You have a problem with the unix paths in Mac OS X (see GDAL: Building On Mac)
- The GDAL pre-compiled binaries of Kyng Chaos use the Framework way (installed in
/Library/Frameworks/GDAL.framework).
Control
$ /Library/Frameworks/GDAL.framework/Versions/2.2/unix/bin/gdal-config --libs
-L/Library/Frameworks/GDAL.framework/Versions/1.11/unix/lib -lgdal
$ /Library/Frameworks/GDAL.framework/Versions/2.2/unix/bin/gdal-config --cflags
-I/Library/Frameworks/GDAL.framework/Versions/1.11/Headers2
- The Homebrew way installs all in
/usr/local/Cellar/with symbolic links in/usr/local/bin/
Control
$ gdal-config --libs
-L/usr/local/Cellar/gdal2/2.2/lib -lgdal
$ gdal-config --cflags
-I/usr/local/Cellar/gdal2/2.2/include
So, if you only use the Homebrew solution, it is normal that
I do not see "GDAL.framework" in my "Library/Frameworks/..".
And there's no need to add /Library/Frameworks/GDAL.framework/Programs to your PATH
Now to find the gdal_polygonize.py file in the terminal, simply use
locate gdal_polygonize.py