Projective Geometry

Projective geometry studies the properties of geometric figures that remain invariant under projective transformations, focusing on applications in computer vision and machine learning. Current research emphasizes efficient algorithms for homography decomposition and marker-based pose estimation, including novel marker designs for curved surfaces and the development of projective-geometry-aware neural networks like the Geometric Algebra Transformer and DProST for tasks such as 3D reconstruction and 6D pose estimation. These advancements improve the accuracy and efficiency of computer vision systems, impacting areas such as augmented reality, robotics, and 3D modeling by enabling more robust and reliable object recognition and scene understanding.