Halftoning method using space filling curves

Claim 1

A printing system, including a processor preparing documents for printing, said documents including a set of image signals describing optical density with c density levels, while a destination printer is capable of rendering density with d density levels where c and d are integers greater than zero, comprising: a printer, adapted to print the document; a source of image signals each image signal representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y; a halftone processor operatively connected to said source of image signals and reducing the number of levels c representing optical density to a number of levels d representing optical density including a first memory storing an ordered set of threshold values T, indexable by a length along a predetermined space filling curve; a second memory storing a set of unexpanded space filling curve lengths mod M, where x and y are real numbers, indexed by pixel and scan line position; a third memory storing a set of expanded space filling curve lengths Mod M, indexed by pixel and scan line position; a fourth memory storing a set of direction indicators; direction transformation circuit determining modified x, y coordinates indicated by a direction indicator and corresponding to a change in orientation of a space filling curve, producing a pixel and scan line position indicator to the third memory; a calculating circuit determining a threshold value T to be applied to a selected image signal x,y by adding the length mod M of the unexpanded portion of curve leading to the section containing the pixel to the indexed, direction-transformed expanded space filling curve length mod M to obtain a length L, number, for the selected image signal x,y, and using said value to index said first memory to retrieve T(x,y), where T(x,y) is the threshold value for a particular x, y position; a comparator, comparing the image signal at position x,y with threshold value T(x,y) to determine an output signal that is one of d levels representative of the original image signal at position x,y; an image processor directing signals processed at said halftone processor to said printer to print said halftoned image.

Claim 11

A method of halftoning image signals representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y, to reduce said signals to represent density with one of d levels, where c and d are integers greater than zero, and x and y are real numbers and including: receiving image signals, each image signal representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y; storing in a first memory an ordered set of threshold values T, where T is a real number, indexable by a length along a predetermined space filling curve; storing in a second memory a set of unexpanded space filling curve lengths mod M, where M is a real number, indexed by pixel position and scan line position; storing in a third memory a set of expanded space filling curve lengths Mod M, indexed by pixel position and scan line position; storing in a fourth memory a set of direction indicators indexed by pixel position and scan line position; determining modified pixel position and scan line position indicated by a direction indicator and corresponding to a change in orientation of a space filling curve, producing a pixel and scan line position indicator to the third memory; determining a threshold value T to be applied to a selected image signal at position x,y by adding the length mod M of the unexpanded portion of curve leading to the section containing the pixel to the indexed, direction-transformed expanded space filling curve length mod M to obtain a length L where L is a real number, for the selected image signal x,y, and using said value to index said first memory to retrieve T(x,y), where T(x,y) is the threshold value for a particular x,y position indication; comparing the image signal x,y with threshold value T(x,y) to determine an output signal that is one of d levels representative of the original image signal x,y; directing signals processed to said printer to print said halftoned image.

Claim 12

A method of halftoning image signals representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y, to reduce said signals to represent density with one of d levels, where c and d are integers greater than zero, and x and y are real numbers and including: receiving image signals, each image signal representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y; storing in a first memory an ordered set of threshold values T, where T is a real number, indexable by a length along a predetermined space filling curve; storing in a second memory a set of unexpanded space filling curve lengths mod M, where M is a real number, indexed by pixel position and scan line position; storing in a third memory a set of expanded space filling curve lengths Mod M, indexed by pixel position and scan line position; storing in a fourth memory a set of direction indicators indexed by pixel position and scan line position; determining modified pixel position and scan line position indicated by a direction indicator and corresponding to a change in orientation of a space filling curve, producing a pixel and scan line position indicator to the third memory; determining a threshold value T to be applied to a selected image signal at position x,y by adding the length mod M of the unexpanded portion of curve leading to the section containing the pixel to the indexed, direction-transformed expanded space filling curve length mod M to obtain a length L where L is a real number, for the selected image signal x,y, and using said value to index said first memory to retrieve T(x,y), where T(x,y) is the threshold value for a particular x,y position indication; comparing the image signal x,y with threshold value T(x,y) to determine an output signal that is one of d levels representative of the original image signal x,y; directing signals processed to said printer to print said halftoned image.

Claim 13

A method of preparing documents for printing, said documents including a set of image signals describing optical density with c density levels, while a destination printer is capable of rendering density with d density levels where c and d are integers greater than zero, comprising: receiving image signals representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y, where x and y are real numbers; reducing the number of levels c representing optical density to a number of levels d representing optical density by: for each image signal, calculating a first length along an unexpanded space filling curve as a function of pixel position x and scan line position y; for each image signal, calculating a second length along an expanded space filling curve as a function of pixel position x and scan line position y; adding said calculated first and second length together, to derive a curve length value; using said curve length value mod M, where M is a real number as an index to a threshold memory, to obtain a prestored threshold value T(x,y) where T is a real number and T(x,y) is the threshold value for a particular x,y position; comparing an image signal at x, y, with T(x,y) to determine an output value that is one of d levels.

Claim 14

A method of preparing documents for printing, said documents including a set of image signals describing optical density with c density levels, while a destination printer is capable of rendering density with d density levels where c and d are integers greater than zero, comprising: receiving image signals representing optical density with one of c levels for a discrete area of the document indexed by pixel position x and scan line position y, where x and y are real numbers; reducing the number of levels c representing optical density to a number of levels d representing optical density by: for each image signal, calculating a first length along an unexpanded space filling curve as a function of pixel position x and scan line position y; for each image signal, calculating a second length along an expanded space filling curve as a function of pixel position x and scan line position y; adding said calculated first and second length together, to derive a curve length value; using said curve length value mod M, where M is a real number as an index to a threshold memory, to obtain a prestored threshold value T(x,y) where T is a real number and T(x,y) is the threshold value for a particular x,y position; comparing an image signal at x, y, with T(x,y) to determine an output value that is one of d levels.