Question

What is the zigzag order of the DCT coefficients and why is it being used?

Answer 1

DCT operates on one block at a time. Because there are 64 elements in an 8x8 block, this is called the 64-element or 64-coefficientDCT. The DCT transform operates on this block in a left- to-right, top-to-bottom manner. Pzy cos [(2x +1) jTu/16] co:s C, C-1A2 when i,j-o C, C otherwise The results of a 64-element DCT transfomare 1 DC coefficient and 63 AC coefficients. The DC coefficient represents the average color of the 8x8 region. The 63 AC coefficients represent color change across the block. Low-numbered coefficients represent low-frequency color change or gradual color change across the region. High-numbered coefficients represent high-frequency color change, or color which changes rapidly from one pixel to anotherwithin the block. These 64 results are written in a zig-zag order as follows, with the DC coefficient followed by AC coefficients of increasing frequency

ig ag sequencing: AC10 AC AC20 AC21 AC'22 AC'23 AC24 AC30 AC31 AC"32 AC33 AC34 AC1 A 14 AC 16АС 25 27 AC36 ACs ACs 56 57 AC60 AC61 Ас"62 AC'63 AC'64 AC'65 AC'66 AC67 Important of its use: There are many transforms, most of which are very slow. This is important to consider since video demands real-time encoding and decoding. The JPEG committee took suggestions and empirically studied the use of several different transforms. Of the transforms studied, DCT (Discrete Cosine Transform) proved superior. If we thinkof a block of 8x8 pixels out of a coherent image, the pixels are likely to be very similar. If we run DCT on 64 pixels which are very similar, we will get a DC coefficient and some values for the low-frequency AC coefficients; the remaining coefficients will likely be at or near zero