No.2 – (a) What is the entropy ( η ) of the image below, where numbers (0, 20, 50, 99) denote the gray-level intensities? (b) Show step by step how to construct the Huffman tree to encode the above four intensity values in this image. Show the resulting code for each intensity value. Answer: (c) What is the average number of bits needed for each pixel, using your Huffman code? How does it compare to η ? Answer: Average number of bits = 0.5×1 + 0.25×2 + 2×0.125×3 = 1.75 This happens to be identical to η - it only happens when all probabilities are 2 −k where k is an integer. Otherwise, this number will be larger than η .