Not three colours. Three signal components.

The prime indicates that Y′ is computed from nonlinearly encoded R′G′B′. It is video luma, not linear colorimetric Y, perceptual lightness or a direct display-luminance measurement in cd/m². A number needs context.

Identify the RGB representation and transfer function before choosing the component matrix. Applying the formula to linear RGB instead of its expected R′G′B′ is mathematically possible but produces a different representation. Keep physical light, signal codes and scope readings distinct when validating a workflow.

For a non-constant-luminance representation, Y′ = Kr·R′ + Kg·G′ + Kb·B′, with Kg = 1 − Kr − Kb. Cb normalises B′ − Y′; Cr normalises R′ − Y′. Neutral R′ = G′ = B′ gives Cb = Cr = 0: these components describe deviations from the neutral axis, not separate blue and red images.

With known coefficients and all components retained, the conversion is reversible in exact arithmetic. Rounding, clipping, subsampling and compression are additional operations that can destroy reversibility. The matrix alone has not reduced the number of spatial samples.

This matrix uses Kr = 0.2126, Kg = 0.7152 and Kb = 0.0722. For normalised components, Cb = (B′ − Y′)/1.8556 and Cr = (R′ − Y′)/1.5748. These constants need the corresponding inverse. A large green coefficient does not mean that the green channel contains all image detail.

The matrix is only one part of a BT.709 video description. It does not change gamut, specify code range or replace the transfer function. The lab keeps these layers separate: matrix choice is independent of optional Video-range quantisation.

BT.601 uses Kr = 0.299, Kg = 0.587 and Kb = 0.114, different from BT.709. Encoding coloured material with one matrix and decoding with another changes coloured regions. Neutral signals with zero Cb/Cr can remain neutral.

A correct grey ramp therefore does not prove matrix correctness; include coloured patches. File dimensions offer historical context, not unconditional proof: an SD source may have been scaled, edited or mistagged. Inspect metadata and transformation history.

BT.2020 NCL uses Kr = 0.2627, Kg = 0.6780 and Kb = 0.0593. The colour-difference formula resembles the earlier matrices but uses different constants. Habitually substituting 709 is wrong even if the final screen is ordinary SDR.

BT.2020 also defines a constant-luminance representation with a different component-formation process. It cannot be implemented merely by substituting Kr and Kb into an NCL matrix. The lab explicitly labels the option “2020 NCL”; it does not pretend to decode CL, ICtCp or HDR. Transfer and gamut handling remain separate stages.

Normalised Cb/Cr can be negative. Video-range integer encoding offsets them around a centre: neutral is 128 at 8 bits and 512 at 10 bits. Nominal chroma edges are 16…240 and 64…960; luma uses 16…235 and 64…940. These spans are different.

At 8 bits, Ycode = round(16 + 219Y′), Ccode = round(128 + 224C). Ten-bit offsets and spans scale by four. Nominal boundaries are not identical to every allowed value of a particular transport or file format. The lab does not clip calculated numbers before reporting them.

Y′CbCr can retain a complete grid for all three components: 4:4:4. Chroma-grid reduction is a separate operation. Typical progressive 4:2:2 halves horizontal Cb/Cr density; 4:2:0 halves both horizontal and vertical density. Y′ retains its full grid.

Downsampling needs filtering, and reconstruction needs interpolation. That alone can remove fine coloured structure before any lossy codec is applied. The inverse RGB matrix reconstructs from the retained samples; it cannot recover measurements that were discarded.

Plane dimensions do not identify where a chroma sample lies relative to Y′. Locations may be co-sited or offset, depending on standard, format and frame structure. Interlaced footage must not automatically inherit a progressive 2×2 model.

Two filters may agree on plane size yet disagree on positions, shifting a coloured boundary relative to luma. Upscaling again does not necessarily fix this. Match input location, reconstruction filter and output location, especially during resizing, keying and intermediate export.

YUV, Y′PbPr and Y′CbCr historically describe different representations and uses. Software APIs nevertheless often use yuv as a broad label for digital planar colour-difference formats. That prefix alone does not establish coefficients, range or transfer.

For example, yuv420p describes plane organisation and sampling but does not replace color_space, color_range, color_transfer and color_primaries fields. A 10le suffix adds information about 10-bit sample storage and byte order; it does not automatically indicate HDR or a gamut.

A matrix mismatch often affects coloured regions while leaving grey unchanged. A range mismatch changes interpretation of black, white and intermediate codes. A chroma-location mismatch moves or changes a colour edge relative to Y′. Multiple errors can coexist.

Start with a controlled chart: a neutral ramp, saturated patches and fine coloured lines. Change only one interpretation layer at a time. Saturation and contrast are risky universal fixes: a locally pleasing image can hide wrong values that reappear at the next conversion.

A decoder normally turns stored components into the image processed downstream. A node CST is not a universal manual decoder for every Y′CbCr file. Once incorrect values have entered the processing path, later colour-space work may not undo the original mistake.

Compare metadata, interpretation settings and an independent controlled export. Use scopes for numeric levels, the Viewer for structure and colour edges, and ffprobe for file descriptions. Combine these observations: a properly tagged file does not prove correct samples, while an attractive Viewer does not prove correct tags.