Modeling the Histogram of the Halftone Image to Determine
the Area Fraction of Ink

Yat-Ming Wong

Appendix


Appendix A 
Sum of Two Gaussians Algorithm developed in MathCad

Appendix B 
Equivalent Straight Edge Algorithm developed in MathCad


Appendix A--Sum of Two Gaussians Model Developed in MathCad

Appendix B --The Summary Fit -- algorithms done in MathCad Software
First, define the edge that represents the bimodal image.
This makes the edge reflectance versus position, x, from 0 to 1.0, with points defined in equal intervals of x.  We want to define the edge in equal intervals in terms of r, and turn it on its side.
Next we take the derivative of the xx versus rr function.




The result is a histogram corresponding to the edge image.  Note the sharpness of the peaks.
Next we add noise (RMS granularity) to the image.
The noise is modeled as a gaussian function and then convolved with the histogram.
We end up with a phase shift.
We fix this by shifting the histogram.
The FFT and inverse FFT process lost one element from the h2 vector of data.  We artificially restore it so we can use the "linterp" function to match the data and the model.
Now read in a histogram.
And we normalizethe measured histogram to unity.
We normalize the model to unity and compare the model to the data.
Next we calculate the differece


Table of Contents|Thesis