Edge detection on pool table

Question

I am currently working on an algorithm to detect the playing area of a pool table. For this purpose, I captured an image, transformed it to grayscale, and used a Sobel operator on it. Now I want to detect the playing area as a box with 4 corners located in the 4 corners of the table.

Detecting the edges of the table is quite straightforward, however, it turns out that detecting the 4 corners is not so easy, as there are pockets in the pool table. Now I just want to fit a line to each of the side edges, and from those lines, I can compute the intersects, which are the corners for my table.

I am stuck here, because I could not yet come up with a good solution to find these lines in my image. I can see it very easily when I used the Sobel operator. But what would be a good way of detecting it and computing the position of the corners?

EDIT: I added some sample Images

Basic Image:

Grayscale Image

Sobel Filter (horizontal only)

Answer 1

If color segmentation (as suggested by @Dima) works, get the outline of the blob using contour following. Then simplify the outline to a quadrilateral (or a polygon of few sides) by the Douglas-Peucker algorithm. You should find the four table edges this way.

For more accuracy, you can refine the edge location by local search of transitions across it and perform line fitting. Then intersect the lines to get the corners.

Answer 2

For a general solution, there will be many sources of noise: problems with cloth around the rails, wood texture (or no texture) on the rails, varying lighting, shadows, stains on the cloth, chalk on the rails, and so on.

When color and lighting aren't dependable, and when you want to find the edges of geometric objects, then it's best to think in terms of edge pixels rather than gray/color pixels.

A while back I was thinking of making a phone-based app to save ball positions for later review, including online, so I've though a bit about this problem. Although I can provide some guidance for your current question, it occurs to me you'll run into new problems each step of the way, so I'll try to provide a more complete answer.

1. Convert the image to grayscale. If we can't get an algorithm to work in grayscale, we'll inevitably run into problems with color. (See below)
2. [TBD] Do some preprocessing to reduce noise.
3. Find edge points using Sobel or (if you must) Canny.
4. Run Hough lines detection, but with a few caveats and parameterizations as described below.
5. Find the lines described a keystone-shaped quadrilateral. (This will likely be the inner quadrilateral of two: one inside the rail on the bed, and the other slightly larger quadrilateral at the cloth/wood rail edge at top.)
6. (Optional) Use the side pockets to help determine the orientation of the quadrilateral.
7. Use an affine transform to map the perspective-distorted table bed to a rectangle of [thankfully] known relative dimensions. We know the bed sizes in advance, so you can remap the distorted rectangle to a proper rectangle. (We'll ignore some optical effects for now.)
8. Remap the color image to the perspective-corrected rectangle. You'll probably need to tweak the positions of some balls.

General notes:

• Filtering by color in the general sense can be difficult. It's tempting to think of the cloth as being simply green, blue, or red (or some other color), but when you look at the actual RGB values and try to separate colors you'll begin to appreciate what a nightmare working in color can be.
• Optical distortion might throw off some edges.
• The far short rail may be difficult to detect, BUT you do this: find the inside lines for the two long rails, then search vertically between the two rails for the first strong horizontal-ish edge at the far side of the image. That'll be the far short rail.
• Although you probably want to use your phone camera for convenience, using a Kinect camera or similar (preferably smaller) device would make the problem easier. Not only would you have both color data and 3D data, but you would eliminate some problems with lighting since the depth data wouldn't depend on visible lighting.
• For your app, consider limiting the search region for rail edges to a perspective-distorted rectangle. The user might be able to adjust the search region. This could greatly simplify the processing, and could help you work around problems if the table isn't lit well (as can be the case).

Answer 3

The following answer assumes you have already found the positions of the lines in the image. This however can be done "easily" by directly looking at the pixels and seeing if they are in a "line". Usually it is easier to detect this if the image has been deskewed first as well, i.e. Rotated so the rectangle (pool table) is more like this: [] than like /=/. Then it is just a case of scanning the pixels and if there are ones of similar colour alongside it assuming a line is between them.

The code works by looping over the lines found in the image. Whenever the end points of each line falls within a tolerance on within the x and y coordinates it is marked as a corner. Once the corners are found I take the average value between them to find where the corner lies. For example:

A horizontal line ending at 10, 10 and a vertical line starting at 12, 12 will be found to be a corner if there is a tolerance of 2 or more. The corner found will be at: 11, 11

NOTE: This is just to find Top Left corners but can easily be adapted to find all of them. The reason it has been done like this is because in the application where I use it, it is faster to sort each array first into an order where relevant values will be found first, see: Why is processing a sorted array faster than an unsorted array?.

Also note that my code finds the first corner for each line which might not be applicable for you, this is mainly for performance reasons. However the code can easily be adapted to find all the corners with all the lines then either select the "more likely" corner or average through them all.

Also note my answer is written in C#.

private IEnumerable<Point> FindTopLeftCorners(IEnumerable<Line> horizontalLines, IEnumerable<Line> verticalLines)
{
    List<Point> TopLeftCorners = new List<Point>();

    Line[] laHorizontalLines = horizontalLines.OrderBy(l => l.StartPoint.X).ThenBy(l => l.StartPoint.Y).ToArray();
    Line[] laVerticalLines = verticalLines.OrderBy(l => l.StartPoint.X).ThenBy(l => l.StartPoint.Y).ToArray();

    foreach (Line verticalLine in laVerticalLines)
    {
        foreach (Line horizontalLine in laHorizontalLines)
        {
            if (verticalLine.StartPoint.X <= (horizontalLine.StartPoint.X + _nCornerTolerance) && verticalLine.StartPoint.X >= (horizontalLine.StartPoint.X - _nCornerTolerance))
            {
                if (horizontalLine.StartPoint.Y <= (verticalLine.StartPoint.Y + _nCornerTolerance) && horizontalLine.StartPoint.Y >= (verticalLine.StartPoint.Y - _nCornerTolerance))
                {
                    int nX = (verticalLine.StartPoint.X + horizontalLine.StartPoint.X) / 2;
                    int nY = (verticalLine.StartPoint.Y + horizontalLine.StartPoint.Y) / 2;

                    TopLeftCorners.Add(new Point(nX, nY));
                    break;
                }
            }
        }
    }

    return TopLeftCorners;
}

Where Line is the following class:

public class Line
{
    public Point StartPoint { get; private set; }

    public Point EndPoint { get; private set; }

    public Line(Point startPoint, Point endPoint)
    {
        this.StartPoint = startPoint;
        this.EndPoint = endPoint;
    }
}

And _nCornerTolerance is an int of a configurable amount.

Answer 4

A playing area of a pool table typically has a distinctive color, like green or blue. I would try a color-based segmentation approach first. The Color Thresholder app in MATLAB gives you an easy way to try different color spaces and thresholds.