I have this assets table:
asset_id | mediumint(8)
asset_type_id | mediumint(8)
asset_name | varchar(200)
SELECT
l.product_id, t.asset_type_id, COUNT(*)
FROM
lookup l
CROSS JOIN
(SELECT 1 AS asset_type_id UNION ALL SELECT 2 UNION ALL SELECT 3) t
LEFT JOIN
assets a ON l.asset_id = a.asset_id AND t.asset_type_id = a.asset_type_id
GROUP BY
l.product_id, t.asset_type_id;
Edit: as separate columns
SELECT
l.product_id,
COUNT(CASE WHEN a.asset_type_id = 1 THEN 1 END) AS asset_count_image,
COUNT(CASE WHEN a.asset_type_id = 2 THEN 1 END) AS asset_count_video,
COUNT(CASE WHEN a.asset_type_id = 3 THEN 1 END) AS asset_count_sound
FROM
lookup l
LEFT JOIN
assets a1 ON l.asset_id = a.asset_id AND a.asset_type_id IN (1, 2, 3)
GROUP BY
l.product_id;