Data Compression Lec#15

Block Truncation Coding

Block Truncation Coding, or BTC, is a type of lossy image compression technique for greyscale images. It divides the original images into blocks and then uses quantize to reduce the number of grey levels in each block whilst maintaining the same mean and standard deviation. BTC has also been adapted to video compression
BTC was first proposed by Professors Mitchell and Delp at Purdue University. Another variation of BTC is Absolute Moment Block Truncation Coding or AMBTC, in which instead of using the standard deviation the first absolute moment is preserved along with the mean. AMBTC is computationally simpler than BTC. AMBTC was proposed by Lema and Mitchell.
Sub blocks of 4x4 pixels allow compression of about 25% assuming 8-bit integer values are used during transmission or storage. Larger blocks allow greater compression ("a" and "b" values spread over more pixels) however quality also reduces with the increase in block size due to the nature of the algorithm.
Compression procedure
A 256x256 pixel image is divided into blocks of typically 4x4 pixels. For each block the Mean and Standard Deviation are calculated, these values change from block to block. These two values define what values the reconstructed or new block will have, in other words the blocks of the BTC compressed image will all have the same mean and standard deviation of the original image. A two level quantization on the block is where we gain the compression, it is performed as follows:

Where x(i,j) are pixel elements of the original block and y(i,j) are elements of the compressed block. In words this can be explained as: If a pixel value is greater than the mean it is assigned the value "1", otherwise "0". Values equal to the mean can have either a "1" or a "0" depending on the preference of the person or organization implementing the algorithm.
This 16 bit block is stored or transmitted along with the values of Mean and Standard Deviation. Reconstruction is made with two values "a" and "b" which preserve the mean and the standard deviation. The values of "a" and "b" can be computed as follows: