Based on

Based on the trail of blood, the killer went through the kitchen and...

Based on your appearance, you had a close encounter with a mud puddle.

These stand for the internal speculation, such as:

Based on the trail of blood, it appears that the killer went through the kitchen and...

Based on your appearance, I'm guessing you had a close encounter with a mud puddle.

In careful writing, it would be something like "The tail of blood indicates that..." or "Your appearance suggestions..." or "This picture makes it clear that..."

To avoid the ambuiguity, rephrase slightly and get rid of "based on": Using the picture as a guide, they rebuilt ...

That would be difficult. In the passive, the builders are not mentioned, but it is the builders who used the picture as a guide - so you can't assign "using the picture as a guide" to unmentioned builders.

The picture was used as a guide when the temple was rebuilt. I guess that works - the unnamed builders both used the picture and built the temple.