Initializing C++ const fields after the constructor

I want to create an immutable data structure which, say, can be initialized from a file.

class Image {
public:
   const int width,height;
   Image(const char *filename) {
     MetaData md((readDataFromFile(filename)));
     width = md.width();   // Error! width  is const
     height = md.height(); // Error! height is const
   }
};

What I could do to fix the problem is

class Image {
   MetaData md;
public:
   const int width,height;
   Image(const char *filename):
     md(readDataFromFile(filename)),
     width(md.width()),height(md.height()) {}
};

However

1. It forces me to save MetaData as a field in my object. Which I don't always want.
2. Sometimes the logic in the constructor is much more complex than a single read (say, error handling can take a few lines)

So the only solution I thought of is along the lines of

class A {
  int stub;
  int init(){/* constructor logic goes here */}
  A():stub(init)/*now initialize all the const fields you wish
  after the constructor ran */{}
};

Is there a better idea? (In Java, you're allowed initializing finals in the constructor).