Queries regarding Paper Equations

[hyunskyu]

I have some questions about your paper

1. In the "Method" section, µ represents the center position and it has 3 parameters (possibly x, y, z). When projecting the Gaussian into 2D pixel space, Et and µ are multiplied together. Does this mean Et is a 3 x 3 matrix containing rotation and translation? Or µ is transformed to homogeneous coordinate?

2. Did you not use Spherical Harmonics (SH) for color representation? (Was optimization done using just the RGB 3 channels?)

3. Is the Gaussian always isotropic because the radius r is represented in only 1 channel?

[Nik-V9]

Hi, Thanks for these questions!

1. E_t is a standard 3 x 4 extrinsic matrix. µ is transformed to homogenous coordinates as shown here:

   SplaTAM/utils/slam_helpers.py

   Line 249 in bbaf5cc

   transformed_pts = (rel_w2c @ pts4.T).T[:, :3]

2. No, we didn't use Spherical Harmonics since we didn't observe a significant change in rendering performance with SH present. As you mentioned, we just use 3 RGB channels as defined here:

   SplaTAM/scripts/splatam.py

   Line 138 in bbaf5cc

   'rgb_colors': init_pt_cld[:, 3:6],

3. Yes, the Gaussians are Isotropic. Please see this for more info: PLY Output Format & Isotropic Gaussians #22 (comment)