This metric quantifies the temporal consistency of brightness distribution between each frame and the initial frame in video sequences, addressing insufficient visual stability caused by inter-frame brightness shifts and abrupt changes. Unlike scalar metrics that compare only global mean luminance, Brightness Consistency preserves dark/mid/bright pixel ratios and is therefore more sensitive to changes in exposure distribution shape.
WorldAtlas uses this algorithm as the official metric brightness_distribution_consistencybrightness_consistency is documented for compatibility; use the configured canonical metric to avoid double counting.
Pixel grayscales are categorized into dark , mid , and bright levels to construct a 3-D brightness distribution vector:
v t = ( p d a r k p m i d p b r i g h t ) \mathbf{v}_t
=
\begin{pmatrix}
p_{\mathrm{dark}} \\
p_{\mathrm{mid}} \\
p_{\mathrm{bright}}
\end{pmatrix} v t = p dark p mid p bright where p d a r k p_{\mathrm{dark}} p dark p b r i g h t p_{\mathrm{bright}} p bright p m i d = 1 − p d a r k − p b r i g h t p_{\mathrm{mid}} = 1 - p_{\mathrm{dark}} - p_{\mathrm{bright}} p mid = 1 − p dark − p bright dark_threshold=85, bright_threshold=170 (OpenCV gray scale [ 0 , 255 ] [0,255] [ 0 , 255 ]
The distribution similarity of frame t t t t ≥ 2 t \geq 2 t ≥ 2 v 1 \mathbf{v}_1 v 1
S ( a , b ) = a ⋅ b ∥ a ∥ ∥ b ∥ = ∑ i = 1 n a i b i ∑ i = 1 n a i 2 ∑ i = 1 n b i 2 (3) S(a, b)
=
\frac{a \cdot b}{\|a\|\,\|b\|}
=
\frac{\sum_{i=1}^{n} a_i b_i}{
\sqrt{\sum_{i=1}^{n} a_i^2}\,\sqrt{\sum_{i=1}^{n} b_i^2}
}
\tag{3} S ( a , b ) = ∥ a ∥ ∥ b ∥ a ⋅ b = ∑ i = 1 n a i 2 ∑ i = 1 n b i 2 ∑ i = 1 n a i b i ( 3 ) A modified Softmax transform enhances high-score segments for single-sample scores x ∈ [ 0 , 1 ] x \in [0,1] x ∈ [ 0 , 1 ] λ > 0 \lambda > 0 λ > 0
T ( x ) = e λ x − 1 e λ − 1 (4) T(x)
=
\frac{e^{\lambda x} - 1}{e^{\lambda} - 1}
\tag{4} T ( x ) = e λ − 1 e λ x − 1 ( 4 ) Default λ = 4.0 \lambda = 4.0 λ = 4.0 softmax_lambda).
For frame distance d ∈ [ 1 , T − 1 ] d \in [1, T-1] d ∈ [ 1 , T − 1 ] d = 1 d=1 d = 1 α > 0 \alpha > 0 α > 0
w ( d ) = e − α ⋅ d , w ^ ( d ) = w ( d ) ∑ k = 1 T − 1 w ( k ) (5) w(d) = e^{-\alpha \cdot d},
\qquad
\hat{w}(d)
=
\frac{w(d)}{\sum_{k=1}^{T-1} w(k)}
\tag{5} w ( d ) = e − α ⋅ d , w ^ ( d ) = ∑ k = 1 T − 1 w ( k ) w ( d ) ( 5 ) Default α = 0.05 \alpha = 0.05 α = 0.05 temporal_decay). The comprehensive brightness consistency score is:
S B r i g h t n e s s = ∑ d = 1 T − 1 w ^ ( d ) ⋅ T ( S ( v d + 1 , v 1 ) ) (6) S_{\mathrm{Brightness}}
=
\sum_{d=1}^{T-1}
\hat{w}(d) \cdot T\!\left(S(\mathbf{v}_{d+1}, \mathbf{v}_1)\right)
\tag{6} S Brightness = d = 1 ∑ T − 1 w ^ ( d ) ⋅ T ( S ( v d + 1 , v 1 ) ) ( 6 ) Audit manifest: docs/assets/metric_examples/curated_same_case_manifest.json.
Input image
Input verified · same benchmark case · gap 0.3876
image_static_stylized_living_spaces_0031Suite: image_static Scene: stylized / indoor / living_spaces
Benchmark prompt target
Camera move right. A cozy living room with fireplace, Christmas tree, and armchair.
prompt source: prompt_target
Both first frames passed geometric matching against the displayed input; labels compare this metric only.
Higher metric score Score 0.9936
Lower metric score Score 0.6060
Input image
Input verified · same benchmark case · gap 0.5377
image_static_stylized_suburb_0081Suite: image_static Scene: stylized / outdoor / suburb
Benchmark prompt target
Camera pan right. A stone house with red roof, vintage car, and wooden fence.
prompt source: prompt_target
Both first frames passed geometric matching against the displayed input; labels compare this metric only.
Higher metric score Score 0.9969
Lower metric score Score 0.4591
Input image
Input verified · same benchmark case · gap 0.3634
image_static_stylized_passageways_0084Suite: image_static Scene: stylized / indoor / passageways
Benchmark prompt target
Camera pan right. A stylized hallway with ornate wallpaper, ceiling lights, and framed pictures.
prompt source: prompt_target
Both first frames passed geometric matching against the displayed input; labels compare this metric only.
Higher metric score Score 0.9934
Lower metric score Score 0.6300
WorldAtlas — Brightness Consistency metric family
Three-bin brightness distribution vectors with cosine similarity to the initial frame, modified Softmax enhancement, and normalized exponential temporal weighting.
