Featured image for first post only

You can use the_post_thumbnail() to output the thumbnail image directly.

<?php $count = 1; ?>
<?php while (have_posts()){ the_post(); ?>
<article id="<?php echo $post->post_name; ?>" class="post<?php post_class(); ?>" itemscope itemtype="http://schema.org/Article"><?php
    if ($count == 1 && has_post_thumbnail( get_the_ID() ) ){
        the_post_thumbnail('blog-thumbnail', array('class' => 'banner', 'item_prop' => 'image'));
    } 
    $count++; ?>
    <header>
        <h1 itemprop="name"><a href="https://wordpress.stackexchange.com/questions/35617/<?php the_permalink(); ?>" title="<?php printf(esc_attr__('%s', 'schema'), the_title_attribute('echo=0')); ?>" rel="bookmark" itemprop="url"><?php the_title(); ?></a></h1>
    </header>
    <footer>
        <?php schema_posted_on(); ?>
    </footer><?php
    if (is_archive() || is_search()){
        the_excerpt();
    } else {
        the_content(__('Continue reading <span class="meta-nav">&rarr;</span>', 'schema'));
        wp_link_pages(array('before' => '<div class="page-link">' . __('Pages:', 'schema'), 'after' => '</div>'));
    }
    edit_post_link(__('Edit', 'schema'), '<p class="edit-link">', '</p>'); ?>
</article>
<?php } ?>