Questions in a Character Degradation Model Paper

Question

I have questions in the ‘Noise region definition’ and ‘Noise generation process’ of the paper “A character degradation model for grayscale ancient document images”.

1. In Noise region definition, g controls the flatness of the regions. What does it exactly mean? How can we say that a noise region is flatter compared to another noise region?

Below is the illustration of the ellipse noise region within the document image. The green ellipse shape is defined to be the noise region.

2. According to paragraph below, the average value bj of its 8-neighbours (in the initial grayscale image) is used for calculating values of all pixels in the line CiBj.

Does the average value of bj calculated by averaging the greyscale value of the adjacent pixels in north, northeast, east, south east, south, south west, west and north west?

3. Does the formula for getting Pk is below.

   

Please refer to the paragraph below:

I just want to assess , if my comprehension in reading the article is right. Thanks.

Answer 1

1. All g is doing is saying whether the area is closer to a circle (less flat) or a line (completely flat ellipse).

2. Yes.

3. No. $N(\mu, \sigma^2)$ is a distribution. You can say $$P_k \tilde{} N(\mu, \sigma^2)$$ read as $P_k$ is distributed normal, with mean $\mu$ and variance $\sigma^2$.

To find a value for $P_k$ you need to generate a random number with the mean given by equation (1) in the last screenshot:

$$ \mu = \bar{c}_i + (\bar{b}_j - \bar{c}_i) \left( \frac{d_{ik}}{d_{ij}} \right) $$

In matlab, this would be something like normrnd(mu, sigma), though what sigma value to choose is not clear from your extractions from the paper.