Abstract:
The teachings provided herein disclose a method for producing digital image objects with enhanced halftone edges. The method operates by selecting a target pixel location within the digital image; observing a set of pixels within a pixel observation window superimposed on the digital image relative to the target pixel location; generating edge-state codes for a plurality of pairs of neighboring vectors of pixels within the pixel observation window; generating edge-identification codes from the plurality of edge-state codes using at least one look-up table; and, utilizing the edge-identification code to select and apply to the digital image at the target pixel either a first halftone screen having a first fundamental frequency and a first angle or a second halftone screen having a second fundamental frequency and a second angle, wherein the second frequency and second angle are harmonically matched to the first frequency and first angle. The method solves the problem of ragged edges on halftone tints as an automated, operation, with a computing architecture that is readily adapted to a wide variety of tinted edge conditions, and which can be readily adapted to real-time applications.

Description:
CROSS-REFERENCE TO COPENDING APPLICATIONS  
       [0001]     Attention is directed to copending Applications co-filed at the same time with the present Application: U.S. Application No. ______, Attorney Docket No. 20050631-US-NP, entitled “EDGE PIXEL IDENTIFICATION”; U.S. Application No. ______, Attorney Docket No. 20051786-US-NP, entitled “ANTI-ALIASED TAGGING USING LOOK-UP TABLE EDGE PIXEL IDENTIFICATION”; and U.S. Application No. ______, Attorney Docket No. 20051787-US-NP, entitled “CORNER SHARPENING USING LOOK-UP TABLE EDGE PIXEL IDENTIFICATION”. The disclosure found in each of these copending applications is hereby incorporated by reference in its entirety.  
       CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0002]     Cross reference is made to the following applications, the disclosures of each of which are totally incorporated by reference herein: U.S. application Ser. No. 10/973,725, entitled “TINTED EDGE ENHANCEMENT USING HARMONIC HALFTONES FOR THE BOUNDARY PIXELS”, to C. Purdum, R. Loce, B. Xu, D. Lieberman, M. Gwaltney, J. McEvain, C. Hains, and U.S. patent application Ser. No. 10/909,627, entitled “METHOD FOR MINIMIZING BOUNDARY DEFECTS USING HALFTONE CLASSES WITH MATCHED HARMONICS” to Inventors Robert P. Loce, Charles M. Hains, Beilei Xu, Connie F. Purdum, and Xiaoxue (Shirley) Cheng. The appropriate components and processes of the above co-pending application may be selected for the invention of the present application in embodiments thereof.  
       BACKGROUND AND SUMMARY  
       [0003]     This disclosure relates generally to digital processing of image data. This disclosure also relates generally to halftoning methods, and more particularly to an edge identification and edge halftoning method for producing halftone screens with improved edge appearance. This disclosure relates particularly to tinted edges and their enhancement.  
         [0004]     Printers that utilize halftones can suffer from an edge defect on halftoned tints, which includes tinted text. The periodicity of the halftone can produce a significant raggedness at the edges of tints. In some marking processes small fragmented edge dots do not print, or print undersized, thereby leaving a gap that appears very ragged. This defect is a significant dissatisfier for many consumers of printed tints. The problem is illustrated in  FIGS. 17 and 18 .  
         [0005]      FIG. 17A  is a photomicrograph of a print from an offset printer depicting a printed edge.  FIG. 17B  is a schematical blow-up of the circled area in  FIG. 17A  and depicts in greater clarity the pixels of  FIG. 17A . As can be seen by  FIGS. 17A and 17B  the edge rendering as provided by an offset printer achieves a very clean cut edge.  FIG. 18A  is a photomicrograph of a print from an electro-photographic digital printer.  FIG. 18B  is a blow-up of the circled area in  FIG. 18A . Here the rendered edge is not only less clean but halftone dots that are split by the edge may print proportionally too small or too large, with respect to an un-split dot, depending upon the physical conditions of the marking process, thus effecting a ragged appearance.  
         [0006]     An edge within an image is a sharp change in local intensity or lightness. In other words, edges are features within an image that possess strong intensity contrast. Edges occur between distinct objects in a scene, or within textures and structure within an object. For instance, typographic characters on a white page background produce distinct edges. Edge pixels in a digital image are those pixels that occur at and about an edge in the image.  
