Probabilistic Neural Network (PNN) for Image Classification with Wavelet Processing

In this process, we employ wavelet transforms for image pre-processing. Wavelet analysis enables effective extraction of multi-scale image features, capturing both frequency and spatial information through decomposition using functions like Daubechies or Haar wavelets. The feature extraction typically involves computing approximation coefficients (low-frequency components) and detail coefficients (high-frequency components) across multiple resolution levels. Following feature extraction, we utilize Probabilistic Neural Networks (PNN) for image classification. PNN operates based on Bayesian decision theory and kernel density estimation, implemented through four layers: input layer, pattern layer, summation layer, and output layer. The pattern layer computes Gaussian kernel functions using extracted feature vectors, while the summation layer aggregates probabilities for each class. The output layer then applies a competitive transfer function to determine the final classification based on maximum probability. This approach provides fast training and inherent parallel processing capabilities suitable for real-time image recognition systems. Key implementation steps include: 1. Wavelet decomposition using pywt.wavedec2() for 2D images 2. Feature vector construction from wavelet coefficients 3. PNN training with smooth factor optimization via Parzen window estimation 4. Classification using probabilistic decision boundaries with minimal misclassification risk