You already got your answer from other users. So, there's no need for me to further repeat that for you here.
But, you should actually learn what 755 and 777 means rather than thinking of it as some sort of psuedo-security level setting. 777 does not instantly mean insecure. And quite frankly, I see no immediate issue with you setting your image upload folder as 777.
owner, root, php executer, etc are not equivalent, though may be the same.
These words are based in English and you should take them at english value rather than some foreign construct of programming world.
Root user is like a dictator. Whatever he says goes. There's no one who can say otherwise.
When there is an object, there's an owner user. And you set the laws as to what the owner can do: read, write or execute.
You can also set laws to what a specific group can do.
Lastly, you can also set laws to what everyone else can do.
Now the dictator doesn't go around doing ALL the work. The one running the PHP can be one person. And the one who owns the file can be another. They could certainly be the same person, but such definitions are not equivalent. I hope you see the difference.
Here's another analogy. Think of a private park. If you allow everyone (ie 777) to enter and play in the park, are you posing some sort of a security risk? No.
If you have a safe, who would you allow? Just yourself (the owner), right? So, that would be like 700 in linux permissions. No one else has any permission but yourself (except the dictator, because he can come to your house, kill you and take your things if he felt like it).