源碼地址

colab.research.google.com/drive/1qoclD7HJ3-o0O1R8cvV3PxLhoDCMsH8W

核心代碼

surface_splatting

def surface_splatting(means3D, scales, quats, colors, opacities, intrins, viewmat, projmat):# Rasterization setupprojmat = torch.zeros(4,4).cuda()projmat[:3,:3] = intrinsprojmat[-1,-2] = 1.0projmat = projmat.T# T 是論文中的 MT, colors, opacities, center, depth, radii = setup(means3D, scales, quats, opacities, colors, viewmat, projmat)# Rasterization# 1. Generate pixelsW, H = (intrins[0,-1] * 2).long(), (intrins[1,-1] * 2).long()W, H = W.item(), H.item()pix = torch.stack(torch.meshgrid(torch.arange(W),torch.arange(H), indexing='xy'), dim=-1).to('cuda')# 2. Compute ray splat intersection # Eq.9 and Eq.10x = pix.reshape(-1,1,2)[..., :1]y = pix.reshape(-1,1,2)[..., 1:]k = -T[None][..., 0] + x * T[None][..., 3] # 這個是 h_u, 因為公式8 h_u = ? · h_x = ? · (?1, 0, 0, 𝑥) = -T_0 + x · T_3l = -T[None][..., 1] + y * T[None][..., 3] # 這個是 h_v# 因為論文中 h_u 和 (𝑢, 𝑣, 1, 1) 點成為0， h_v 和 (𝑢, 𝑣, 1, 1) 點成為0# 所以 h_u 和 h_v  與 (𝑢, 𝑣, 1, 1) 垂直# h_u 和 h_v 的 叉乘是 (𝑢, 𝑣, 1, 1)points = torch.cross(k, l, dim=-1) # 叉乘s = points[..., :2] / points[..., -1:]# 3. add low pass filter # Eq. 11# when a point (2D Gaussian) viewed from a far distance or from a slended angle# the 2D Gaussian will falls between pixels and no fragment is used to rasterize the Gaussian# so we should add a low pass filter to handle such aliasing.dist3d = (s * s).sum(dim=-1)filtersze = np.sqrt(2) / 2dist2d = (1/filtersze)**2 * (torch.cat([x,y], dim=-1) - center[None,:,:2]).norm(dim=-1)**2# min of dist2 is equal to max of Gaussian exp(-0.5 * dist2)dist2 = torch.min(dist3d, dist2d)# dist2 = dist3ddepth_acc = (homogeneous(s) * T[None,..., -1]).sum(dim=-1)# 4. accumulate 2D gaussians through alpha blending # Eq.12image, depthmap = alpha_blending_with_gaussians(dist2, colors, opacities, depth_acc, H, W)return image, depthmap, center, radii, dist2