Q1: 8-point and 7-point algorithm (40 points)

Implementation

The fundamental matrix for the example images were computed as follows:

• Normalize the input pixel coordinates to be zero mean and unit variance
• Construct one row of a constraint matrix $A$ using the outer product of the homogeneous annotated points from the second and first image (order is significant)
• Solve $Af = 0$ for $f$ where $|f| = 1$ by obtaining the least singular vector of $A$ via SVD
• Reorder the resulting $f$ into a 3x3 $F$ matrix
• Project $F$ to rank 2 via SVD
• Scale the $F$ matrix using the mean and standard deviation measured from the input annotation pixel coordinates

Results

In the following results, the annotated points are drawn in circles, and the corresponding epipolar line from the annotated points in the other image are visualized with the same color.

Bench

Remote

Q4: Reconstruct your own scene! (20 points)

Implementation

Used COLMAP to estimate sparse, then dense 3D structure. Default settings were used from the GUI.

Church

The following images were used for a 3D reconstruction of First United Methodist Church in Shadyside:

The following video shows an animated fly around the resulting dense point cloud:

Ginny

The following images were used for a 3D reconstruction of Ginny the dog:

The following video shows an animated fly around the resulting dense point cloud: