Question

In lectures we discussed how bitmap images are stored as a grid of pixel values. Each pixel has a colour value, and colour can be encoded using the RGB encoding scheme. In lectures we also discussed using the RLE compression technique. Examples of the RLE technique being used to compress text were given. Instead of storing every single character individually, if there is a sequential run of identical characters, data on one character is stored along with a count of the number of occurrences of that character. Therefore text like "AAAABBB" could be compressed using the RLE technique to "A4B3". For the next two questions we will look at using this same RLE technique for compressing image data. We can store the colour value for one pixel, followed by an integer value indicating how many sequential pixels with the same colour value there are. Look at the bitmap image below. Each square represents a pixel. The colour value for each pixel will be encoded using the RGB encoding scheme. You can assume that a 16 bit integer value will be used to indicate the number of sequential pixels with the same colour value. How much memory, in bytes will be required to store the image above uncompressed? Please answer with a decimal value. Do not use any spaces, punctuation letters or symbols. How much memory, in bytes will be required to store the image if we compressed it using the RLE compression technique discussed? Please answer with a decimal value. Do not use any spaces, punctuation letters or symbols. What compression ratio have we achieved? Please answer with a decimal value. Do not use any spaces, punctuation letters or symbols

Answer 1

a.

Color representation scheme - RGB - typically uses 24 bits (3 bytes) to represent the color of pixel with 8 bits each for Red, Green and Blue intensities.

1. Since the above image consists of 10 pixels and each pixel need 3 bytes of storage, hence total number of bytes needed to store given image in uncompressed format = 10*3 = 30 bytes

2. When RLE technique is used, then since all the 10 pixels have same color, hence total number of bits needed to represent image in RLE compressed format = Number of bits for color of pixel + number of bits needed to indicate number of sequential pixels = 24 + 16 = 40 bits = 5 bytes

3. Compression ratio = (size of image in compressed format)/(size of image in uncompressed format) = 30/5 = 6

b. Since there are 12 pixels here with each pixel needs 3 bytes to represent color of pixel.

1. Total number of bytes needed to store given image = 12*3 = 36 bytes

2. When RLE technique is used, then since there are 3 different sequence of colors and each sequence will need 24 bits to represent color of pixel and 16 bits for number of sequential pixels with same colors.

Hence total number of storage needed = 3*(24+16) = 120 bits = 15 bytes

3. Compression ratio = 36/15 = 2.4

Please comment for any clarification.