This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Stages of analysis

### From Mathematics Is A Science

Suppose we have found the topology graph of the gray scale image.

Image -> its topology graph -> one of the possible topologies

Having the topology graph isn’t enough for the complete analysis of the image. It provides all possible topologies in the image, but we have to choose only one. This is to be done by the user based on his criteria of what is noise:

Some of the principal cycles will have to be discarded by the user. The remaining ones will represent the simplified topology of the image and, accordingly, we have the *simplified topology graph*. Ideally, the remaining cycles of the same dimension shouldn't contain each other, see Objects in gray scale images.

See also Filtering output data.

To see how Pixcavator does it with real images, watch this short clip.