Random Sampling of the Above Image Using a 9×9 Window

In the following steps, we will detail the image processing procedure to obtain feature vectors: 1. First, we will perform random sampling on the image using a 9×9 pixel window. A total of 200 sub-images will be extracted from the original image through this sampling process. In code implementation, this can be achieved using random coordinate generation with boundary checks to ensure valid window positions. 2. Next, each 9×9 sub-image will be converted into an 81-dimensional row vector by flattening all columns sequentially. This vectorization step is typically implemented using reshape operations that convert 2D image blocks into 1D arrays while preserving spatial relationships. 3. We will apply Karhunen-Loève (KL) transformation to all 200 row vectors and compute the eigenvectors and eigenvalues of their covariance matrix. The eigenvalues and corresponding eigenvectors will be sorted in descending order. This PCA-based approach can be implemented using eigenvalue decomposition functions (e.g., numpy.linalg.eig) to extract the principal components. 4. To capture the principal components, we will select the top 40 eigenvectors corresponding to the largest eigenvalues. Each original image block will be projected onto these 40 eigenvectors using dot product operations, with the resulting projection coefficients serving as the feature vector for that sub-block. This dimensionality reduction step preserves the most significant variance in the data. 5. Finally, we will obtain feature vectors for all sub-blocks. These vectors represent compressed yet informative descriptors of the original image patches, suitable for subsequent pattern recognition or machine learning tasks. Through these steps, we comprehensively describe the image processing pipeline and obtain distinctive feature vectors for each sub-image block, enabling efficient image analysis and comparison.