Epipolar Geometry

本页定义三组 GVGC-style 正式极线几何指标 [Li et al., 2024]，用于检验生成视频相邻帧是否具备稳定的双视角极线解释 [Hartley and Zisserman, 2004]。它们只依赖 prediction 视频本身，不需要相机位姿标注或 reference video；核心问题是：局部特征对应关系是否近似满足 epipolar constraint，从而说明两帧能否被同一个 pinhole 相机模型下的相对运动解释。

在经典多视角几何中，若两帧来自同一场景、仅发生刚体相机运动，则第一帧中的点 $x$ 在第二帧中的对应点 $x'$ 必然落在由基础矩阵 $F$ 诱导的极线 $l' = F x$ 上。生成视频若出现背景扭曲、物体局部漂移、深度层次不稳定，或相邻帧并非同一三维结构的投影，RANSAC inlier 将难以同时满足该约束，Sampson 误差会升高、inlier 比例下降。因此，极线指标提供一种轻量、可解释的双视角几何信号；但它只检查稀疏特征点的 epipolar 一致性，不能替代 MEt3R、重投影误差或重建类指标对全局三维自洽性的判断。

WorldAtlas 在 prediction 的采样帧上，按 pair_stride 构造相邻（或跨步）帧对，默认使用 SIFT 特征与 Lowe 比率测试进行匹配，再以 OpenCV RANSAC 估计基础矩阵 $F$ 。对 RANSAC inlier 计算 Sampson 误差，并统计 inlier 比例与覆盖率；若主路径失败，runtime 还可依次尝试放宽匹配阈值或 Shi-Tomasi + Lucas-Kanade 跟踪 fallback。三个子指标共享同一次 backend 分析，分别报告如下：

指标	原始统计量	方向
`epipolar_error`	基础矩阵 RANSAC 后 inlier 的 Sampson 误差中位数	越低越好
`epipolar_inlier_rate`	RANSAC inlier 数 / Lowe 比率过滤后的匹配数	越高越好
`feature_match_coverage`	RANSAC inlier 数 / 较少一侧关键点数	越高越好

对匹配齐次点 $x_i, x'_i$ ，Sampson 误差为

d_i = \frac{|{x'_i}^{\mathsf T} F x_i|}{\sqrt{(Fx_i)_1^2 + (Fx_i)_2^2 + (F^{\mathsf T}x'_i)_1^2 + (F^{\mathsf T}x'_i)_2^2}} \tag{1}

每个有效帧对以 RANSAC inlier 的 $d_i$ 中位数作为 pair 级 epipolar_error；视频级取各 pair 中位数，并在 $[0, 5]$ 上反向归一化。

每个有效帧对的 inlier 率与覆盖率为

r = \frac{\#\mathrm{inliers}}{\#\mathrm{good\ matches}}, \qquad c = \min\!\left(\frac{\#\mathrm{inliers}}{\min(\#\mathrm{kp}_\mathrm{left}, \#\mathrm{kp}_\mathrm{right})},\, 1\right) \tag{2}

视频级 epipolar_inlier_rate 与 feature_match_coverage 分别对 $r$ 、 $c$ 取均值，在 $[0,1]$ 上恒等归一化。epipolar_error 取各有效帧对中位数的中位数，并在 $[0, 5]$ 上反向归一化到 $[0, 1]$ （归一化分数越高表示极线一致性越好）。若所有帧对都无法形成足够 inlier，三项均返回 not_applicable。这三项均为 official 榜单指标，发布时核验完整覆盖率和有效测量；在弱纹理、强非刚性运动或 dynamic prompt 场景下可能频繁失效，宜与 MEt3R、重投影误差等互补阅读。

已核验的同输入案例

下方展示 19 组 image_static 对比，来自站点已选的同输入案例 docs/assets/metric_examples/paired_manifest.json（paired_same_input_prompt，verified_exact），且两条示例视频都已导出。顺序按各子指标的站点 case rank 轮流排列 epipolar_error、epipolar_inlier_rate、feature_match_coverage。分数是对应子指标的归一化分数。 Audit manifest: docs/assets/metric_examples/paired_manifest.json.

