Homography

• Image Homographies

 

Adjust the angle.

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Here are several consecutive images taken.

 

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Attach these images in order.

Images are put together alternately. This is because the angle of the picture is different.

 

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Use Homography to adjust the angle.

 

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It requires 3 conditions.

 

1. The subject should be plane. 

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2. If it's not a plane, at least it should be close to a plane.

Because even if it's not actually a plane, we'll assume that it's a plane, that is, we'll think of it as a plane.

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3. The two images must be taken from the same center.

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• Determining a Homography

 

Let's determine the Homography between two different images.

 

1. Convert 2D coordinate(p) to homogeneous coordinates(P).

 

\begin{equation}p=\begin{bmatrix}x\\y\end{bmatrix}\quad\Rightarrow\quad P=\begin{bmatrix}x\\y\\1\end{bmatrix}\end{equation}

 

2. Assume there are P' that is matching with P.

 

\begin{equation}P'=H\cdot P\quad\text{or}\quad\left[\begin{array}{c}x'\\y'\\1\end{array}\right]=\alpha\left[\begin{array}{ccc}h_1&h_2&h_3\\h_4&h_5&h_6\\h_7&h_8&h_9\end{array}\right]\left[\begin{array}{c}x\\y\\1\end{array}\right]\end{equation}

 

https://velog.io/@richpin/Computer-Vision-08-Image-Homographies