Contour analysis and shape matching

Contour analysis is a very useful tool in the field of computer vision. We deal with a lot of shapes in the real world and contour analysis helps in analyzing those shapes using various algorithms. When we convert an image to grayscale and threshold it, we are left with a bunch of lines and contours. Once we understand the properties of different shapes, we will be able to extract detailed information from an image.

Let's say we want to identify the boomerang shape in the following image:

In order to do that, we first need to know what a regular boomerang looks like:

Now using the above image as a reference, can we identify what shape in our original image corresponds to a boomerang? If you notice, we cannot use a simple correlation based approach because the shapes are all distorted. This means that an approach where we look for an exact match won't work! We need to understand the properties of this shape and match the corresponding properties to identify...