Public Images Link

The best way to make bespoke changes to the way Imagepicker (or any other module) does things is to write a helper module for your site (eg my_helper_module) and use hook_menu() to create a path and hook_user_view() to create an entry in the user profile page
This is not tested, but it should work:

function my_helper_module_menu() {
  $items['user/%imagepicker_uid/my_helper_module/images/browse_public'] = array(
    'title'            => 'Browse Public',
    'description'      => 'Browse public imagepicker files.',
    'page callback'    => 'imagepicker_user_page',
    'page arguments'   => array(1, 3, 4, 5),
    'access callback'  => 'imagepicker_access_user_public',
    'type'             => MENU_CALLBACK,
    'file'             => 'imagepicker.user.inc',
  );
  return $items;
}

I haven't used hook_user_view() but there is information on how to add stuff to the user profile in api.drupal.org, search for "hook_user_view". Basically you create a function my_helper_module_user_view() and add whatever you want to appear on the profile page.

Change of sentence to describe things better