Half-full, there are many ways to prove that.
From objective point of view, glasses are not premade with water inside it, so someone had to fill it before observation and happened to pour only so much water in it.
From subjective point of view, if I am thirsty, I will be glad to have at least half of water in the glass rather than nothing. Whether this would be enough for me to quench my thirst or not is another question and it will only be asked when I finish this glass, so it will not be half-full or half-empty anymore. Not to mention that I'm unlikely to finish whole glass full of water at once, kinda too much. Besides, what's the point of having full or empty glass at all? Empty one is useless and full doesn't differ much from half-full until you begin drinking and learn that you want for more - but it will not be full anymore at that moment. The more important question is the glass on the picture HAS water in it.
Finally, if I'm not thirsty, then I don't even care about this glass. Except maybe that full glass will make more mess should it fall from a surface, than half-full.