Some Progress

I wrote some code that computes Hu moments for labeled data and then gives a label to a new image based upon this data.  Hu moments are rotation and scale invariant features of an image.  Currently I am manually thresholding input images since I haven't written code to do it automatically.

Hu moments are calculated by first finding the Central moments of an image, which in turn are calculated by subtracting the centroid and then finding the raw image moments.  Central image moments are made scale invariant by scaling them by a scaled 0th moment, which corresponds to the area of an object in a binary image.  Images are made translation invariant by subtracting the centroid.

We use seven rotation invariant moments (so called Hu moments) which are based upon the scale invariant moments discussed earlier.  Each one is some (usually nonlinear) combination of the scale invariant moments.

The following are some of the images I've been playing with.  The original is from an actual target and then the rotated versions are synthetically created.

The moments for the two previous figures are:

R           R_271
0.4463 0.4441
0.0553 0.0571
0.0041 0.0038
0.0140 0.0129
0.0001 0.0001
0.0031 0.0029
0.0001 -0.0001

As you can see, even though the images themselves look very different, the features extracted are very similar.

The values for the following rotations of E (0, 22, 90, 132 degrees) are:

1.3308 1.3185 1.3308 1.3336
0.6832 0.6780 0.6832 0.6911
0.1851 0.1730 0.1851 0.1905
0.1071 0.1059 0.1071 0.1228
0.0057 0.0057 0.0057 0.0090
-0.0003 0.0027 -0.0003 0.0153
-0.0017 -0.0109 0.0017 -0.0160

Once again you can see that the values are all very similar.

Once the algorithm has been given labeled data, we simply feed it a new image, calculate its Hu moments, and perform a nearest neighbor classification based upon Mahalanobis distance.

This distance metric differs from euclidean distance in that it takes into account correlations of the data sets and is scale invariant.

The code I have to do this is acting a little strangely right now so the results aren't very reliable.  However, from manual inspection we can see that the Hu moments give a surprisingly good signature for a letter, even under rotation.  I will have to include more letters and different versions of each letter to see whether it will be suitable enough for our purposes or whether we will require something more complex.