Light Field Duality: Concept and Applications: Difference between revisions

Light Field Duality: Concept and Applications (view source)

970 bytes added , 23 December 2020

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 ==CHL Light Field Rendering==
-Each camera <math>i</math> is a point in world coordinates which corresponds to a hyperline in the light field.
+Each camera <math>i</math> is a point in world coordinates which corresponds to a hyperline <math>\mathbf{l}_i=(a_i, b_i, c_i, d_i)</math> in the light field.
 If we want to render from a new viewpoint, for each render pixel, we have a target ray which corresponds a point on the light field <math>\mathbf{r} = (s_r, t_r, u_r, v_r)</math>.
+For each camera/hyperline <math>i</math>, you can find the ray/hyperpoint which minimizes some distance function:
+<math>
+\begin{aligned}
+d^2 &= \Vert (s_i,t_i,u_i,v_i) - (s_r,t_r,u_r,v_r) \Vert^2_2\\
+&= (s_i - s_r)^2 + (t_i - t_r)^2 + (u_i - u_r)^2 + (v_i - v_r)^2
+\end{aligned}
+</math>.
+There is a closed form solution provided in the paper.
+Then simply blend with weights as inverse distance.
+===Dynamic focal plane===
+You can add a slope loss to the distance function to make sure rays point in the same direction:
+<math>
+\begin{aligned}
+d^2 &= \Vert (s_i,t_i,u_i,v_i) - (s_r,t_r,u_r,v_r) \Vert^2_2 +\\
+&\hspace{5mm}\beta\Vert (s_i-u_i, t_i-v_i) - (s_r-u_r, t_r-v_r) \Vert^2_2
+\end{aligned}
+</math>.
+If the virtual camera is not at the same position as the source cameras, then the lines will not be parallel and will intersect.
+<math>\beta</math> can be used to control the depth at which they intersect.
 ==GHL Light Field Rendering==