Questions about PBA jacobian about dsol HOT 11 CLOSED

Yes, PBA does not use inverse compositional algorithm.

from dsol.

thanks!
CalcJacGeo func in adjust.cpp
p1' = R10 * n0 + t10 * q0; R10 = R^w_1.inv * R^w_0; t10 = R^w_1.inv * (t^w_0 - t^w_1)
when i calculate the jacobian of warp function to T^w_1 and T^w_0, the jacobian to R^w_1 and R^w_0 is same as the code;
but diff when i calculate dp1_dt1 and dp1_dt0
i thought that dp1_dt1 = partial t10*q0 / partial t^w_1 = -R^w_1.inv q0
dp1_dt0 = R^w_1.inv q0
but in code, dp1_dt1 = -q0 identity
dp1_dt0 = R10q0

from dsol.

The function is not computing jacobian wrt t^w_1, but wrt delta t^w_1, which is the error state.

from dsol.

i don't understand this error state, does it means the error function is: I1(W(x,T^w_1,T^w_0,dT^w_1,dT^w_0,q0))-I0(x)?
so the T10 = (T^w_1* dT^w_1).inv * (T^w_0*dT^w_0)
then i need to compute jacobian of warp to dT?

from dsol.

Yes

from dsol.

Thank u so much! i got the same as code.

from dsol.

But still i have a question : why not compute jacobian to T^w_1 T^w_0 directly, instead compute jacobian to delta

from dsol.

Because that's how nonlinear least squares works: you linearize at some nominal state x_0 using first order Taylor approximation, f(x) = f(x_0) + f'(x_0) dx. Therefore, the quantity you solve for is dx, which is the error/delta state.

from dsol.

Oh, i see. now i understand. thanks a lot! By the way, the code is beautiful!

from dsol.

Thanks for your open source, why not use inverse compositional algorithm in PBA? It's a lot fast.

from dsol.

Because inverse depth is a variable to be optimized. If I use inverse compositional, then the jacobian wrt inverse depth is zero.

from dsol.