同一输入与 prompt · image_static · gap 0.0593

`image_static_photorealistic_workspaces_0016`

套件: image_static指标: epipolar_error场景: photorealistic / workspaces

Benchmark prompt

Camera pan right. A modern office with desks, computers, and office chairs. Everything in the scene remains completely motionless.

来源: generation_records

较高分: lingbot_world_image_static。较低分: matrix_game2_5s_image_static。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9814lingbot_world_image_static内点 Sampson 误差中位数 0.0932

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9221matrix_game2_5s_image_static内点 Sampson 误差中位数 0.3897

同一输入与 prompt · image_static · gap 0.5595

`image_static_photorealistic_passageways_0079`

套件: image_static指标: epipolar_inlier_rate场景: photorealistic / passageways

Benchmark prompt

Camera move right. A bright hallway with wooden floor, armchair, and small table. Everything in the scene remains completely motionless.

来源: generation_records

较高分: astronex_world_image_static。较低分: matrix_game2_5s_image_static。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9745astronex_world_image_static内点率 97.5%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.4150matrix_game2_5s_image_static内点率 41.5%

同一输入与 prompt · image_static · gap 0.4021

`image_static_photorealistic_workspaces_0074`

套件: image_static指标: feature_match_coverage场景: photorealistic / workspaces

Benchmark prompt

Camera orbit left. A modern workspace with sneaker wall, vault door, and futuristic car. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_distilled_image_test_balanced_5000_5s。较低分: hy_worldplay_ar_rl_image_test_balanced_5000_5s。好坏标签仅比较 feature_match_coverage。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.5724hy_worldplay_ar_distilled_image_test_balanced_5000_5s特征匹配覆盖率 57.2%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.1703hy_worldplay_ar_rl_image_test_balanced_5000_5s特征匹配覆盖率 17.0%

同一输入与 prompt · image_static · gap 0.0396

`image_static_photorealistic_public_spaces_0014`

套件: image_static指标: epipolar_error场景: photorealistic / public_spaces

Benchmark prompt

Camera pan right. A pet care room with pet cages, feeding station, and water bowls.

来源: generation_records

较高分: hy_worldplay_ar_image_static。较低分: ac3d-image-static。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9725hy_worldplay_ar_image_static内点 Sampson 误差中位数 0.1375

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9329ac3d-image-static内点 Sampson 误差中位数 0.3357

同一输入与 prompt · image_static · gap 0.2254

`image_static_photorealistic_public_spaces_0150`

套件: image_static指标: epipolar_inlier_rate场景: photorealistic / public_spaces

Benchmark prompt

Camera pan left. A historic building with flower beds, stone path, and hedges. Everything in the scene remains completely motionless.

来源: generation_records

较高分: dreamx_world_image_static。较低分: matrix_game2_5s_image_static。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9759dreamx_world_image_static内点率 97.6%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.7505matrix_game2_5s_image_static内点率 75.0%

同一输入与 prompt · image_static · gap 0.3860

`image_static_photorealistic_terrestrial_landscape_0067`

套件: image_static指标: feature_match_coverage场景: photorealistic / terrestrial_landscape

Benchmark prompt

Camera pan left. A rural field with palm trees, haystacks, and green field. Everything in the scene remains completely motionless.

来源: generation_records

较高分: lyra-2-image-static-openenvision。较低分: matrix_game3_5s_image_static_dynamic。好坏标签仅比较 feature_match_coverage。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.4469lyra-2-image-static-openenvision特征匹配覆盖率 44.7%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.0609matrix_game3_5s_image_static_dynamic特征匹配覆盖率 6.1%

同一输入与 prompt · image_static · gap 0.0704

`image_static_stylized_living_spaces_0037`

套件: image_static指标: epipolar_error场景: stylized / living_spaces

Benchmark prompt

Camera pan right. A bedroom corner with wardrobe, chair, and rug. Everything in the scene remains completely motionless.