         [0007]     Two key properties of an edge are strength and orientation. Edge strength is a measure of the contrast of an edge. A black typographic character on a white background produces stronger edges than a gray character on a white background. Edge orientation can be described by a variety of measures, such as angle quantified in degrees or by classes such as vertical, horizontal, and diagonal.  
         [0008]     Other attributes of edges are also useful to image analysis and image processing. For instance, classification of combined edges, such as corners, has been used in object recognition and in image enhancement applications. Edge thickness is a measure that provides information on the breadth of a local contrast change and can indicate a degree of blur in an image, see for example: U.S. Pat. No. 6,763,141, entitled “ESTIMATION OF LOCAL DEFOCUS DISTANCE AND GEOMETRIC DISTORTION BASED ON SCANNED IMAGE FEATURES,” to inventors B. Xu, R. Loce, which is hereby incorporated in its entirety for its teachings. Inner edges and outer edges refer to regions just inside of or just outside of a given object, respectively, and have been used in applications such as character stroke thinning and thickening. The presence or absence of an edge is an edge-related property that has been used in applications such as image classification and recognition. Distance from an edge is also an edge-related property that has been used in image enhancement applications.  
         [0009]     Edge detection in digital image processing typically employs a collection of methods used to identify or modify edge pixels or indicate properties of edges and edge pixels within an image. Edge detection methods are sometimes referred to simply as edge detectors. There are numerous applications of edge detectors in digital image processing for electronic printing. For example, identification of corner pixels has been used to sharpen corners within an image, see: U.S. Pat. No. 6,775,410, entitled “IMAGE PROCESSING METHOD FOR SHARPENING CORNERS OF TEXT AND LINE ART,” to inventors R. Loce, X. Zhu, C. Cuciurean-Zapan. Identification of inner and outer border pixels has been used to control the apparent darkness of character strokes, see: U.S. Pat. No. 6,606,420, entitled “METHOD AND APPARATUS FOR DIGITAL IMAGE DARKNESS CONTROL IN SATURATED IMAGE STRUCTURES”, to Loce et al; and U.S. Pat. No., 6,181,438, entitled “METHOD AND APPARATUS FOR DIGITAL IMAGE DARKNESS CONTROL USING QUANTIZED FRACTIONAL PIXELS,” to Bracco et al. Also identification of anti-aliased pixels has been used for preferred rendering of those same pixels, see: U.S. Pat. No. 6,243,499, entitled “TAGGING OF ANTIALIASED IMAGES,” to Loce et al.; U.S. Pat. No. 6,144,461, entitled “METHOD FOR GENERATING RENDERING TAGS TO FACILITATE THE PRINTING OF ANTIALIASED IMAGES,” to Crean, et al.; and U.S. Pat. No. 6,167,166, entitled “METHOD TO ENABLE THE RECOGNITION AND RENDERING OF ANTIALIASED IMAGES,” to Loce et al. All of the above cited are hereby incorporated by reference in their entirety for their teachings.  
         [0010]     Edge detectors typically operate using a convolution mask and are based on differential operations. Differentials for edge/line detection are used to define color or brightness changes of pixels and their change directions. If there is an abrupt change of brightness within a short interval within an image, it means that within that interval there is high probability that an edge exists. One example of a convolution-based edge detector is the Roberts edge detector, which employs the square root of the magnitude squared of the convolution with the Robert&#39;s row and column edge detectors. The Prewitt edge detector employs the Prewitt compass gradient filters and returns the result for the largest filter response. The Sobel edge detector operates using convolutions with row and column edge gradient masks. The Marr-Hildreth edge detector performs two convolutions with a Laplacian of Gaussians and then detects zero crossings. The Kirsch edge detector performs convolution with eight masks that calculate gradient.  
