"Any" can be used with either singular or plural. You can say, for example, "You may choose any one box" or "You may choose any two boxes."
The problem with your example sentence is the combination of the singular noun, "object", with a plural adjective, "their". As the sentence appears to be considering objects one at a time, it probably should read, "Any object can be recognized by detecting its primitive shape ..." It would also be acceptable to write, "Any objects can be recognized by detecting their primitive shapes ..."
Also, "assuming" in this sentence should have an object. If what you mean is that you are assuming that the objects can be recognized, remove the comma: "Assuming that any object can be recognized by detecting its primitive shape, a new approach will be developed." If there is some other assumption here and the ability to recognize objects is the result of that assumption, then you should state it after the word "assuming", like "Assuming that the objects are [whatever], then any object can be recognized ..."