This metric evaluates the consistency of environmental atmosphere (color-temperature logic) in generated videos. We analyze the Hue channel in HSV color space: the hue spectrum [0,179] is divided into 7 core intervals to construct a hue feature vector ht∈R7. We then compute a weighted perceptual similarity of the full sequence relative to the initial frame. To balance global constancy and local transition, the similarity at frame t (t≥2) is the arithmetic mean of current-to-first and current-to-previous similarities. The similarity S(⋅,⋅) follows the cosine inner product (same as Eq. (3) in the brightness-distribution metric):
For each frame It, RGB is converted to HSV; a saturation-weighted histogram over 7 hue bins on [0,180) is normalized to form ht (WorldAtlas default hue_bins=7).
The final score uses a normalized exponentially decaying weighted sum, where weights w^′(d) are an improved variant of w^(d) with faster decay (β>α), and similarities are passed through the modified Softmax transform T(⋅) (Eq. (4), default λ=4.0):
Here d∈[1,T−1] is the frame distance (d=1 for the second frame relative to the first), and β is the decay coefficient. The default β=0.10 exceeds the brightness metric’s α=0.05, so w^′(d) decays faster than w^(d) and long-video color drift is penalized more strongly. The comprehensive score is:
SColor=d=1∑T−1w^′(d)⋅T(Sˉd+1)(9)
In WorldAtlas this algorithm is implemented as the official metric color_temperature_constraint (hue_distribution backend). Under the default normalization config, raw and normalized outputs lie in [0,1] with higher is better. The legacy scalar alias color_temperature_consistency is documented for compatibility; use the configured canonical metric to avoid double counting.
