How to translate custom fields in taxonomy terms? I would like to have custom fields with translatable content in taxonomy terms. Is this possible with existing modules?

I know that this is possible if I use nodes instead of taxonomy terms: I can make fields translatable using the entity translation module and edit the different versions of the field by switching the language on the node edit page.

I am also aware that the taxonomy translation module allows to "localize" a vocabulary in the sense that its terms can have a different name and description for each language. I want not only name and description to be localizable but also custom fields that I have attached to the vocabulary, in particular text and image fields. Is this possible with existing modules?
If you use 'Localize' option for taxonomy translation mode, it is possible to add taxonomy custom fields to string translation: 


/**
 * Implements hook_i18n_string_list_TEXTGROUP_alter().
 */
function YOUR_MODULE_i18n_string_list_taxonomy_alter(&$strings, $type, $object) {
  if ($type == 'taxonomy_term' && $object) {
    if (isset($object->FIELD_NAME)) {
      $term_FIELD_NAME = field_get_items('taxonomy_term', $object, 'FIELD_NAME');
      $strings['taxonomy']['term'][$object->tid]['FIELD_NAME']['string'] = $term_FIELD_NAME[0]['value'];
    }
  }
}


After clearing cache the field will be available in translation form.