A 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 obtain. 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, the lower-frequency the computed color field. From this insight, given a reconstructed density field and 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. Our code is available at https://github.com/qihangGH/IMRC.

翻译：辐射场是三维场景的一种有效表示方法，已被广泛应用于新视角合成和三维重建。由于几乎无法获取真实几何结构（即密度场）的真值，因此评估其质量仍是一个开放且具有挑战性的问题。一种替代的间接解法是将密度场转换为点云，并计算其与扫描得到的真实点云之间的倒角距离。然而，许多广泛使用的数据集缺乏点云真值，因为扫描过程及设备昂贵且复杂。为此，我们提出一种新型度量指标——逆平均残差颜色（Inverse Mean Residual Color, IMRC），该指标仅需观测图像即可评估几何结构。我们的核心见解是：几何结构越优，计算得到的颜色场频率越低。基于这一见解，给定重建的密度场和观测图像，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，表示几何结构越优。定性与定量实验结果验证了所提出的IMRC指标的有效性。我们还利用IMRC对多种先进方法进行了基准测试，以推动未来相关研究。我们的代码已开源：https://github.com/qihangGH/IMRC。