         [0011]     As indicated above, common edge detection methods employ a convolution-type computing architecture, usually with fixed coefficients. In the field of image processing, and in particular, for image processing in anticipation of electronic printing, the edge detection needs are numerous and varied. Further, image processing for electronic printing often requires that any processing method operate “real-time”, within a small number of fixed clock cycles, thereby excluding more complicated methods as too computationally intensive. What is needed is a technique which will solve the problem of ragged edges on halftone tints as an automated, non-manual processing operation, with a computing architecture that is more readily adapted to a wide variety of tinted edge conditions than are the common convolution-based methods, and which can be readily adapted to real-time applications.  
         [0012]     Disclosed in embodiments herein is an image processing method for producing digital image objects with enhanced halftone edges. The method includes the steps of selecting a target pixel location within the digital image; observing a set of pixels within a pixel observation window superimposed on the digital image relative to the target pixel location; generating edge-state codes for a plurality of pairs of neighboring vectors of pixels within the pixel observation window; generating edge-identification codes from the plurality of edge-state codes using at least one look-up table; and, utilizing the edge-identification code to select and apply to the digital image at the target pixel either a first halftone screen having a first fundamental frequency and a first angle or a second halftone screen having a second fundamental frequency and a second angle, wherein the second frequency and second angle are harmonically matched to the first frequency and first angle.  
         [0013]     Further disclosed in embodiments herein is an image processing method for producing a digital image with enhanced halftone edges. The method comprises the steps of observing a set of pixels within a pixel observation window superimposed on the digital image relative to a target pixel location; generating edge-state codes for a plurality of pairs of neighboring vectors of pixels within the pixel observation window; generating edge-identification codes from the plurality of edge-state codes using at least one look-up table; wherein the edge-identification codes indicate proximity to a tinted edge; and, utilizing the edge-identification code to select and apply to the digital image at the target pixel either a first halftone screen having a first fundamental frequency and a first angle or a second halftone screen having a second fundamental frequency and a second angle, wherein the second frequency and second angle are harmonically matched to the first frequency and first angle.  
         [0014]     Further disclosed in embodiments herein is an image processing method for producing a digital image with enhanced halftone edges. The method comprises observing a set of pixels within a pixel observation window superimposed on the digital image relative to a target pixel location; generating edge-state codes for a plurality of pairs of neighboring vectors of pixels within the pixel observation window; generating edge-identification codes from the plurality of edge-state codes using at least one look-up table; wherein the edge-identification codes indicate proximity to a tinted edge; and, utilizing the edge-identification code to select and apply to the digital image at the target pixel either a first halftone screen having a first fundamental frequency and a first angle or a second halftone screen having a second fundamental frequency and a second angle, wherein the second frequency and second angle are harmonically matched to the first frequency and first angle. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]      FIG. 1  is a general representation of a suitable system-level embodiment for one or more aspects of the teachings presented herein.  
         [0016]      FIG. 2  depicts a flow chart of an image processing system containing an embodiment of the teachings presented herein.  
         [0017]      FIG. 3  schematically depicts an embodiment of an observation window.  
         [0018]      FIG. 4  is a generalized data flow representation of one embodiment of the teachings presented herein.  
         [0019]      FIG. 5  is a generalized data flow representation of another embodiment of the teachings presented herein.  
         [0020]      FIG. 6  is a schematic of an embodiment of the computing architecture of an embodiment of the teachings presented herein.  
         [0021]      FIG. 7  is an example input digital image possessing edges and an array of output edge identification codes according to the teachings presented herein.  
         [0022]      FIG. 8  is a schematic of harmonically related halftones applied to the image border as per the disclosure where the same angles and frequencies as the body are employed in the border but with a boosted signal.  
         [0023]      FIG. 9  is a schematic of harmonically related halftones applied to the image border as per the disclosure where the angles and frequencies employed in the border are rotated 45°, frequency increased by √2.  
         [0024]      FIG. 10  is a schematic of a low frequency dot screen and a high frequency dot screen that share harmonics.  
         [0025]      FIG. 11  illustrates a frequency vector diagram of the halftone screens used in  FIG. 10 .  
         [0026]      FIG. 12  is a schematic of harmonically related halftones applied to the image border as per the disclosure where the angles and frequencies employed in the border are frequency doubled.  
