Remove specific category from a post

Question

I have enabled categories on attachments, and I am trying to implement the logic to automatically handle the "Uncategorized" category, like this:

1) If the attachment has no categories, set it to "Uncategorized"

2) If the attachment has some category besides "Uncategorized", remove "Uncategorized" from the post's category list

I have tackled most of the logic, except that now I dont know how to remove the category from the Attachment. This is my code:

<?php

// Enable categories with attachments
register_taxonomy_for_object_type( 'category', 'attachment' );

if( is_admin() ) {

    add_action('add_attachment', 'emt_set_attachment_category');
    add_action('edit_attachment', 'emt_set_attachment_category');
    function emt_set_attachment_category( $post_ID ) {

        $attachmentCategories =  wp_get_object_terms( $post_ID, 'category' );

        // if attachment has many categories, remove the default category
        if (count($attachmentCategories) > 1) {
            foreach ($attachmentCategories as $key => $category)
                if ($category->name == "Uncategorized")
                    // How to delete it??

            return;
        }

        // if attachment already have categories, stop here
        if (count($attachmentCategories) == 1)
            return;

        // if attachment has no categories, set default category
        wp_set_post_categories( $post_ID, array( get_option('default_category') ) );
    }
}

Answer 1

You want wp_remove_object_terms().

if ($category->name == "Uncategorized") {
    wp_remove_object_terms( $post_ID, 'uncategorized', 'category' );
}

Untested but "Attachments" are pretty much just posts under the hood, so I am fairly sure that should work.