Learn English – Central determiners “some” and “any” used with singular count nouns

I would take that to be a typo. The verb should agree with the noun:

• Is any particular image satisfying the requirements?
• Are any particular images satisfying the requirements?

Any can be safely used in both cases. Have a look at these example sentences from Wiktionary:

• Choose any items you want. [items — plural]
• Any person may apply. [person — singular]
• I haven't got any money. [money — uncountable]

Merriam-Webster defines any as follows:

1. one or some indiscriminately of whatever kind [...]
2. one, some, or all indiscriminately of whatever quantity [...]

Emphasis mine.

Lastly, note psmears' comment that it might be more appropriate to use present simple rather than present continuous in your case (though further context might justify either). I will also add that there should be no space before the question mark.

Like most pedagogical grammars, your book gives simplified advice that does not reflect the complexity of English as it is actually used.

The key point here is not whether the noun is countable or not but whether it is countable and concrete or countable and abstract. If the noun is a concrete noun such as girl then it is probably better to say: Is there a girl in the room? or Are there any girls in the room?

Constructions such as:

• Is there any girl in the room?
• Is there any dog on the street?
• Did you borrow any book from the library?

may be considered suspect by some careful grammarians.

However, there are many countable but abstract nouns where any is perfectly acceptable:

• Is there any difference between .. ?
• Is there any way I can .. ?
• Is there any reason why .. ?
• Is there any chance .. ?
• Is there any need to .. ?