How to determine the centers of zones of certain colors in an image?

Question

Image processing

We have an image filled with different colors and separated by black borders. We need to determine the center of each zone. The most economical algorithm is needed and libraries cannot be used to work with images. In the arsenal, only getting the pixels of the image as an array:


we also need to take into account that we will need to know the x \ y position of the pixel in the image.