Using a combination of the ImageMagick source installation instructions and some instructions from a blog, I got the following to work:
Get rid of the old version
yum remove ImageMagick
Install the dependencies You will need the appropriate ImageMagick dependencies for whatever graphic types you expect to convert.
yum install wget tcl-devel libpng-devel libjpeg-devel ghostscript-devel bzip2-devel freetype-devel libtiff-devel
curl
and extract the ImageMagick source
cd ~/
curl -O http://www.imagemagick.org/download/ImageMagick.tar.gz
tar zxvf ImageMagick.tar.gz
Test configuration
cd ImageMagick-xxx
./configure
Confirm configuration There should be a yes next to all the image types you anticipate needing to convert, if not see the dependencies step above.
Build and install
make
make install