Why divided by f3dArea in IMT computation?

[Qinja]

In line 1542 of the file [UVAtlas\isochart\imtcomputation.cpp] the code is :
for (size_t ii = 0; ii < IMT_DIM; ii++) { (*pfIMTArray)[ii] /= f3dArea; }

But the first formula in page 4, section 3.3 in the document "Signal Specialized Parameterization", IMT should be multiplied by the area of the triangle.

My questions:

1. How to understand the difference between paper and code practice.
2. When I call UVAtlasComputeIMTFromTexture, how do I get the IMT array converted to Eh(S) which is finally used to measure the stretch of the signal.

Thanks for every answer.

[Qinja]

As per my understanding and guesswork.
The calculation process of Eh(S) is:

where

where

So what should be the value represented by the array obtained when I call the “UVAtlasComputeIMTFromTexture”, is that "Mh(▲i)" or "Mh(si, ti)" , or neither.
And why do divide before output these values in line 1542?