这意味着 (这些都是近似值):

• \(68.27\%\) 的输出像素值在输入值的 \(\pm1\times\mathtt{var}\) 倍以内
• \(95.45\%\) 的输出像素值在输入值的 \(\pm2\times\mathtt{var}\) 倍以内
• \(99.73\%\) 的输出像素值在输入值的 \(\pm3\times\mathtt{var}\) 倍以内
• \(50\%\) 的输出像素值在输入值的 \(\pm0.675\times\mathtt{var}\) 倍以内
• \(90\%\) 的输出像素值在输入值的 \(\pm1.645\times\mathtt{var}\) 倍以内
• \(95\%\) 的输出像素值在输入值的 \(\pm1.960\times\mathtt{var}\) 倍以内
• \(99\%\) 的输出像素值在输入值的 \(\pm2.576\times\mathtt{var}\) 倍以内

简而言之：为每个亮度组创建一个蒙版，使用双曲线调整大小，用锐度控制b和c来调整纹理的大小，然后应用这个。 时间平均法只是使用misc.AverageFrames对当前帧和其直接邻接的纹理进行平均。

一个明亮的场景，基于亮度的应用产生了很大的差异:

一个整体较暗的场景，其中的差异要小得多:

一个黑暗的场景，在画面中的每一个地方都均匀地（几乎）应用了颗粒:

Size and Sharpness

adptvgrnMod的颗粒化部分与GrainFactory3的相同；它在尺寸参数定义的分辨率下创建一个 "空白"（比特深度的中间点）剪辑，然后通过一个使用由sharp决定的b和c值的二次方内核进行扩展:

$$\mathrm{grain\ width} = \mathrm{mod}4 \left( \frac{\mathrm{clip\ width}}{\mathrm{size}} \right)$$

例如，一个1920x1080的片段，尺寸值为1.5:

$$ \mathrm{mod}4 \left( \frac{1920}{1.5} \right) = 1280 $$

这决定了颗粒器所操作的帧的大小。

现在，决定使用bicubic kernel的参数:

$$ b = \frac{\mathrm{sharp}}{-50} + 1 $$ $$ c = \frac{1 - b}{2} $$

这意味着，对于默认的50的锐度，使用的是Catmull-Rom过滤器:

$$ b = 0, \qquad c = 0.5 $$

Values under 50 will tend towards B-Spline (b=1, c=0), while ones above 50 will tend towards b=-1, c=1. As such, for a Mitchell (b=1/3, c=1/3) filter, one would require sharp of 100/3.

The grained "blank" clip is then resized to the input clip's resolution with this kernel. If size is greater than 1.5, an additional resizer call is added before the upscale to the input resolution:

$$ \mathrm{pre\ width} = \mathrm{mod}4 \left( \frac{\mathrm{clip\ width} + \mathrm{grain\ width}}{2} \right) $$

With our resolutions so far (assuming we did this for size 1.5), this would be 1600. This means with size 2, where this preprocessing would actually occur, our grain would go through the following resolutions:

$$ 960 \rightarrow 1440 \rightarrow 1920 $$

Fade Edges

The fade_edges parameter introduces the option to attempt to maintain overall average image brightness, similar to ideal dithering. It does so by limiting the graining at the edges of the clip's range. This is done via the following expression:

x y neutral - abs - low < x y neutral - abs + high > or
x y neutral - x + ?

Here, x is the input clip, y is the grained clip, neutral is the midway point from the previously grained clip, and low and high are the edges of the range (e.g. 16 and 235 for 8-bit luma). Converted from postfix to infix notation, this reads:

\[x = x\ \mathtt{if}\ x - \mathrm{abs}(y - neutral) < low\ \mathtt{or}\ x - \mathrm{abs}(y - neutral) > high\ \mathtt{else}\ x + (y - neutral)\]

The effect here is that all grain that wouldn't be clipped during output regardless of whether it grains in a positive or negative direction remains, while grain that would pass the plane's limits isn't taken.

In addition to this parameter, protect_neutral is also available. This parameter protects "neutral" chroma (i.e. chroma for shades of gray) from being grained. To do this, it takes advantage of AddGrainC working according to a Guassian distribution, which means that $$max\ value = 3 \times \sigma$$ (sigma being the standard deviation - the strength or cstrength parameter) is with 99.73% certainty the largest deviated value from the norm (0). This means we can perform a similar operation to the one for fade_edges to keep the midways from being grained. To do this, we resize the input clip to 4:4:4 and use the following expression:

\[\begin{align}x \leq (low + max\ value)\ \mathtt{or}\ x \geq (high - max\ value)\ \mathtt{and}\\ \mathrm{abs}(y - neutral) \leq max\ value\ \mathtt{and}\ \mathrm{abs}(z - neutral) \leq max\ value \end{align}\]

With x, y, z being each of the three planes. If the statement is true, the input clip is returned, else the grained clip is returned.

I originally thought the logic behind protect_neutral would also work well for fade_edges, but I then realized this would completely remove grain near the edges instead of fading it.

Now, the input clip and grained clip (which was merged via std.MergeDiff, which is x - y - neutral) can be merged via the adaptive_grain mask.