3D reconstruction system | L3 dual view motion recovery structure (SFM binocular SFM)

One 、 Triangulation

Definition ： Given image matching points and camera parameters to restore the 3D coordinates of matching points .

As shown in the figure above , A ray can be determined from the coordinates of three-dimensional points and the internal and external parameters of a camera , The possible three-dimensional point of the target is on this ray , So you need at least two camera angles , And the possible positions obtained from the intersection of two pairs are calculated by the least square method .
among , The first i Camera projection matrix ：

in addition , In the i The coordinates of the projected image in each angle of view are ：

among ,Pin It is known that , That is, an observation point provides 2 A constraint , So at least 2 Point to point . That is to say ：

Expand to ：

The last part SVD The corresponding feature points are obtained by decomposition .

Two 、 Bundle adjustment （BA）

Definition ： At the same time, the internal and external parameters of the camera and the three-dimensional point coordinates are non-linear optimized at the same time to obtain a globally optimal solution .

Suppose this scenario has n Three dimensional points , Yes m A camera , But because of n There's a point in m Not all cameras are visible , So by the corresponding relation Xij（0 or 1） To control , And optimize the projection points .

Finally, according to the re projection point uij The constant approach of , To optimize Cj( Camera parameters ),Xi（ Three dimensional point coordinates ）

therefore , The problem is transformed into an unconstrained nonlinear optimization problem