matching jigsaw puzzle pieces

Question

I have nothing useful to do and was playing with jigsaw puzzle like this:

alt text http://manual.gimp.org/nl/images/filters/examples/render-taj-jigsaw.jpg

and I

Answer 1

Data acquisition

(This is known as Chroma Key, Blue Screen or Background Color method)

1. Find a well-lit room, with the least lighting variation across the room.
2. Find a color (hue) that is rarely used in the entire puzzle / picture.
3. Get a color paper that has that exactly same color.
4. Place as many puzzle pieces on the color paper as it'll fit.
   • You can categorize the puzzles into batches and use it as a computer hint later on.
   • Make sure the pieces do not overlap or touch each other.
   • Do not worry about orientation yet.
5. Take picture and download to computer.
   • Color calibration may be needed because the Chroma Key background may have upset the built-in color balance of the digital camera.

Acquisition data processing

1. Get some computer vision software
   • OpenCV, MATLAB, C++, Java, Python Imaging Library, etc.
2. Perform connected-component on the chroma key color on the image.
   • Ask for the contours of the holes of the connected component, which are the puzzle pieces.
3. Fix errors in the detected list.
4. Choose the indexing vocabulary (cf. Ira Baxter's post) and measure the pieces.
   • If the pieces are rectangular, find the corners first.
   • If the pieces are silghtly-off quadrilateral, the side lengths (measured corner to corner) is also a valuable signature.
   • Search for "Shape Context" on SO or Google or here.
   • Finally, get the color histogram of the piece, so that you can query pieces by color later.
5. To make them searchable, put them in a database, so that you can query pieces with any combinations of indexing vocabulary.

Answer 2

A step back to the problem itself. The problem of building a puzzle can be easy (P) or hard (NP), depending of whether the pieces fit only one neighbour, or many. If there is only one fit for each edge, then you just find, for each piece/side its neighbour and you're done (O(#pieces*#sides)). If some pieces allow multiple fits into different neighbours, then, in order to complete the whole puzzle, you may need backtracking (because you made a wrong choice and you get stuck).

However, the first problem to solve is how to represent pieces. If you want to represent arbitrary shapes, then you can probably use transparency or masks to represent which areas of a tile are actually part of the piece. If you use square shapes then the problem may be easier. In the latter case, you can consider the last row of pixels on each side of the square and match it with the most similar row of pixels that you find across all other pieces.

You can use the second approach to actually help you solve a real puzzle, despite the fact that you use square tiles. Real puzzles are normally built upon a NxM grid of pieces. When scanning the image from the box, you split it into the same NxM grid of square tiles, and get the system to solve that. The problem is then to visually map the actual squiggly piece that you hold in your hand with a tile inside the system (when they are small and uniformly coloured). But you get the same problem if you represent arbitrary shapes internally.