         [0027]      FIG. 13  illustrates a frequency vector diagram of the halftone screens used in  FIG. 12 .  
         [0028]      FIG. 14  is a schematic of harmonically related halftones applied to the image border as per the disclosure where the angles and frequencies employed in the border are a line screen aligned with one frequency vector.  
         [0029]      FIG. 15  illustrates a frequency vector diagram for halftone screens used in  FIG. 14 .  
         [0030]      FIG. 16  is a schematic of harmonically related halftones applied to the image border as per the disclosure where the angles and frequencies employed in the border are a double frequency line screen.  
         [0031]      FIG. 17A  is a photomicrograph of a print from an offset printer.  
         [0032]      FIG. 17B  is a blow-up of the circled area in  FIG. 17A .  
         [0033]      FIG. 18A  is a photomicrograph of a print from an electro-photographic digital printer.  
         [0034]      FIG. 18B  is a blow-up of the circled area in  FIG. 18A .  
     
    
     DETAILED DESCRIPTION  
       [0035]     It is to be understood that the disclosure of embodiments following describe a digital data technique which identifies and enhances the edges of halftone tints to avoid a objectionable ragged appearance. For a general understanding of the present disclosure, reference is made to the drawings. In the drawings, like reference numerals have been used throughout to designate identical elements. In describing the present disclosure, the following term(s) have been used in the description.  
         [0036]     The term “data” refers herein to physical signals that indicate or include information. An “image”, as a pattern of physical light or a collection of data representing said physical light, may include characters, words, and text as well as other features such as graphics. A “digital image” is by extension an image represented by a collection of digital data. An image may be divided into “segments”, each of which is itself an image. A segment of an image may be of any size up to and including the whole image. The term “image object” or “object” as used herein is believed to be considered in the art generally equivalent to the term “segment” and will be employed herein interchangeably.  
         [0037]     In a digital image composed of data representing physical light, each element of data may be called a “pixel”, which is common usage in the art and refers to a picture element. Each pixel has a location and value. Each pixel value is a bit in a “binary form” of an image, a gray scale value in a “gray scale form” of an image, or a set of color space coordinates in a “color coordinate form” of an image, the binary form, gray scale form, and color coordinate form each being a two-dimensional array defining an image. Although described herein as continuous tone processing, the present invention applies equally as well to the processing of color images, wherein each separation is treated, effectively, as a gray scale or continuous tone image. Accordingly, references herein to the processing of continuous tone (contone) or gray scale images is intended to include the processing of color image separations as well. An operation performs “image processing” when it operates on an item of data that relates to part of an image.  
         [0038]     Digital “halftoning” refers to encoding methods that are used to reduce the number of quantization levels per pixel in a digital image, while maintaining the gray appearance of the image at normal viewing distance. Halftoning is widely employed in the printing and display of digital images. The need for halftoning encoding arises either because the physical processes involved are binary in nature or the processes have been restricted to binary operation for reasons of cost, speed, memory or stability in the presence of process fluctuations. Examples of such processes are most printing presses, ink jet printers, binary cathode ray tube (CRT) displays, and laser xerography. In most printing and display applications, the halftoned image is composed ideally of two gray levels, black and white. Spatial integration, plus higher level processing performed by the human visual system, of local area coverage of black and white pixels, provides the appearance of a gray level, or “continuous tone,” image. Many halftone techniques readily extend to color and to quantization using more than two levels.  
         [0039]     In the context of the present teaching “tint” refers to a color or colored object within an image that is not fully saturated. That is, the color is not represented by 100% area coverage of each of the individual colorants or color primaries that are used to form the color.  
         [0040]     Turning now to  FIG. 1 , depicted therein is an embodiment of a digital imaging system suitable for one or more aspects of the present invention. In the system  110 , image source  120  is used to generate image data that is supplied to an image processing system  130 , and which produces output data for rendering by print engine  140 . Image source  120  may include scanner  122 , computer  124 , network  126  or any similar or equivalent image input terminal. On the output end printer engine  140  is preferably a xerographic engine however print engine  140  may include such equivalent print technology alternatives as wax, ink jet, etc. The teachings presented herein are directed toward aspects of image processor  130  depicted in  FIG. 1 . In particular, the intention of the teachings presented herein is to identify, and process accordingly, edge pixels of tints within a digital image. It will be appreciated by those skilled in the art that the rendering of an image into a printable or displayable output format may be accomplished at any of a number of locations, which herein is provided for in but one example only as occurring within the image processing system  130  or within in the print engine  140 .  
