Show prev and next post links on attachment page?

I use this code to show previous and next posts (in same category) on post pages (single.php).

<?php
$next_post = get_next_post(TRUE); // TRUE = in same category
if (!empty( $next_post )): ?>
<div><a href="<?php echo get_permalink( $next_post->ID ); ?>" title="<?php echo $next_post->post_title; ?>" rel="next"><?php echo $next_post->post_title; ?></a></div>
<?php endif; ?>

<?php
$prev_post = get_previous_post(TRUE); // TRUE = in same category
if (!empty( $prev_post )): ?>
<div><a href="<?php echo get_permalink( $prev_post->ID ); ?>" title="<?php echo $prev_post->post_title; ?>" rel="prev"><?php echo $prev_post->post_title; ?></a></div>
<?php endif; ?>

It works fine, and I wish to display same thing on attachment page (image.php).

How to make it work on attachment page of post featured image (image.php)?