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!
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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,...
Simple answer: 'In order to help the system make a better guess of the corner locations,' is an adverb telling us why we do something, not a sentence. The actual sentence follows this adverbial phrase. Adverbs do not require finite verbs.
In order to help the system make a better guess of the corner locations, we need to improve the 'corner location function'.
You can leave out the adverbial phrase:
We need to improve the 'corner location function'.
You cannot just write the adverbial phrase, that makes no sense:
In order to help the system make a better guess of the corner locations.
In order to [do something], I/you/she must/needs to/should [do something else]
"Make" is subjunctive rather than indicative, meaning that instead of describing an action that definitely occurs, occurred, etc., it is a theoretical occurrence, or one that may or may not happen.
I am walking to the park to see my friend.
"Walk" is indicative, because it is currently happening, while "see" is subjunctive. It does not use "seeing" because it is what I am intending to do, but may or may not happen. (Note that "to" is used to denote purpose, not to set "see" off as an infinitive.)