Rückgabe der Seiten-ID in einem benutzerdefinierten Walker

Question

Ich versuche, einen benutzerdefinierten Walker zu verwenden, um Seitenminiaturen mit benutzerdefinierten Navigationsmenüpunkten zurückzugeben. Meine vollständige Walker ist unten, es scheint, dass dieser Abschnitt

$thumbnail = '';
if( $id = has_post_thumbnail( (int)$item->object_id ) ) {
$thumbnail = get_the_post_thumbnail( $id );
}

zieht nicht die Seiten-ID und so bekomme ich keine Thumbnails.

/*
* Create HTML list of nav menu items.
* Replacement for the native Walker, using the description.
*
* @see    http://wordpress.stackexchange.com/q/14037/
* @author toscho, http://toscho.de
*/
class Thumbnail_Walker extends Walker_Nav_Menu
{
/**
* Start the element output.
*
* @param  string $output Passed by reference. Used to append additional content.
* @param  object $item   Menu item data object.
* @param  int $depth     Depth of menu item. May be used for padding.
* @param  array $args    Additional strings.
* @return void
*/
function start_el(&$output, $item, $depth, $args)
{
$classes     = empty ( $item->classes ) ? array () : (array) $item->classes;

$class_names = join(
    ' '
,   apply_filters(
        'nav_menu_css_class'
    ,   array_filter( $classes ), $item
    )
);

! empty ( $class_names )
    and $class_names = ' class="'. esc_attr( $class_names ) . '"';

$output .= "<li id='menu-item-$item->ID' $class_names>";

$attributes  = '';

! empty( $item->attr_title )
    and $attributes .= ' title="'  . esc_attr( $item->attr_title ) .'"';
! empty( $item->target )
    and $attributes .= ' target="' . esc_attr( $item->target     ) .'"';
! empty( $item->xfn )
    and $attributes .= ' rel="'    . esc_attr( $item->xfn        ) .'"';
! empty( $item->url )
    and $attributes .= ' href="'   . esc_attr( $item->url        ) .'"';

// insert thumbnail
// you may change this
$thumbnail = '';
if( $id = has_post_thumbnail( (int)$item->object_id ) ) {
    $thumbnail = get_the_post_thumbnail( $id );
}

$title = apply_filters( 'the_title', $item->title, $item->ID );

$item_output = $args->before
    . "<a $attributes>"
    . $args->link_before
    . $title
    . '</a> '
    . $args->link_after
    . $thumbnail
    . $args->after;

// Since $output is called by reference we don't need to return anything.
$output .= apply_filters(
    'walker_nav_menu_start_el'
,   $item_output
,   $item
,   $depth
,   $args
);
}
}