$$

Exercise $1\mathrm{.}1$: Box Detection

In the first exercise, you will implement a small program that estimates the size of a box from a distance image. As discussed in the lecture, we will use Python as the programming language of your choice. While the slides of the first lecture provide most of the tools, you will need to research how to solve the task best. The following description will serve as a guideline to complete the task.

Feel free to write your own helper functions and try to keep your code structured and easy to understand. You may include your own ideas and extensions as you like.

Have a look at the following libraries, as they contain valuable functions: numpy, scipy, scikit$-$learn, matplotlib

Getting and reading the data Download the example files from StudOn and extract them into your working directory. The four $.$ mat$-$files contain different examples that you can use for testing your implementation. Each example consists of an amplitude image A$,$ a distance image D$,$ and a point cloud PC$.$ Pixels can be accessed via A $[$height$,$width, :$].$ Please note that all three representations are registered. This means that the information at the position