Geometric correction of digital images using orthonormal decomposition

Area of Science:

• Computer Science
• Image Processing
• Numerical Analysis

Background:

• Geometric distortion is a common issue in digital images.
• Accurate correction is crucial for various image analysis tasks.
• Existing methods may lack efficiency or numerical stability.

Purpose of the Study:

• To develop a novel algorithm for correcting geometric image distortion.
• To enhance computational efficiency and numerical stability in geometric correction.
• To compare the proposed algorithm with existing image processing techniques.

Main Methods:

• Utilizes orthonormal decomposition and a two-dimensional Horner's scheme.
• Constructs and evaluates polynomial equations of arbitrary degree.
• Employs a least-squares criterion for determining corrected pixel positions.

Main Results:

• The algorithm demonstrates reduced mathematical operations and increased flexibility.
• Achieves numerical stability superior to or comparable with existing methods.
• Provides corrected pixel positions with accuracy at or exceeding the pixel size.

Conclusions:

• The developed algorithm offers an efficient and numerically stable solution for geometric image distortion correction.
• The method achieves high accuracy, meeting or surpassing pixel-level precision.
• Presents a valuable advancement in digital image processing techniques.