AI 中文总结
本文提出皮肤受限的Reinhard变换，通过亮度保持约束和对角仿射映射实现皮肤重着色中色素与阴影的分离，在保持亮度对比的同时最小化色度误差。
AI 中文摘要
目录皮肤重新着色必须改变色素而保留阴影。经典的Reinhard映射并未实现这种分离：它通过标准差之比重新缩放亮度，因此平坦的参考色块会压平肢体。本文形式化了我们流程中使用的校正方法，即皮肤受限的Reinhard变换。它是CIE Lab空间中的对角仿射映射，平移亮度，匹配色度均值，并将色度增益限制在[0.72, 1.18]区间，矩在每通道中央84%的数据上计算。对角仿射映射有六个实参数。阴影约束迫使亮度增益为+1，亮度平移为均值之差；在每个色度轴上的一维二次最优传输，随后通过欧几里得投影到增益区间，确定其余四个参数。在该族内，四个条件决定所有参数。结果的内容是强制的亮度增益；这不是对角仿射类之外的唯一性声明。对于高斯边缘分布，色度步骤不仅仅是最佳仿射映射：它是无约束的Wasserstein-2映射。使用修剪矩的相同公式仍然是最优的，因为正仿射图像与分位数修剪可交换。在九张照片和三个参考色调的手、手臂、腿和脚上，该映射将亮度对比度比率保持在0.974±0.029，色度误差为0.77 CIE Lab单位。Reinhard匹配、线性Monge映射和直方图匹配达到更小的色度误差，但仅通过将亮度对比度削减至约一半。
英文摘要
Catalog skin recolouring has to change pigment and leave shading alone. The classical Reinhard map does not make that split: it rescales lightness by the ratio of standard deviations, and a flat reference swatch therefore flattens the limb. This paper formalises the correction used in our pipeline, the skin-restricted Reinhard transform. It is the diagonal affine map in CIE Lab that translates lightness, matches the chromatic mean, and clamps the chromatic gain to [0.72, 1.18], with moments taken on the central 84% of each channel. A diagonal affine map has six real parameters. The shading constraint forces the lightness gain to +1 and the lightness shift to the difference of means; one-dimensional quadratic optimal transport on each chromatic axis, followed by Euclidean projection onto the gain interval, fixes the other four. Inside that family the four conditions determine every parameter. The content of the result is the forced lightness gain; it is not a uniqueness claim outside the diagonal affine class. For Gaussian marginals the chromatic step is not merely the best affine map: it is the unrestricted Wasserstein-2 map. The same formulae with trimmed moments remain optimal because a positive affine image commutes with quantile trimming. On hands, arms, legs, and feet of nine photographs and three reference tones, the map keeps the lightness contrast ratio at 0.974 +/- 0.029 with chromatic error 0.77 CIE Lab units. Reinhard matching, the linear Monge map, and histogram matching reach a smaller chromatic error only by cutting lightness contrast to about half.
CommentsCode: https://github.com/vijeshkpaei/skin-restricted-reinhard-transform
