We thank the reviewer for their insightful comments. We are encouraged that the reviewer acknowledges that our method achieves good results on the typically challenging task of reconstructing reflective objects and outperforms existing methods quantitatively. We respond to the weaknesses and questions below (Weakness 1 - W1, Question 1 - Q1):
W1. To validate the effectiveness of our method on diffuse objects, we processed the raw capture of the Camera scene in PMVIR. A visual comparison is shown in Appendix C.3. Since the ground truth mesh isn't provided, quantitative evaluation is unavailable. However, Fig. 9 shows that our method reconstructs more details of small structures such as buttons, knobs, and slots of the camera. This proves that our method can handle diffuse objects effectively.
W2. The setting of hyper-parameters is relatively fixed in our method. For clarification, we rearrange the notation of the weights of loss functions in Eq. 9 and add a description of the settings in Appendix D.3. The only hyper-parameter that needs to be tuned is alpha. We tested different choices of alpha on the Bunny scene, as shown in Appendix D.3.2, to facilitate the practical implementation of the method.
W3. In the initial submission, we showed reconstructed meshes of the Owl, Black Vase, Cat, and Vase scenes in the Appendix. Moreover, we rendered two additional synthetic scenes (Bunny and Dragon) with ground truth normals during the discussion time, and qualitative and quantitative comparisons are shown in Appendix C.2, along with an additional evaluation metric, Mean Angular Error (MAE) of normals.
W4. Thank you for pointing out the errors. We have fixed them.
Q1. As mentioned in W2, we list them in Appendix D.3.
Q2. Yes, as parameterized by the covariance matrix, the learned Gaussians are anisotropic. Normal vector can be seen as the mean of 3D Gaussians, and changes of normal vectors within the neighborhood are captured by covariance of Gaussians. Therefore, we claim that the 3D Gaussians capture more details. We have modified the description in Sec. 2.4.
Q3. As mentioned in W2, the required experiments are listed in Appendix D.3.2. Due to the limitation of computational resources, ablation studies were only done on two of the objects in Table 1. We plan to complete them when the computational resources become available. We’ll post them if the results are available during the discussion.
Q4. The first term supervises the eigenvalues of the covariance matrix, and the second term supervises the eigenvectors of the covariance matrix. Similar to PCA techniques, the covariance matrix determines the magnitude and direction of normal changes through eigenvalues and eigenvectors. If the local shape is like a plane, normals will change smoothly in all directions, and the difference between eigenvalues will be small, resulting in the Anisotropy (defined as the ratio of eigenvalues in the paper) approaching 1. If there are some details like edges, normals tend to change abruptly and exhibit directionality, which is represented by eigenvectors. We have modified the description in Sec. 3.2.3.