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Original filter can be set.

E-mail to Twitter ID

function set_twitter_id($twitter_id, $email = '') {
    if ( $email == 'hoge@example.com' )
        $twitter_id = 'hoge';
    return $twitter_id;
}
add_filter('twitter_id/twicon.php', 'set_twitter_id', 10, 2);

Set profile image

function set_profile_image_url($profile_image_url, $id_or_email = '') {
    if ( $id_or_email == 'fuga@example.com' )
        $profile_image_url = get_option('siteurl') . '/images/fuga.png';
    return $profile_image_url;
}
add_filter('profile_image_url/twicon.php', 'set_profile_image_url', 10, 2);