Why is the verb used without “-s” in this sentence?

In order to help the system make a better guess of the corner locations,...

In this sentence, why is "make" not succeeded by "s"? It seems it is needed!

Answer

The construction used here is help + object + bare infinitive. Here are two more examples:

Can you help me fix my bike?

I helped my father cut the grass.

An equally grammatical equivalent to the above construction is to include the to before the bare form:

Can you help me to fix my bike?

I helped my father to cut the grass.

It is clear that the verbs fix and cut are infinitives and are therefore not determined by the number of the object (system in your example).

You could rewrite your sentence as:

In order to help the system to make a better guess of the corner
locations,...