FFmpeg Glossary: DAR, PAR, and SAR

The SAR and DAR output in the FFmpeg terminal are as follows

Input #0, mov,mp4,m4a,3gp,3g2,mj2, from 'test.mp4':
  Metadata:
    major_brand     : mp42
    minor_version   : 0
    compatible_brands: mp42mp41
    creation_time   : 2018-05-25T12:42:26.000000Z
  Duration: 00:02:00.02, start: 0.000000, bitrate: 50449 kb/s
  Stream #0:0[0x1](eng): Video: h264 (Main) (avc1 / 0x31637661), yuv420p(tv, bt709, progressive), 1920x1080, 50126 kb/s, 29.97 fps, 29.97 tbr, 30k tbn (default)

SAR (Sample Aspect Ratio) : 单个像素的宽度和像素的高度的比 (That is the width of a pixel divided by the height of the pixel.)

DAR (Display Aspect Ratio) : 预期显示的宽度与高度的比 (The intended display’s width-to-height aspect)

PAR (Picture Aspect Ratio) : 宽度与高度像素个数的比 (‘horizontal_size’:’vertical_size’)

What’s confusing:

Storage aspect ratio (SAR) is the ratio of numbers of pixels.

Pixel aspect ratio (PAR) is a mathematical ratio that describes how the width of a pixel in a digital image compared to the height of that pixel.

先查看FFmpeg中的avcodec_string函数:

void avcodec_string(char *buf, int buf_size, AVCodecContext *enc, int encode)
{
  	 AVRational display_aspect_ratio;
    ...
 
        if (enc->width) {
            av_bprintf(&bprint, "%s%dx%d", new_line ? separator : ", ",
                       enc->width, enc->height);
    ...
 
            if (enc->sample_aspect_ratio.num) {
                av_reduce(&display_aspect_ratio.num, &display_aspect_ratio.den,
                          enc->width * (int64_t)enc->sample_aspect_ratio.num,
                          enc->height * (int64_t)enc->sample_aspect_ratio.den,
                          1024 * 1024);
                av_bprintf(&bprint, " [SAR %d:%d DAR %d:%d]",
                         enc->sample_aspect_ratio.num, enc->sample_aspect_ratio.den,
                         display_aspect_ratio.num, display_aspect_ratio.den);
    ...

PAR 对应 enc->width, enc->height:

typedef struct AVCodecContext {
    ...
   
    /* video only */
    /**
     * picture width / height.
     *
     * @note Those fields may not match the values of the last
     * AVFrame output by avcodec_receive_frame() due frame
     * reordering.
     *
     * - encoding: MUST be set by user.
     * - decoding: May be set by the user before opening the decoder if known e.g.
     *             from the container. Some decoders will require the dimensions
     *             to be set by the caller. During decoding, the decoder may
     *             overwrite those values as required while parsing the data.
     */
    int width, height;

[FFmpeg-user] Glossary: DAR, PAR, and SAR 中有详细介绍, 其中关于PAR:

PAR (picture aspect ratio [1]) [noun]: 1, The metadata ratio:
   'horizontal_size':'vertical_size' [3], as a minimized, H:V, integer
   ratio (e.g. 5:4, 3:2) [2][4] (also see "SAR", note [2]).
[1] It's mistakenly asserted by some that "PAR" is an acronym for "pixel aspect ratio".
[2] PAR can also be calculated from DAR & SAR thusly: PAR = DAR/SAR.
[3] Note that PAR is virtual (i.e. defined by dataset indexes, not
       physical dimensions).
[4] H.262 doesn't define PAR, however, it does define a quotent that correlates with PAR, to wit: H.262 §6.3.3, aspect_ratio_information:
         "SAR = DAR × horizontal_size/vertical_size".

SAR 对应 enc->sample_aspect_ratio:

typedef struct AVCodecContext {
    ...
   
    /**
     * sample aspect ratio (0 if unknown)
     * That is the width of a pixel divided by the height of the pixel.
     * Numerator and denominator must be relatively prime and smaller than 256 for some video standards.
     * - encoding: Set by user.
     * - decoding: Set by libavcodec.
     */
    AVRational sample_aspect_ratio;

DAR 对应 display_aspect_ratio:

av_reduce(&display_aspect_ratio.num, &display_aspect_ratio.den,

enc->width * (int64_t)enc->sample_aspect_ratio.num,

enc->height * (int64_t)enc->sample_aspect_ratio.den,

1024 * 1024);

DAR = SAR × PAR

再来看 Wikipedia 中的词条 Pixel Aspect Ratio (PAR)和 Storage aspect ratio (SAR)

先说结论:

Pixel Aspect Ratio == Sample Aspect Ratio

Storage Aspect Ratio == Picture Aspect Ratio

Pixel aspect ratio (PAR)

是描述数位影像的像素中，宽和高之间的比率。大多数的数位成像系统，会将影像显示为很多微小的正方型像素格。但部分成像系统，尤其是必须与标准画质电视相容者，会将影像显示为长方形的像素格。像素格的宽和高不一定等长，因此就用像素宽高比来描述之。

像素宽高比通常会用于描述标准画质电视相关的影像，除了少数特例以外。大多数的成像系统，包括遵守电影电视工程师协会标准和实务的系统，皆是使用正方像素。

Storage aspect ratio (SAR)

显示宽高比 Display Aspect Ratio（DAR），不同于存储宽高比 Storage Aspect Ratio（SAR），后者指的是像素总数的比值。当影像是用长方像素而非正方像素显示时，这两种宽高比就会不一样。像素本身的比例，称之为像素宽高比 Pixel Aspect Ratio （PAR），譬如正方像素就是1:1。三者之间的关系为：

DAR = SAR × PAR

一个 640 x 480 的 VGA 影像其 SAR 为 640/480 = 4:3，当显示在一个 4:3 的显示器上时（DAR = 4:3），其像素宽高比就为 1:1。相对而言，一个 720 x 576 的 D-1 PAL 影像其 SAR 为 5:4，若也显示在 4:3 的显示器上（DAR = 4:3），可知其像素宽高比就为 (4:3)/(5:4) = 16:15。

令人困惑的地方

origin	formula
FFmpeg:	DAR (Display Aspect Ratio) = SAR (Sample Aspect Ratio) × PAR (Picture Aspect Ratio)
Wikipedia:	DAR (Display Aspect Ratio) = SAR (Storage Aspect Ratio) × PAR (Pixel Aspect Ratio)