The best solution is to provide a path relative to the folder where the md document is located.
Probably a browser is in trouble when it tries to resolve the absolute path of a local file. That can be solved by accessing the file trough a webserver, but even in that situation, the image path has to be right.
Having a folder at the same level of the document, containing all the images, is the cleanest and safest solution. It will load on GitHub, local, local webserver.
images_folder/img.jpg < works
/images_folder/img.jpg < this will work on webserver's only (please read the note!)
Using the absolute path, the image will be accessible only with a url like this: http://hostname.doesntmatter/image_folder/img.jpg