how to know how many number of symbol needed for huffman coding ?

hi, I want to perform Huffman coding for 512x512 image. I'm new to this. how do I know how many numbers of symbols (NOS) do I need to create for Huffman table?

Answer 1

[Walter Roberson]

The number you need is length(unique(YourMatrix)), possibly plus one for an end of stream marker.

[nur aqila]

I don't understand. so what is the minimum NOS that I can create? because some people they used 15, 20 number of symbols. what I'm planning right now is I want to perform multiple Huffman table but I don't know how many numbers of symbol should I be doing

[Walter Roberson]

You have a 512 x 512 image. Suppose that the image is an 8 color image that uses only the colors [0, 0, 0], [0, 0, 255], [0, 255, 0], [0, 255, 255], [255, 0, 0], [255, 0, 255], [255, 255, 0], and [255, 255, 255]. Although there are 8 distinct colors, there are only 2 distinct values, unique() would be 0 and 255, length(unique()) is 2, so only 2 distinct huffman symbols would be needed, plus possibly an "end of stream" symbol (if you do not have an "end of stream" symbol then you need some way of storing exactly how many bits are used in the stored huffman tables, as huffman tables are bit aligned not byte aligned.)

[Walter Roberson]

Except for the case where the 512 x 512 image is all 0 or all 255, the minimum number of input symbols you can use for the huffman process is 2, one symbol for binary 0 and 1 symbol for binary 1. With the huffman encoding process it is legal to interpret the source numbers bit by bit, or 2 bits at a time, or 3 bits at a time, or any other number of bits at a time that factors into the total number of bits in the data. With the huffman encoding process, if it just happened that the binary stream included a bunch of occurrences of binary 00 and binary 111 it would be legal to create one input symbol for binary 00 and another for binary 111 . The huffman encoding process doesn't care... but your choice of symbols can end up influencing the length of the output.

[nur aqila]

i got it. thanks for your help