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sRGB↔XYZ conversionBy Michał ‘mina86’ NazarewiczUpdated on 21st of March 2021Share on BlueskyIn an earlier post, I’ve shown how to calculate an RGB↔XYZ conversion matrix. It’s only natural to follow up with a code for converting between sRGB and XYZ colour spaces. While the matrix is a significant portion of the algorithm, there is one more step necessary: gamma correction.What is gamma correction?Human perception of light’s brightness approximates a power function of its intensity. This can be expressed as \(P = S^\alpha\) where \(P\) is the perceived brightness and \(S\) is linear intensity. \(\alpha\) has been experimentally measured to be less than one which means that people are more sensitive to changes to dark colours rather than to bright ones.Based on that observation, colour space’s encoding can be made more efficient by using higher precision when encoding dark colours and lower when encoding bright ones. This is akin to precision of floating-point numbers scaling with value’s magnitude. In RGB systems, the role of precision scaling is done by gamma correction. When colour is captured (for example from a digital camera) it goes through gamma compression which spaces dark colours apart and packs lighter colours more densely. When displaying an image, the opposite happens and encoded value goes through gamma expansion.1.00.90.80.70.60.50.40.30.20.10.0EncodedIntensityMany RGB systems use a simple \(S = E^\gamma\) expansion formula, where \(E\) is the encoded (or non-linear) value. With decoding \(\gamma\) approximating \(1/\alpha\), equal steps in encoding space correspond roughly to equal steps in perceived brightness. Image on the right demonstrates this by comparing two colour gradients. The first one has been generated by increasing encoded value in equal steps and the second one has been created by doing the same to light intensity. The former includes many dark colours while the latter contains a sudden jump in brightness from black to the next colour.sRGB uses slightly more complicated formula stitching together two functions: $$ \begin{align} E &= \begin{cases} 12.92 × S & \text{if } S ≤ S_0 \\ 1.055 × S^{1/2.4} - 0.055 & \text{otherwise} \end{cases} \\[.5em] S &= \begin{cases} {E \over 12.92} & \text{if } E ≤ E_0 \\ \left({E + 0.055 \over 1.055}\right)^{2.4} & \text{otherwise} \end{cases} \\[.5em] S_0 &= 0.00313066844250060782371 \\ E_0 &= 12.92 × S_0 \\ &= 0.04044823627710785308233 \end{align} $$The formulæ assume values are normalised to [0, 1] range. This is not always how they are expressed so a scaling step might be necessary.sRGB encodingMost common sRGB encoding uses eight bits per channel which introduces a scaling step: \(E_8 = ⌊E × 255⌉\). In an actual implementation, to increase efficiency and accuracy of gamma operations, it’s best to fuse the multiplication into aforementioned formulæ. With that arguably obvious optimisation, the equations become: $$ \begin{align} E_8 &= \begin{cases} ⌊3294.6 × S⌉ & \text{if } S ≤ S_0 \\ ⌊269.025 × S^{1/2.4} - 14.025⌉ & \text{otherwise} \end{cases} \\[.5em] S &= \begin{cases} {E_8 \over 3294.6} & \text{if } E_8 ≤ 10 \\ \left({E_8 + 14.025 \over 269.025}\right)^{2.4} & \text{otherwise} \end{cases} \\[.5em] S_0 &= 0.00313066844250060782371 \\ \end{align} $$This isn’t the only way to represent colours of course. For example, 10-bit colour depth changes the scaling factor to 1024; 16-bit high colour uses five bits for red and blue channels while five or six for green producing different scaling factors for different primaries; and HDTV caps the range to [16, 235]. Needless to say, correct formulæ need to be chosen based on the standard in question.The implementationAnd that’s it. Encoding, gamma correction and the conversion matrix are all the necessary pieces to get the conversion implemented. Like before, Rust programmers can take advantage of the srgb crate which implemented full conversion. However, to keep things interesting, in addition, here’s the conversion code written in TypeScript:type Tripple = [number, number, number];，这一点在必应排名_Bing SEO_先做后付中也有详细论述
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不止林俊旸，同日Qwen后训练负责人郁博文等也正式离职。多位Qwen核心人员突然离职，带着遗憾，更带着巨大问号。有人将其归因于开源模型商业化效率的困惑——Qwen虽声名显赫，但究竟能转化为多少云上API的调用收入，阿里内部或许已有分歧。也有人提及，除夕夜亮相的Qwen-3.5曾被内部高管评价为“半成品”，林俊旸在最新的内部会议上产生了分歧。，推荐阅读服务器推荐获取更多信息