来源: generation_records

较高分: dreamx_world_image_static。较低分: matrix_game2_5s_image_static。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9715dreamx_world_image_static内点 Sampson 误差中位数 0.1424

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9011matrix_game2_5s_image_static内点 Sampson 误差中位数 0.4946

同一输入与 prompt · image_static · gap 0.1651

`image_static_photorealistic_terrestrial_landscape_0006`

套件: image_static指标: epipolar_inlier_rate场景: photorealistic / terrestrial_landscape

Benchmark prompt

Camera orbit left. An indoor pool with wooden railings, decorative plants, and upper level. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_distilled_image_test_balanced_5000_5s。较低分: matrix_game3_image_static。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9675hy_worldplay_ar_distilled_image_test_balanced_5000_5s内点率 96.7%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.8024matrix_game3_image_static内点率 80.2%

同一输入与 prompt · image_static · gap 0.8906

`image_static_stylized_living_spaces_0034`

套件: image_static指标: feature_match_coverage场景: stylized / living_spaces

Benchmark prompt

Camera move left. A minimalist living room with bookshelf, window, and armchair. Everything in the scene remains completely motionless.

来源: generation_records

较高分: cameractrl_image_static。较低分: astra_image_static。好坏标签仅比较 feature_match_coverage。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 1.0000cameractrl_image_static特征匹配覆盖率 100.0%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.1094astra_image_static特征匹配覆盖率 10.9%

同一输入与 prompt · image_static · gap 0.0545

`image_static_photorealistic_aquatic_landscape_0070`

套件: image_static指标: epipolar_error场景: photorealistic / aquatic_landscape

Benchmark prompt

Camera pan left. A frozen lake with snow-covered mountains, evergreen trees, and distant peak. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_image_test_balanced_5000_5s。较低分: motionctrl_image_static_official_default_tmp2。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9875hy_worldplay_ar_image_test_balanced_5000_5s内点 Sampson 误差中位数 0.0625

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9330motionctrl_image_static_official_default_tmp2内点 Sampson 误差中位数 0.3351

同一输入与 prompt · image_static · gap 0.5392

`image_static_stylized_workspaces_0008`

套件: image_static指标: epipolar_inlier_rate场景: stylized / workspaces

Benchmark prompt

Camera orbit left. A modern conference room with bookshelves, glass walls, and modern chairs. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_distilled_image_test_balanced_5000_5s。较低分: matrix_game3_5s_image_static_dynamic。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9507hy_worldplay_ar_distilled_image_test_balanced_5000_5s内点率 95.1%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.4115matrix_game3_5s_image_static_dynamic内点率 41.1%

同一输入与 prompt · image_static · gap 0.3882

`image_static_stylized_public_spaces_0008`

套件: image_static指标: feature_match_coverage场景: stylized / public_spaces

Benchmark prompt

Camera orbit left. A gallery corridor with statues, paintings, and windows. Everything in the scene remains completely motionless.

来源: generation_records

较高分: astra_image_static。较低分: matrix_game3_5s_image_static_dynamic。好坏标签仅比较 feature_match_coverage。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.4870astra_image_static特征匹配覆盖率 48.7%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.0988matrix_game3_5s_image_static_dynamic特征匹配覆盖率 9.9%

同一输入与 prompt · image_static · gap 0.0532

`image_static_stylized_dining_spaces_0097`

套件: image_static指标: epipolar_error场景: stylized / dining_spaces

Benchmark prompt

Camera pull out. Dining spaces with wooden table, chairs, and window with curtains. Everything in the scene remains completely motionless.

来源: generation_records

较高分: cameractrl_image_static。较低分: dreamx_world_image_static。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9890cameractrl_image_static内点 Sampson 误差中位数 0.0549

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9358dreamx_world_image_static内点 Sampson 误差中位数 0.3209

同一输入与 prompt · image_static · gap 0.2484

`image_static_stylized_dining_spaces_0041`

套件: image_static指标: epipolar_inlier_rate场景: stylized / dining_spaces

Benchmark prompt

Camera pull out. A beachside path with sand, lanterns, and ocean. Camera pan left. A beachfront lounge with lounge chairs, palm trees, and ocean. Camera move left. A beach bar with bar counter, stools, and string lights.

