https://blog.csdn.net/weixin_50973728/article/details/136940955
https://blog.csdn.net/weixin_50973728/article/details/136940955
108、3D Gaussian Splatting for Real-Time Radiance Field Rendering
图像为
【转载】3D Gaussian Splatting中的数学推导
http://www.yindaheng98.top/%E5%9B%BE%E5%BD%A2%E5%AD%A6/3D%E9%AB%98%E6%96%AF%E6%95%B0%E5%AD%A6%E6%8E%A8%E5%AF%BC.html#derivation-of-splatting
if (denom2inv != 0)
{
// Gradients of loss w.r.t. entries of 2D covariance matrix,
// given gradients of loss w.r.t. conic matrix (inverse covariance matrix).
// e.g., dL / da = dL / d_conic_a * d_conic_a / d_a
dL_da = denom2inv * (-c * c * dL_dconic.x + 2 * b * c * dL_dconic.y + (denom - a * c) * dL_dconic.z);
dL_dc = denom2inv * (-a * a * dL_dconic.z + 2 * a * b * dL_dconic.y + (denom - a * c) * dL_dconic.x);
dL_db = denom2inv * 2 * (b * c * dL_dconic.x - (denom + 2 * b * b) * dL_dconic.y + a * b * dL_dconic.z);
// Gradients of loss L w.r.t. each 3D covariance matrix (Vrk) entry,
// given gradients w.r.t. 2D covariance matrix (diagonal).
// cov2D = transpose(T) * transpose(Vrk) * T;
dL_dcov[6 * idx + 0] = (T[0][0] * T[0][0] * dL_da + T[0][0] * T[1][0] * dL_db + T[1][0] * T[1][0] * dL_dc);
dL_dcov[6 * idx + 3] = (T[0][1] * T[0][1] * dL_da + T[0][1] * T[1][1] * dL_db + T[1][1] * T[1][1] * dL_dc);
dL_dcov[6 * idx + 5] = (T[0][2] * T[0][2] * dL_da + T[0][2] * T[1][2] * dL_db + T[1][2] * T[1][2] * dL_dc);
// Gradients of loss L w.r.t. each 3D covariance matrix (Vrk) entry,
// given gradients w.r.t. 2D covariance matrix (off-diagonal).
// Off-diagonal elements appear twice --> double the gradient.
// cov2D = transpose(T) * transpose(Vrk) * T;
dL_dcov[6 * idx + 1] = 2 * T[0][0] * T[0][1] * dL_da + (T[0][0] * T[1][1] + T[0][1] * T[1][0]) * dL_db + 2 * T[1][0] * T[1][1] * dL_dc;
dL_dcov[6 * idx + 2] = 2 * T[0][0] * T[0][2] * dL_da + (T[0][0] * T[1][2] + T[0][2] * T[1][0]) * dL_db + 2 * T[1][0] * T[1][2] * dL_dc;
dL_dcov[6 * idx + 4] = 2 * T[0][2] * T[0][1] * dL_da + (T[0][1] * T[1][2] + T[0][2] * T[1][1]) * dL_db + 2 * T[1][1] * T[1][2] * dL_dc;
}
dL_dcov[6 * idx + 0] = (T[0][0] * T[0][0] * dL_da + T[0][0] * T[1][0] * dL_db + T[1][0] * T[1][0] * dL_dc);
// Compute loss gradient w.r.t. matrix M // dSigma_dM = 2 * M glm::mat3 dL_dM = 2.0f * M * dL_dSigma;
https://www.bilibili.com/video/BV1cz421872F/?spm_id_from=333.788&vd_source=f88ed35500cb30c7be9bbe418a5998ca
