Calculation of zernike moments from binary image BW

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Calculation of zernike moments from binary image BW

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Zernike moments are a set of orthogonal moments widely used in image analysis and pattern recognition. They provide powerful descriptors for shape representation, especially when working with binary images. The calculation involves projecting the image onto a set of Zernike polynomials defined over a unit circle.

For a binary image (BW), the process involves several key steps: Image Normalization: The binary image is first mapped to fit within a unit circle, ensuring consistent scale and translation invariance. Moment Computation: Zernike moments are computed by integrating the product of the image function and Zernike polynomials over the unit disk. The orthogonal nature of these polynomials ensures minimal information redundancy. Feature Extraction: The magnitude of Zernike moments is often used as a robust feature set, invariant to rotation and noise.

Zernike moments are particularly useful in applications like object recognition, medical imaging, and shape matching due to their ability to capture fine-grained details while maintaining mathematical stability.

For implementation, efficient algorithms exist to compute these moments by leveraging recursive relations and fast numerical integration techniques. Higher-order moments can capture more intricate shape details but may require careful handling of computational precision.