Masters Thesis, Boise State University, December 2007
The effect of binarization via global thresholding on additive Gaussian noise in high contrast images is explored. A measure of noise in bilevel images called noise spread is developed with the use of a degradation model that applies to many image degradations included in desktop scanning. When high contrast images are binarized, noise is concentrated on the edges of objects in the image. Noise spread is the breadth of the domain in which pixels are affected by noise after binarization. It depends on both the noise level and the gradients of the image prior to thresholding.
There is a strong linear relationship between noise spread and the expected Hamming distance between an image with noise added and the same image without noise added. It is also known that if two images of an object are synthetically generated with independent random phases and zero noise, there is a small Hamming distance between them. Experiments on circles and on a ‘5’ were run to determine the combined effect of random independent phase and noise spread on the expected Hamming distance. The two factors are not additive and that the phase effects become less significant when the noise spread increases. The degree to which this is true depends on the shape of the object being scanned.
In addition to experiments on Hamming distance, experiments were run to determine the geometric precision of images with noise. This includes experiments relating noise spread on the localizability of straight edges at several different orientations. The localizability of and edge is defined by the ability to determine the orientation and position of an edge segment. The quality of edge measurements is quantified by the angle between the measured edge and the true edge and by the distance between the measured edge segment and the midpoint of the true edge segment. Surprisingly the distance measurements for edges at certain orientations actually are precise when the noise spread increases, but this variation is offset by less precision in the measurements of edge orientation. For most edge orientations the precision of both distance measurements and orientation measurements decreases when noise spread increases. Experiments relating noise spread to the localizability of circles were also conducted. These experiments reveal that the positional error in circle measurements has a Rayleigh distribution, while the radius measurements have a normal distribution, and that circle localizability decreases as noise spread increases.
Noise Spread provides a strong theoretical foundation for future research. Since random effects play a critical role in optical character recognition (OCR) and in pattern recognition generally, it is important to understand and quantify them. Future research will focus on relating noise spread to human preference, on finding novel techniques for measuring noise spread directly from binary images, and on developing filters and other techniques which will make OCR systems less susceptible to noise. Noise spread may also have unforeseen applications in problems other than document research.