Accurate calculation of image moments

Area of Science:

• Computer Vision
• Image Processing
• Mathematical Imaging

Background:

• Image moments are vital feature descriptors.
• Quantization errors in discrete signals compromise moment invariance, particularly in small images.
• Existing methods struggle with accuracy due to discretization.

Purpose of the Study:

• To develop a robust technique for calculating image moments from continuous signals.
• To mitigate quantization errors inherent in discrete image data.
• To enhance the stability of moment-based feature descriptors.

Main Methods:

• Piecewise polynomial interpolation to derive continuous signals from discrete images.
• Calculation of image moments using the continuous signal representation.
• Application of the proposed method to compute Zernike moments.

Main Results:

• Significantly increased accuracy in computed image moments.
• Preservation of moment invariant properties.
• Demonstrated enhanced stability of Zernike moments under geometrical transformations.
• Trivial computational overhead compared to traditional methods.

Conclusions:

• The proposed continuous signal approach effectively overcomes quantization errors in image moment calculation.
• This technique offers a more accurate and stable method for feature description, especially for small images.
• It provides a computationally efficient solution for improved image analysis.