Hu Moment Invariants Extraction Algorithm

Moment invariants represent a widely adopted feature extraction method in image processing and pattern recognition systems. Among these, Hu moment invariants stand as one of the most classical and commonly used invariant moment representations. Their primary characteristic lies in maintaining invariance to image translation, rotation, and scaling transformations, making them particularly suitable for applications such as object recognition and image matching.

Hu moment invariants are constructed based on the second and third-order central moments of images. Through specific nonlinear combinations, they yield seven invariant moment features. These features effectively describe the overall shape characteristics of images while remaining unaffected by the aforementioned geometric transformations. From an implementation perspective, the calculation typically involves computing raw moments using integral image techniques, followed by central moment normalization and the application of Hu's seven invariant equations.

In practical applications, Hu moment invariants offer advantages of computational efficiency and straightforward implementation. Modern image processing libraries like OpenCV provide optimized Hu moment calculation functions - typically through methods like cv2.HuMoments() which accepts normalized central moments as input. The entire feature extraction process can often be accomplished with just a few lines of code, making it suitable for real-time systems while maintaining strong performance characteristics.

It's important to note that while Hu moments exhibit invariance to geometric transformations, they demonstrate sensitivity to noise. Practical implementations frequently incorporate preprocessing steps such as Gaussian filtering or morphological operations to enhance feature robustness. Additionally, Hu moments primarily capture global characteristics and have limited descriptive capability for local details. Therefore, they are often combined with local feature descriptors like SIFT or ORB in hybrid recognition systems to achieve comprehensive feature representation.