Geometric transformation is a fundamental operation in image processing, enabling images to be resized, translated, rotated, or projected into new geometric configurations. Unlike grey-level processing, which modifies pixel intensities, geometric transformation remaps pixel coordinates and determines their new intensity values through interpolation. This chapter introduces the principles of coordinate mapping, forward and inverse transformations, and interpolation methods such as nearest-neighbor and bilinear interpolation. It further explains affine transformations and perspective projection using homogeneous coordinates, highlighting their unified matrix representation. By combining basic operations, complex geometric deformations can be achieved, providing essential tools for image correction, alignment, and spatial manipulation in practical vision systems.

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Geometric Transformations

  • Bingqi Chen,
  • Siyao Chen

摘要

Geometric transformation is a fundamental operation in image processing, enabling images to be resized, translated, rotated, or projected into new geometric configurations. Unlike grey-level processing, which modifies pixel intensities, geometric transformation remaps pixel coordinates and determines their new intensity values through interpolation. This chapter introduces the principles of coordinate mapping, forward and inverse transformations, and interpolation methods such as nearest-neighbor and bilinear interpolation. It further explains affine transformations and perspective projection using homogeneous coordinates, highlighting their unified matrix representation. By combining basic operations, complex geometric deformations can be achieved, providing essential tools for image correction, alignment, and spatial manipulation in practical vision systems.