Convolution-based interpolation for fast, high-quality rotation of images

Area of Science:

• Computer Vision
• Image Processing
• Algorithm Design

Background:

• Image rotation is a fundamental operation in digital image processing.
• Existing methods often face trade-offs between speed, quality, and computational complexity.
• Accurate decomposition of rotation into simpler operations is crucial for high-fidelity results.

Purpose of the Study:

• To design fast and high-quality image rotation algorithms.
• To develop a theoretical framework for optimizing 1D translation accuracy in rotations.
• To present an improved least-square formulation for rotation problem optimality.

Main Methods:

• Decomposition of 2D rotation into a sequence of 1D translations.
• Development of a general theoretical framework for translation design and performance.
• Separable three-pass implementation using 1D convolutions and explicit filter formulas for spline and bandlimited signals.

Main Results:

• The proposed algorithm, particularly higher-order versions, significantly outperforms standard high-accuracy rotation techniques.
• The algorithm demonstrates superior speed and image quality compared to existing methods.
• Computational complexity scales linearly with the order of accuracy, offering efficiency gains.

Conclusions:

• The novel decomposition and optimization approach provides a superior method for image rotation.
• The sine-based algorithm, implementable with 1D FFTs, yields the best quality results.
• This work advances the state-of-the-art in fast and accurate digital image rotation.