Radiance field is an effective representation of 3D scenes, which has been widely adopted in novel-view synthesis and 3D reconstruction. It is still an open and challenging problem to evaluate the geometry, i.e., the density field, as the ground-truth is almost impossible to be obtained. One alternative indirect solution is to transform the density field into a point-cloud and compute its Chamfer Distance with the scanned ground-truth. However, many widely-used datasets have no point-cloud ground-truth since the scanning process along with the equipment is expensive and complicated. To this end, we propose a novel metric, named Inverse Mean Residual Color (IMRC), which can evaluate the geometry only with the observation images. Our key insight is that the better the geometry is, the lower-frequency the computed color field is. From this insight, given reconstructed density field and the observation images, we design a closed-form method to approximate the color field with low-frequency spherical harmonics and compute the inverse mean residual color. Then the higher the IMRC, the better the geometry. Qualitative and quantitative experimental results verify the effectiveness of our proposed IMRC metric. We also benchmark several state-of-the-art methods using IMRC to promote future related research.

翻译：辐射场是三维场景的有效表示方法，已被广泛应用于新视角合成和三维重建领域。由于难以获取真实几何（即密度场）的标注数据，如何评估几何质量仍是一个开放且具有挑战性的问题。一种间接替代方案是将密度场转换为点云，并与扫描得到的真实点云计算倒角距离（Chamfer Distance）。然而，由于扫描设备昂贵且操作复杂，许多常用数据集并不提供点云真实值。为此，我们提出一种新型评估指标——逆平均残差颜色（Inverse Mean Residual Color, IMRC），仅通过观测图像即可评估几何质量。我们的核心发现是：几何质量越好，计算得到的颜色场频率越低。基于这一发现，给定重建的密度场与观测图像，我们设计了一种闭式方法，利用低频球谐函数近似颜色场并计算逆平均残差颜色。IMRC值越高，则几何质量越好。定性与定量实验验证了所提IMRC指标的有效性。此外，我们使用IMRC对多种先进方法进行基准测试，以推动未来相关研究。