Homomorphic Filter Implementation in MATLAB

This paper presents our MATLAB implementation of a homomorphic filter, a powerful tool for advanced image processing. Homomorphic filtering is a widely adopted technique particularly effective for image enhancement, segmentation, and various other image processing applications. Our implementation follows the core mathematical framework: applying logarithmic transformation to separate illumination and reflectance components, processing them in the frequency domain using specially designed filter functions (such as Gaussian high-pass filters), and finally reconstructing the enhanced image through exponential transformation. In our experimental validation, we systematically tested the filter's performance across different image types. The accompanying experimental images demonstrate how homomorphic filtering effectively improves image clarity, enhances contrast in shadow regions, and facilitates better analytical capabilities. Key MATLAB functions utilized include fft2 for frequency domain transformation, ifft2 for inverse transformation, and custom filter design routines. We believe these experimental results provide valuable insights for researchers and offer new perspectives on homomorphic filtering applications in digital image processing.