Spectral Angle Calculation and Spectral Angle Matching

The Spectral Angle is a metric used to quantify the correlation between pixels, calculated based on the angular separation between two pixel value vectors. The magnitude of the spectral angle reflects the similarity between two pixels - a smaller angle indicates higher similarity. This program is designed to compute spectral angles and perform spectral angle matching to better understand correlation differences between pixels. To achieve this objective, the implementation incorporates multiple algorithms and techniques including data preprocessing (normalization and dimensionality reduction), feature extraction (spectral signature isolation), and similarity computation using vector dot products and arccosine functions. The core algorithm calculates the spectral angle θ between two n-dimensional vectors A and B using the formula: θ = arccos((A·B) / (||A|| ||B||)), ensuring angular values range between 0 and π/2 radians. Through these methodological applications, the spectral angle calculation results become more precise and reliable, thereby providing stronger support for research in related fields such as hyperspectral image analysis and remote sensing classification.