Mount a partition of image file

Solution 1: losetup

With newer version of losetup, you can easy map parition in image file to /dev/loop*.

sudo losetup --show -Pf <imagefile>
# /dev/loop0

sudo partprobe /dev/loop0

The output will show which loop device has been mapped to image file. Now you can mount partition of it.
Example:

sudo mount /dev/loop0p1 /mnt

To detach, run sudo losetup --detach /dev/loop0.

Load module nbd

sudo modprobe nbd max_part=16

Connect /dev/nbd0 with image file

sudo qemu-nbd -c /dev/nbd0 <imagefile>

Update partition table

sudo partprobe /dev/nbd0

Mount partition of image

sudo mount /dev/nbd0p1 /mnt

To detach, run sudo qemu-nbd -d /dev/nbd0.