Huffman Encoding of Input Images with Image Processing and Comparison

Write a program that performs Huffman encoding on input images, calculates and displays the original image's entropy and the average codeword length after encoding, and reconstructs the image from the encoded data. The implementation should include building a Huffman tree based on pixel frequency distribution, generating optimal prefix codes, and computing entropy using the probability mass function of pixel values. Additionally, implement image smoothing using a Gaussian filter with configurable kernel size and sigma parameters, followed by sharpening using Sobel operators (for edge detection along horizontal and vertical directions) and Laplacian operators (for second-derivative-based enhancement). The code should handle gradient calculation and magnitude computation for Sobel, and negative central coefficient convolution for Laplacian. Finally, compare the results of different processing methods by evaluating image clarity, detail enhancement level, and processing efficiency. This comprehensive analysis should include quantitative metrics like PSNR (Peak Signal-to-Noise Ratio) for reconstruction quality and qualitative assessment of visual features to thoroughly evaluate algorithm effectiveness and performance.