced data analysis methods crucial for handling increasingly complex datasets in various scientific fields.