Add Image field to CPT

Question

I am trying to add an image field that lets the user choose an image from the media library. Adding text fields worked fine, but now that I am adding an image field it is not working. What should I specify as input for an image field that only allows images from the media library?

<p>
    <label>Picture:</label><br />
    <input type="file" name="picture" value="<?= @$custom["cafe_image"][0] ?>" class="width99" accept="image/*" />
</p>

The above code does not work correctly (it creates a file selection button), so do I just put something else in the place of 'file'? The rest of the function is below:

function add_cafe_meta_boxes() {
    add_meta_box("cafe_contact_meta", "Contact Details", "add_contact_details_cafe_meta_box", "cafes", "normal", "low");
}
function add_contact_details_cafe_meta_box()
{
    global $post;
    $custom = get_post_custom( $post->ID );

    ?>
    <style>.width99 {width:99%;}</style>
    <p>
        <label>Address:</label><br />
        <textarea rows="5" name="address" class="width99"><?= @$custom["address"][0] ?></textarea>
    </p>
    <p>
        <label>Website:</label><br />
        <input type="text" name="website" value="<?= @$custom["website"][0] ?>" class="width99" />
    </p>
    <p>
        <label>Phone:</label><br />
        <input type="text" name="phone" value="<?= @$custom["phone"][0] ?>" class="width99" />
    </p>
        <p>
        <label>Picture:</label><br />
        <input type="file" name="picture" value="<?= @$custom["cafe_image"][0] ?>" class="width99" accept="image/*" />
        </p>
    <?php
}

add_action( 'admin_init', 'add_cafe_meta_boxes' );

Answer 1

My solution works but it is a cop-out. I went to CMB2 for adding fields and it works beautifully.

Some people might specifically be looking for an answer to this, so I know this is not helpful for that, but switch to CMB2 if you can.