The math

Before we jump into the code, let's take an overview of the algorithm. There are four key components.

• The first is the pinhole camera model. We try and approximate real world positions to pixels using this matrix.

• The second is the camera motion estimate. We need to use data from the gyroscope to figure out the orientation of the phone at any given moment.

• The third is the rolling shutter computation. We need to specify the direction of the rolling shutter and estimate the duration of the rolling shutter.

• The fourth is the image warping expression. Using all the information from the previous calculations, we need to generate a new image so that it becomes stable.

The camera model

We use the standard pinhole camera model. This model is used in several algorithms and is a good approximation of an actual camera.

There are three unknowns. The o variables indicate the origin of the camera axis in the image plane (these can be assumed to be 0). The two 1s in the matrix indicate the aspect ratio...