How to limit 1 image per post on homepage only?

/**
 * @author: wpreceipes
 * @link: [1]: http://www.wprecipes.com/how-to-get-the-first-image-from-the-post-and-display-it
 */
function wpse18215_catch_that_image() 
{
    global $post, $posts;
    $first_img = '';
    ob_start();
    ob_end_clean();
    $output = preg_match_all( '/<img.+src=[\'"]([^\'"]+)[\'"].*>/i', $post->post_content, $matches );
    $first_img = $matches[1][0];

    //Defines a default image
    if( empty( $first_img ) )
    { 
        $first_img = '/images/default.jpg';
    }
    return $first_img;
}

Example:

echo catch_that_image();

or:

/**
 * @author: Marcelo Mesquita
 * @link: http://marcelomesquita.com/
 * @param (string) $size - valid: 'thumbnail', 'medium', 'large' or 'full_size'
 * @param (string) $add - any additional attributes for the html-img tag
 */
function wpse18215_the_thumb( $size="medium", $add = '' )
{
    global $wpdb, $post;

    $thumb = $wpdb->get_row( 
        "SELECT ID, 
         post_title 
         FROM {$wpdb->posts} 
         WHERE post_parent = {$post->ID} 
         AND post_mime_type 
         LIKE 'image%' 
         ORDER BY menu_order"
    );

    if( ! empty( $thumb ) )
    {
        $image = image_downsize( $thumb->ID, $size );
        return "<img src="https://wordpress.stackexchange.com/questions/18215/{$image[0]}" alt="{$thumb->post_title}" {$add} />";
    }
}

Example:

echo wpse18215_the_thumb( 'medium', 'class="alignleft" width="200" height="175"' );

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Note: You need to wrap the call anyway inside your template into a conditional statement:

if ( is_home() || is_front_page() ) { /* place the function call here */ }