         [0041]     Referring now to  FIG. 2 , shown therein is a diagram depicting the data flow in an example embodiment. Image processing system  130  receives raw (unprocessed) image input image data  200 . Image processing system  130  includes an edge identification and tinted edge enhancement processor  210 , and may contain other image processing operations as well. Within the edge identification and tinted edge enhancement processor  210  a target pixel is selected  220  and an observation window of pixels is located about the target pixel  230 . In one embodiment, this window is 5×5 pixels in dimension with the center pixel as the window origin, where the origin pixel is used to locate the window on the target pixel. However, a smaller widow such as a 3×3, or in the alternative a larger size window, or even a window of a non-square shape, is well within the contemplation of the present disclosure. This window is stepped through the image pixel data. In one embodiment the origin pixel is stepped to target pixels from top to bottom and from left to right through all address locations within an image. Typically, all pixels within the input image become target pixels in a successive manner. At each location the pixel values are extracted from within the window as indicated in step  240 .  
         [0042]      FIG. 3  depicts a 5×5 window  300  with a center pixel  310  as the window origin (p 22 ), which is used in locating the window  300  about a given target pixel. The pixel values in the window are each denoted by some p ij , where the subscripts i and j denote row and column indices respectively, and range from 0 to 4 for the 5×5 window. A circle  311  has been added as a quick visual indicator of the origin pixel location within the window. It is this origin pixel  310  which is typically stepped across all pixel address locations as each pixel location in turn becomes a target pixel. For each target pixel address, the pixel values within the window  300  are applied to the edge identification processing and enhancement as described above and below in the discussion of  FIG. 2 . While the discussion here of  FIGS. 2 and 3  describes the edge identification process as a serial operation, where successive target pixels are defined and processed, it will also be recognized by one skilled in the art that a parallel process could be employed where multiple target pixels could be processed simultaneously using multiple windows and multiple edge identification processors. The bitmap image data may be divided-up in any number of ways in order to achieve this parallel processing of the image data. One approach for example would be using segmentation to divide the image data into text and graphics. Another approach for color images would be to separate out the color planes and process each individually. There are many other approaches that will be apparent to those skilled in the art.  
         [0043]     Returning now to  FIG. 2 , in step  250  the extracted pixel values are used as input into the edge identification processing means  210 . There are alternative computing architectures that may be employed here, such as parallel, serial, or some combination of parallel and serial operations, as will be evident to those skilled in the art. However the computing architecture is configured, the operations are low complexity arithmetic and look-up table operations applied to the extracted pixel values. The edge identification performed in step  250  is encoded to an edge identification code in step  260 . The edge identification code may used in a step to generate an enhanced tinted edge  265 , where enhanced tinted edge has different halftoning structure than the body of the tinted object. Finally, the increment block  270  restarts the process loop over at the next target pixel address until all target pixels have been processed.  
         [0044]      FIG. 4  depicts a flowchart wherein a digital image data  200  is input to edge-identification and tinted edge enhancement process  400 . A target pixel is selected and an observation window of pixels is observed about the target pixel  420 . Edge-state codes are generated for a plurality of pairs of vectors of pixels that run through the observation window  430 .  FIG. 3  depicts one arrangement of vectors of pixels that run through the observation window in horizontal  320  and vertical  330  orientations. Vectors of other orientation, such as diagonal, may be employed in generating edge-state codes. An edge-identification code is generated from the plurality of edge state codes  440  to produce an edge-identification code about the target pixel  450 . A halftoning processes  445  uses the edge-identification code to direct the halftoning performed at the target pixel. If the edge-identification code indicates that the target pixel is at an appropriate distance from an edge, a halftoning process will be applied that is selected for enhanced edge rendering, as will be described below. If the edge-identification code indicates that the target pixel is not at an edge, a conventional halftoning process will be applied, where the conventional process is that process which is applied within the body of the tinted object. If more pixels are to be processed, the edge identification and edge enhancement process returns to step  420 .  
