Question

I think there are some algorithms that evaluate difference between drawn symbol and expected one, or something like that. Any help will be appreciated :))

Answer 1

You can implement a simple Neural Network to recognize handwritten digits. The simplest type to implement is a feed-forward network trained via backpropagation (it can be trained stochastically or in batch-mode). There are a few improvements that you can make to the backpropagation algorithm that will help your neural network learn faster (momentum, Silva and Almeida’s algorithm, simulated annealing).

As far as looking at the difference between a real symbol and an expected image, one algorithm that I’ve seen used is the k-nearest-neighbor algorithm. Here is a paper that describes using the k-nearest-neighbor algorithm for character recognition (edit: I had the wrong link earlier. The link I’ve provided requires you to pay for the paper; I’m trying to find a free version of the paper).

If you were using a neural network to recognize your characters, the steps involved would be:

1. Design your neural network with an appropriate training algorithm. I suggest starting with the simplest (stochastic backpropagation) and then improving the algorithm as desired, while you train your network.
2. Get a good sample of training data. For my neural network, which recognizes handwritten digits, I used the MNIST database.
3. Convert the training data into an input vector for your neural network. For the MNIST data, you will need to binarize the images. I used a threshold value of 128. I started with Otsu’s method, but that didn’t give me the results I wanted.
4. Create your network. Since the images from MNIST come in an array of 28×28, you have an input vector with 784 components and 1 bias (so 785 inputs), to your neural network. I used one hidden layer with the number of nodes set as per the guidelines outlined here (along with a bias). Your output vector will have 10 components (one for each digit).
5. Randomly present training data (so randomly ordered digits, with random input image for each digit) to your network and train it until it reaches a desired error-level.
6. Run test data (MNIST data comes with this as well) against your neural network to verify that it recognizes digits correctly.

You can check out an example here (shameless plug) that tries to recognize handwritten digits. I trained the network using data from MNIST.

Expect to spend some time getting yourself up to speed on neural network concepts, if you decide to go this route. It took me at least 3-4 days of reading and writing code before I actually understood the concept. A good resource is heatonresearch.com. I recommend starting with trying to implement neural networks to simulate the AND, OR, and XOR boolean operations (using a threshold activation function). This should give you an idea of the basic concepts. When it actually comes down to training your network, you can try to train a neural network that recognizes the XOR boolean operator; it’s a good place to start for an introduction to learning algorithms.

When it comes to building the neural network, you can use existing frameworks like Encog, but I found it to be far more satisfactory to build the network myself (you learn more that way I think). If you want to look at some source, you can check out a project that I have on github (shameless plug) that has some basic classes in Java that help you build and train simple neural-networks.

Good luck!

EDIT

I’ve found a few sources that use k-nearest-neighbors for digit and/or character recognition:

• Bangla Basic Character Recognition Using Digital Curvelet Transform (The curvelet coefficients of an
  original image as well as its morphologically altered versions are used to train separate k–
  nearest neighbor classifiers. The output values of these classifiers are fused using a simple
  majority voting scheme to arrive at a final decision.)
• The Homepage of Nearest Neighbors and Similarity Search
• Fast and Accurate Handwritten Character Recognition using Approximate Nearest Neighbors Search on Large Databases
• Nearest Neighbor Retrieval and Classification

For resources on Neural Networks, I found the following links to be useful:

• CS-449: Neural Networks
• Artificial Neural Networks: A neural network tutorial
• An introduction to neural networks
• Neural Networks with Java
• Introduction to backpropagation Neural Networks
• Momentum and Learning Rate Adaptation (this page goes over a few enhancements to the standard backpropagation algorithm that can result in faster learning)