Implementation of 7 Invariant Moments in MATLAB

In the fields of image processing and pattern recognition, invariant moments serve as an important feature description method, particularly suitable for shape recognition and image matching. The key characteristic of invariant moments is their invariance to image translation, rotation, and scaling, making them highly valuable in numerous practical applications. MATLAB, as a powerful scientific computing tool, provides efficient matrix operations and image processing capabilities, making it ideal for implementing invariant moment calculations. The computation of 7 invariant moments in MATLAB typically involves the following steps: Image Preprocessing: First, binarize the input image to ensure it contains only black and white pixel values. This facilitates boundary extraction and centroid calculation for subsequent moment computations. In MATLAB, this can be implemented using functions like im2bw() or graythresh() for automatic thresholding. Calculation of Geometric Moments: Geometric moments (ordinary moments) form the foundation for computing invariant moments. Typically, second and third-order geometric moments need to be calculated, including m00 (area), m10, m01 (centroid coordinates), m20, m11, m02, m30, m21, m12, and m03. MATLAB implementation involves using nested loops or vectorized operations to efficiently compute these moments by iterating through image pixels with appropriate weight factors (x^p * y^q). Normalized Central Moments: Based on geometric moments, central moments can be calculated, which possess translation invariance. Normalized central moments are then derived to further eliminate scale effects. In code implementation, central moments are computed by shifting coordinates to the centroid, while normalized moments are obtained by scaling with appropriate powers of the area (m00). Calculation of Hu Invariant Moments: Hu invariant moments consist of 7 feature quantities combined from second and third-order central moments, exhibiting invariance to translation, rotation, and scaling. These moments are widely applied in shape matching and object recognition. The MATLAB implementation involves combining the normalized central moments using Hu's specific mathematical formulas, which can be efficiently coded using matrix operations and algebraic expressions. In MATLAB, matrix operations can be leveraged to efficiently implement the above steps. For example, geometric moments can be calculated by traversing image pixels, then central moments and normalized central moments can be derived using formulas, finally combining them to obtain the 7 Hu invariant moments. The implementation can be optimized using MATLAB's built-in functions like regionprops for basic moment calculations or custom vectorized code for better performance. Invariant moments find wide applications in image classification, object detection, medical image analysis, and other domains. For instance, in handwritten character recognition, invariant moments can extract geometric features of characters; in industrial inspection, they can be used for part shape matching and quality control. MATLAB's matrix operations and Image Processing Toolbox provide convenience for invariant moment calculations. Developers can further optimize computational efficiency or combine other feature extraction methods according to specific requirements to improve recognition accuracy. The implementation can be extended by incorporating additional moment types or integrating with machine learning classifiers for enhanced pattern recognition capabilities.