Exclude category from fucntion

foreach ($categories as $individual_category) {        
    if( $individual_category->term_id == 81 || $individual_category->term_id == 82 ) 
        continue;
    $category_ids[] = $individual_category->term_id; 
}

explanation:

the above replaces:

foreach($categories as $individual_category) 
        $category_ids[] = $individual_category->term_id;

i.e. the code jumps over the to be excluded categories.