Understanding Perspective Sensor Jacobian in prb_projective

[xxcisxxc]

Hi, I am trying to develop my own integrator based on prb_projective. I am a newbie to the differential rendering and the calculation of the Jacobian matrix is non-trivial to me. I want to verify my understanding of this Jacobian to see if is correct.

The function render_primarily_visible_silhouette samples rays from sensor to silhouette points, and compute the following integral to get gradient image:

$$\frac{\partial I}{\partial \pi}=\int_{\partial\Omega^2}W_e\Delta L_i(\partial_\pi \omega_i\cdot n) d l(\omega_i)\ \ \ \ \ (1)$$

Since we know the motion at the silhouette point $(\partial_\pi x_s\cdot n_s)$, we need to correct it from scene space to image plane by the Jacobian $\textbf{J}$ so that the Equation (1) can be transformed to something like

$$\frac{\partial I}{\partial \pi}=\int_{\partial A}W_e\Delta L_i(\partial_\pi x_s\cdot n_s)\textbf{J} d l(x_s)\ \ \ \ \ (2)$$

Is my understanding correct? And is there any documents or papers that I could read to know more about this calculation?

Thanks!

[njroussel]

I'm closing this, it's practically a duplicate of #1185.

In short, you are correct. That jacobian is to account for the change from scene space to screen space.