# Student Post: OpenSfM Revisited, Epipolar Geometry, and Possibility of Rendering

Greetings,

I’ve continued to delve into the OpenSfM configuration files to attempt to get denser meshes without much promise. The meshes seem to be similar; however, with the yellow spiral I did receive a less distorted image that could be on the road to where we want to be. The figure is shown below:

So within the next week or two, I hope to meet with Professor Bowers to discuss some optimizations that we can make to receive even better meshes.

Epipolar Geometry is basically “two views geometry” in which you match points from two separate images using an epipolar constraint to take the problem from a 2D search problem to a 1D problem. This can be done with either a stereo camera separate (two separate cameras) were the images are acquired simultaneously or a single moving camera where the images are acquired sequentially. Given two images of a scene, the goal is to triangulate the corresponding image points and then back-project the ‘rays’ which intersect at a given 3D point. This is shown in the figure below:

From this triangulation, we use the information that a point in one view “generates” an epipolar line in the other one as shown below:

From this we, the corresponding points x and x` create a plane known as the epipolar plane as shown below in the shaded area:

Ultimately, we see that from each camera plane there is an epipolar line that creates this triangulation in which we can search for the corresponding image points:

From this we can see the true advantage of using epipolar geometry when reconstructing 3D models as shown below:

All in all, I’d like to explore the possibility of using epipolar geometry to creating these mappings of 2D points to reconstruct a 3D image.

In addition to using epipolar geometry for reconstruction, I’d also like to explore the idea of using rendering instead of reconstruction take a 3D image and receive point mappings to compare instead of the the 2D to 3D pipeline that we’ve been attempting so far.

Thank you,