来源: generation_records

较高分: luciddreamer-image-static-8gpu-20260613_151844。较低分: longcat-video-image-static-8gpu-20260612_133950。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9290luciddreamer-image-static-8gpu-20260613_151844内点率 92.9%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.6806longcat-video-image-static-8gpu-20260612_133950内点率 68.1%

同一输入与 prompt · image_static · gap 0.4055

`image_static_stylized_suburb_0007`

套件: image_static指标: feature_match_coverage场景: stylized / suburb

Benchmark prompt

Camera pull out. A path intersection with trees, benches, and people. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_image_test_balanced_5000_5s。较低分: dreamx_world_image_static。好坏标签仅比较 feature_match_coverage。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.4402hy_worldplay_ar_image_test_balanced_5000_5s特征匹配覆盖率 44.0%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.0348dreamx_world_image_static特征匹配覆盖率 3.5%

同一输入与 prompt · image_static · gap 0.0705

`image_static_stylized_verdant_landscape_0087`

套件: image_static指标: epipolar_error场景: stylized / verdant_landscape

Benchmark prompt

Camera pan left. A forest at sunset with trees, open field, and forest edge.

来源: generation_records

较高分: longcat-video-image-static-8gpu-20260612_133950。较低分: ac3d-image-static。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 1.0000longcat-video-image-static-8gpu-20260612_133950内点 Sampson 误差中位数 0.0001

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9295ac3d-image-static内点 Sampson 误差中位数 0.3527

同一输入与 prompt · image_static · gap 0.4548

`image_static_stylized_city_0021`

套件: image_static指标: epipolar_inlier_rate场景: stylized / city

Benchmark prompt

Camera move right. A cityscape silhouette with towers, buildings, and bridge. Everything in the scene remains completely motionless.

来源: generation_records

较高分: motionctrl_image_static_official_default_tmp2。较低分: astra_image_static。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9696motionctrl_image_static_official_default_tmp2内点率 97.0%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.5148astra_image_static内点率 51.5%

同一输入与 prompt · image_static · gap 0.0537

`image_static_stylized_city_0051`

套件: image_static指标: epipolar_error场景: stylized / city

Benchmark prompt

Camera pan right. A city construction site with street, snow, and cars.

来源: generation_records

较高分: longcat-video-image-static-8gpu-20260612_133950。较低分: warp-as-history-image-static-8gpu-20260612_152000。好坏标签仅比较 epipolar_error。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9920longcat-video-image-static-8gpu-20260612_133950内点 Sampson 误差中位数 0.0399

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.9383warp-as-history-image-static-8gpu-20260612_152000内点 Sampson 误差中位数 0.3087

同一输入与 prompt · image_static · gap 0.2243

`image_static_stylized_aquatic_landscape_0123`

套件: image_static指标: epipolar_inlier_rate场景: stylized / aquatic_landscape

Benchmark prompt

Camera pan left. Dense trees with stone pathway and lake. Everything in the scene remains completely motionless.

来源: generation_records

较高分: hy_worldplay_ar_distilled_image_test_balanced_5000_5s。较低分: motionctrl_image_static_official_default_tmp2。好坏标签仅比较 epipolar_inlier_rate。

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较高指标分分数 0.9741hy_worldplay_ar_distilled_image_test_balanced_5000_5s内点率 97.4%

Model result videos will be available with the ModelScope release. / 模型推理视频将在 ModelScope 方案上线后提供。

较低指标分分数 0.7498motionctrl_image_static_official_default_tmp2内点率 75.0%

参考文献

BibTeX

@article{XuanyiLI2024Sora,
    title = {Sora Generates Videos with Stunning Geometrical Consistency},
    author = {Xuanyi Li and Daquan Zhou and Chenxu Zhang and Shaodong Wei and Qibin Hou and Ming-Ming Cheng},
    journal = {arXiv preprint arXiv:2402.17403},
    year = {2024},
    eprint = {2402.17403},
    archivePrefix = {arXiv},
    primaryClass = {cs.CV},
    url = {https://arxiv.org/abs/2402.17403},
}