Planar Curve

Planar curves, the mathematical representation of two-dimensional shapes, are a focus of ongoing research driven by applications in diverse fields like image analysis and machine learning. Current research emphasizes developing robust methods for representing and analyzing these curves, including the use of Gaussian mixture models, deep neural networks for learning differential invariants, and novel series expansions like Chebyshev-Sobolev series for efficient data representation. These advancements improve the accuracy and efficiency of tasks such as shape recognition, curve reconstruction, and uncertainty quantification in shape analysis, impacting fields ranging from computer vision to digital geometry.