Character representation and recognition using quad tree-based fractal encoding scheme

In this paper, we proposed a new method for isolated handwritten Farsi/Arabic numerals recognition using quad tree-based fractal representation and iterated function system. Fractal codes represent affine transformations which when iteratively applied to the range-domain pairs in an arbitrary initial image, the result is close to the given image. Each fractal code consists of six parameters such as the corresponding domain coordinates for each range block, brightness offset and an affine transformation. Based on fixed point theorem in iterated function system, we introduced fractal transformation classifier for optical character recognition. We also used Euclidean distance between fractal codes of a query image and fractal codes of all images in the database as a measure of distance for classification. Since fractal codes have different lengths, we applied PCA algorithm to normalize their lengths. There are ten digits in Farsi/Arabic language and since two of them are not used in Iran postal codes, therefore 8 classes are needed for digits. By using fractal codes with nearest neighbor classifier and fractal transformation, the recognition rate of 92.6% is obtained on our numeral database which contains 480 samples per digit and was gathered from more than 200 people with different ages and different educational background.