Here i present a rational dialectical view.
i.e. When i watch a painting of course i have an idea of the painting but i know under certain circumstances that this is an objective idea. It corresponds to the painting itself and it is not an idea of an elephant camouflaged as a painting tricking my mind. Of course looking and thinking about the painting does not magically present me the "whole reality" of this painting, but i can study it if i like i.e. the paper, the technique, the meaning, the era everything, and at the end i will know that i study this specific painting objectively and not some hidden elephant like the Kantian thing-in-itself. So here it is:
Considering "external reality of objects" is a bit tricky.
External is regarded in opposition with "ourselves"-minds.
Reality is ascribed on objects that exist on themselves in contrast with imaginations, some other type of false existence or non-existence.
Objects are the things under consideration.
So let's consider an example:
I have here in my room a nice drawing above my bed. Is this external object real? I watch it everyday for the last 2 years so it must be real.
Is there a possibility i watch an optical illusion for two years and i can also sense the paper etc?
Sense and assumption can fool me but let's speculate that i confirm the existence of the object in a rational way. (i bring the poor scientists from the other answer so to make their tests on the painting and on me). So it should be real.
On the other hand this painting is a specific object. A lot of people have drawings and have the same type of experience that these objects are real.
Of course all these paintings are not the same object. Each of these is a different one. And we all confirm according to our experience tested in a rational way that these objects are real and different.
Now let's consider that I take the painting and shred it to pieces.
Is the object of the painting still real? No, now it is a shredded painting. Actually it is a mishmash of colored paper.
What happened to the reality of the painting? It no longer exists.
I still have a memory of the painting before i shred it to pieces. But from now on, it is no more an external but an internal presentation in my memory of the object before i destroyed it.
The reality of the painting object was so fragile that it could stand only a small amount of force before it turns to its opposite.
If I come to your house and i brought with me a bulk of shred colored paper and i present it to you and i say "here is a nice painting, i bring it to you as a gift", you will surely suppose that i' m a fool.
Now i have a bulk of paper. Is it real? Yes it is real. What will happen if i burn it, will it still be real? Of course not. The paper is gonna turn to ashes and energy. The paper/object i had has disappeared and is no more real. Now i have to do with the reality of this lump of ash and the heat that diffused in the environment.
So the most influential arguments for the "existence of real external objects" must take into account all aspects of the being. Existence is a dialectical category and is contradicted with non-existence.
Worst of all, objects are real and not real at the same time. I'm real as a man but also I'm not really an elephant.