The sum of absolute transformed differences (SATD) is a block matching criterion widely used in fractional

motion estimation Motion estimation is the process of determining ''motion vectors'' that describe the transformation from one 2D image to another; usually from adjacent frames in a video sequence. It is an ill-posed problem as the motion is in three dimensions b ...

for video compression. It works by taking a

frequency transform This is a list of linear transformations of functions related to Fourier analysis. Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in ...

, usually a

Hadamard transform The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal ...

, of the differences between the pixels in the original

block Block or blocked may refer to: Arts, entertainment and media Broadcasting * Block programming, the result of a programming strategy in broadcasting * W242BX, a radio station licensed to Greenville, South Carolina, United States known as ''96.3 ...

and the corresponding pixels in the block being used for comparison. The transform itself is often of a small block rather than the entire macroblock. For example, in

x264 x264 is a free and open-source software library and a command-line utility developed by VideoLAN for encoding video streams into the H.264/MPEG-4 AVC video coding format. It is released under the terms of the GNU General Public License. History ...

, a series of 4×4 blocks are transformed rather than doing the more processor-intensive 16×16 transform.

Comparison to other metrics

SATD is slower than the

sum of absolute differences In digital image processing, the sum of absolute differences (SAD) is a measure of the similarity between image blocks. It is calculated by taking the absolute difference between each pixel in the original block and the corresponding pixel in the ...

(SAD), both due to its increased complexity and the fact that SAD-specific MMX and

SSE2 SSE2 (Streaming SIMD Extensions 2) is one of the Intel SIMD (Single Instruction, Multiple Data) processor supplementary instruction sets first introduced by Intel with the initial version of the Pentium 4 in 2000. It extends the earlier SSE ins ...

instructions exist, while there are no such instructions for SATD. However, SATD can still be optimized considerably with

SIMD Single instruction, multiple data (SIMD) is a type of parallel processing in Flynn's taxonomy. SIMD can be internal (part of the hardware design) and it can be directly accessible through an instruction set architecture (ISA), but it should ...

instructions on most modern

CPU A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, an ...

s. The benefit of SATD is that it more accurately models the number of bits required to transmit the residual error signal. As such, it is often used in video compressors, either as a way to drive and estimate rate explicitly, such as in the

Theora Theora is a free lossy video compression format. It is developed by the Xiph.Org Foundation and distributed without licensing fees alongside their other free and open media projects, including the Vorbis audio format and the Ogg container ...

encoder (since 1.1 alpha2), as an optional metric used in wide motion searches, such as in the

Microsoft Microsoft Corporation is an American multinational corporation, multinational technology company, technology corporation producing Software, computer software, consumer electronics, personal computers, and related services headquartered at th ...

VC-1 SMPTE 421, informally known as VC-1, is a video coding format. Most of it was initially developed as Microsoft's proprietary video format Windows Media Video 9 in 2003. With some enhancements including the development of a new Advanced Profile, ...

encoder, or as a metric used in sub-pixel refinement, such as in x264.

References

*{{cite book , last = E. G. Richardson , first = Iain , title = H.264 and MPEG-4 Video Compression: Video Coding for Next-generation Multimedia , publisher = John Wiley & Sons Ltd. , year = 2003 , location = Chichester Video compression Signal processing metrics Loss functions

Comparison to other metrics

See also

References