Color Search Database Design Schema - php

Question

I am building a color search function utilizing php and mysql. The requirement of the search is that it needs to be fast, not use joins, and allow for 1-5 hex color inputs that query the database and return the "most accurate" results. By "most accurate" I mean that results will be reflective of the search input. I have a few pieces of data to help that such as the distance between the mapped color value (mapped against an array of pre-defined colors) and the original search input hex value (eg. ff0000).
The way the color search engine works is that you input 1-5 hex values (eg. #ff0000, #000000, #9ef855, etc), click search, and it searches the database to find images that contain the highest percentage of those colors. See this color search for reference to how a color search engine works. Note: I built this one, but it has a completely different schema, which has scaling problems and cant add indexes because the number of colors is directly related to the number of table columns which is 120. Suggesting I use what I have built is out of the question for right now.
The data in the database comes from measurements taken on images. Up to 5 colors are extracted from an image, and then each hex color value (hex) is mapped to the closest predefined hex value (map_hex). Both of these pieces of data as well as the following are stored in the database:
media_id
hex (actual true value from image measurement)
map_hex (mapped value of the previous hex value)
percentage (the amount of this color found in the image)
distance (the distance between the true hex value and the mapped hex value)
sequence (unix timestamp, for ordering)
Before a color search query gets sent to the database, it is mapped to a set of colors so we can use the mapping to do a direct lookup on map_hex. This to me seemed like a faster way than trying to do a range type of query.
As of right now I am experimenting with two database design schemas but both seem to have their own problems.
Schema 1
CREATE TABLE `media_has_colors` (
`media_id` int(9) unsigned NOT NULL,
`hex` varchar(6) NOT NULL DEFAULT '',
`map_hex` varchar(6) NOT NULL,
`percentage` double unsigned NOT NULL,
`distance` double unsigned NOT NULL,
`sequence` int(11) unsigned NOT NULL,
PRIMARY KEY (`media_id`,`hex`),
KEY `index_on_hex` (`hex`),
KEY `index_on_percentage` (`percentage`),
KEY `index_on_timestamp` (`sequence`),
KEY `index_on_media_id` (`media_id`),
KEY `index_on_mapping_distance` (`distance`),
KEY `index_on_mapping_hex` (`map_hex`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
Sample query:
SELECT sql_no_cache media_id, hex, map_hex, distance,
avg(percentage) as percentage,
SUM((IF(map_hex = '61615a',1,0)) + (IF(map_hex = '34362d',1,0)) + (IF(map_hex = 'dbd5dd',1,0))) as matchCount
FROM media_has_colors
WHERE map_hex = '61615a' or map_hex = '34362d' or map_hex = 'dbd5dd'
GROUP BY media_id
ORDER BY matchCount DESC, distance, percentage DESC
LIMIT 100;
The First problem I see with schema 1 is that I am forced to use group by and sum. I'll admit I have not tested with a ton of records yet but it seems like it could get slow. On top of that I can't tell what map_hex values are matching (which is why I'm trying to get with matchCount.
Schema 2
CREATE TABLE `media_has_colors` (
`media_id` int(9) unsigned NOT NULL,
`color_1_hex` varchar(6) NOT NULL DEFAULT '',
`color_2_hex` varchar(6) NOT NULL DEFAULT '',
`color_3_hex` varchar(6) NOT NULL DEFAULT '',
`color_4_hex` varchar(6) NOT NULL DEFAULT '',
`color_5_hex` varchar(6) NOT NULL DEFAULT '',
`color_1_map_hex` varchar(6) NOT NULL DEFAULT '',
`color_2_map_hex` varchar(6) NOT NULL DEFAULT '',
`color_3_map_hex` varchar(6) NOT NULL DEFAULT '',
`color_4_map_hex` varchar(6) NOT NULL DEFAULT '',
`color_5_map_hex` varchar(6) NOT NULL DEFAULT '',
`color_1_percent` double unsigned NOT NULL DEFAULT '0',
`color_2_percent` double unsigned NOT NULL DEFAULT '0',
`color_3_percent` double unsigned NOT NULL DEFAULT '0',
`color_4_percent` double unsigned NOT NULL DEFAULT '0',
`color_5_percent` double unsigned NOT NULL DEFAULT '0',
`color_1_distance` double unsigned NOT NULL DEFAULT '0',
`color_2_distance` double unsigned NOT NULL DEFAULT '0',
`color_3_distance` double unsigned NOT NULL DEFAULT '0',
`color_4_distance` double unsigned NOT NULL DEFAULT '0',
`color_5_distance` double unsigned NOT NULL DEFAULT '0',
`sequence` int(11) unsigned NOT NULL,
PRIMARY KEY (`media_id`),
KEY `index_on_timestamp` (`sequence`),
KEY `index_on_map_hex` (`color_1_map_hex`,`color_2_map_hex`,`color_3_map_hex`,`color_4_map_hex`,`color_5_map_hex`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
This second schema is not as simple but it does avoid using group by only allowing 1 row per media. However, it seems to have the same problem of figuring out what map_hex values are matching. Here is a sample query:
SELECT sql_no_cache media_id,
(IF(color_1_percent = '61615a',color_1_percent,1)) *
(IF(color_2_percent = '34362d',color_2_percent,1)) *
(IF(color_3_percent = 'dbd5dd',color_3_percent,1)) as percentage,
(IF(color_1_distance = '61615a',color_1_distance,1)) +
(IF(color_2_distance = '34362d',color_2_distance,1)) +
(IF(color_3_distance = 'dbd5dd',color_3_distance,1)) as distance,
color_1_map_hex, color_2_map_hex, color_3_map_hex, color_4_map_hex, color_5_map_hex,
(IF(color_1_map_hex = '61615a',1,1)) +
(IF(color_2_map_hex = '34362d',1,1)) +
(IF(color_3_map_hex = 'dbd5dd',1,1)) as matchCount
FROM media_has_colors
WHERE color_1_map_hex IN ('61615a','34362d','dbd5dd') OR
color_2_map_hex IN ('61615a','34362d','dbd5dd') OR
color_3_map_hex IN ('61615a','34362d','dbd5dd')
ORDER BY matchCount DESC, distance, percentage DESC
LIMIT 100;
You can see that there is a problem with calculating percentage and distance because the actual map_hex value may not appear in those specific columns.
Update:
I don't need to know specifically what colors matched in the query but I do need to sort by which has the highest matches.
So my question is, How can the schema or queries be fixed? If not, is there a better solution?