Compile ImageMagick with WEBP and HEIC support on Ubuntu 16.04

install.sh

# $ lsb_release -a
# No LSB modules are available.
# Distributor ID:	Ubuntu
# Description:	Ubuntu 16.04.5 LTS
# Release:	16.04
# Codename:	xenial

# $ uname -a
# Linux xps 4.4.0-134-generic #160-Ubuntu SMP Wed Aug 15 14:58:00 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux


# install base dependencies
sudo apt-get install libwebp-dev libde265-dev

# install library for reading heif/heic files
wget https://github.com/strukturag/libheif/archive/v1.3.2.tar.gz
tar -xvf v1.3.2.tar.gz 
cd libheif-1.3.2/
./autogen.sh 
./configure 
make
sudo make install

# install ImageMagick with WEBP and HEIC support
wget http://www.imagemagick.org/download/ImageMagick.tar.gz
tar -xvf ImageMagick.tar.gz
cd ImageMagick-7.0.8-11/
./configure --with-heic=yes --with-webp=yes
make
sudo make install
sudo ldconfig /usr/local/lib

identify --version
# $ identify -version
# Version: ImageMagick 7.0.8-11 Q16 x86_64 2018-09-06 https://www.imagemagick.org
# Copyright: © 1999-2018 ImageMagick Studio LLC
# License: https://www.imagemagick.org/script/license.php
# Features: Cipher DPC HDRI OpenMP 
# Delegates (built-in): bzlib djvu fontconfig freetype gvc heic jbig jng jpeg # lcms lqr lzma openexr pangocairo png tiff webp wmf x xml zlib

Nice Thanks

Feels like you should install more dependencies to make it work. Otherwise you'll have a heic and webp, but may not have jpeg support. Found this out while trying to port your solution to ubuntu 20.04
https://gist.github.com/hurricup/e14ae5bc47705fca6b1680e7a1fb6580