An image processing device usable with an image forming apparatus to determine a clustered-dot screen to form an original image using a model of the image forming apparatus, the image processing device comprising:
- a cluster center unit to determine a plurality of cluster centers for a screen;
- and
- a screen design unit to select a sub-dot growth sequence about the plurality of cluster centers, to measure a difference between a visual perception of the original image and a print out of the original image that is output according to the selected sub-dot growth sequence, and to adjust the selected sub-dot growth sequence one or more times to minimize the difference between the visual perception and the print out to determine an optimal sub-dot growth sequence for the image forming apparatus model,
- wherein the selected sub-dot growth sequence is based on an argument of the minimum function that returns an input that minimizes an output of a cost function,
- wherein the screen design unit adjusts the selected sub-dot growth sequence using the following equation:
- arg min(e[*],g[*],x0[*],y0[*]) for all g[*],
- where e[*] represents the difference between the visual perception and the print out, g[*] represents the selected sub-dot growth sequence used to print the print out, x0[*] and y0[*] represent x and y components of the plurality of cluster centers, and arg min(*) is a function that returns an input value that makes an output value of a function a minimum.