In header.php and / or footer.php, wrap the conditional statement around the code you wish to disable for a given page, for example if the page ID is 1:

<?php if( !is_page( '1' ) ) : ?>

<?php endif; ?>

via http://wordpress.org/support/topic/how-to-remove-header-and-footer-from-a-single-page>

More options: hide the image (or other elements) in the header in a specific page via CSS.

Another solution via CSS.