         [0045]      FIG. 5  depicts how an observation window of pixels  300  about a target pixel  310  is input  510  to step  520  where a plurality of sums of weighted pixel values are generated, where each sum is taken over a vector of pixels that run through the observation window. The weights can be applied as multiplicative coefficients, or another means, such as by an additive or subtractive operation. Step  530  receives the weighted sums of vectors of pixels, and generates vector-sum-to-vector-sum differences between pairs of neighboring vectors. For instance, when employing horizontal vectors  320  for pixel observation window rows  0  through  4 , differences can be generated for the respective sums of row  0  and  1 , the respective sums of rows  1  and  2 , the respective sums of rows  2  and  3 , and the respective sums of rows  3  and  4 . Alternatively, differences may be taken between neighboring vectors other than the nearest neighboring vectors. For instance, differences can be generated for the respective sums of row  0  and  2 , the respective sums of rows  1  and  3 , and the respective sums of rows  2  and  4 .  
         [0046]     The vector-sum-to-vector-sum differences are input to step  540  where an “edge-slope state” between each of the plurality of vector pairs is determined. “Edge-slope state” refers to the presence of an edge and the orientation of the edge (rising or falling) between the vectors of pixels. Large differences between the sums indicate the presence of an edge, while positive and negative signs to the difference indicate a rising or falling edge, respectively. Step  550  receives the plurality of edge-slope states and encodes those states as a plurality of respective bit patterns. For instance, the presence or strength of an edge between two vectors of pixels may be encoded in some number of bits, and the sign, or orientation, of the edge may be encoded by another bit. For applications that do not require high precision definition of edges, it may be sufficient to encode the presence and strength of an edge in 1 bit, i.e., an edge is significantly present or an edge is not significantly present. For other applications requiring finer identification of edges, more than one bit may be used to define the presence and strength of an edge.  
         [0047]     The plurality of edge states for the vectors generated in step  550  are input to an encoding process  560  that generates a code for the edge state of the plurality of vectors of the window. In other words, step  560  will receive a plurality of bit patterns, i.e., edge-state codes for the vector differences, and may employ a look-up table to map those bit patterns, to a bit pattern representing a general state of the edges for the plurality of vectors examined. For instance, an edge-state code about a target pixel may indicate rising and falling edges for multiple locations within the pixel observation window. The edge-state code is used in a halftoning processes  565  to direct the halftoning performed at the target pixel. If the edge-identification code indicates that the target pixel is at an appropriate distance from an edge, a halftoning process will be applied that is selected for enhanced edge rendering, as will be described below. If the edge-identification code indicates that the target pixel is not at an edge, a conventional halftoning process will be applied, where the conventional process is that process which is applied within the body of the tinted object.  
         [0048]      FIG. 6  depicts a detailed high-level block diagram schematic for one embodiment consistent with the teachings provided herein. An observation window of pixels  300  is shown with the window origin pixel denoted p 22 . Pixels aligned in a particular orientation are used to form a plurality of vectors of pixels associated with that orientation. In  FIG. 6 , rows of pixels in the observation window are used to form respective horizontal vectors of pixels  320  and columns of pixels are used to form respective vertical vectors of pixels  330 . As will be evident to those skilled in the art, other or additional vectors of pixels of other orientations may be formed from pixels in the observation window. For example, vectors of pixels may be formed from pixels aligned at some angle, such as ±45°.  
         [0049]     In a next step, the plurality of vectors of pixels are received, and weighted sums of pixels within each vector are generated.  FIG. 6  illustrates multiplicative weighting with weights a ij  applied to the pixel values within a vector, whereupon the weighted values are summed. These weights a ij  can be selected and optimized for particular applications. For instance, in the presence of background noise in the image, the weights may be made uniform (e.g., all 1&#39;s) in an attempt to suppress the effect of noise on the edge identification. Conversely, a low noise setting or in situations where images possess very small edge features it may be required to utilize larger values of weights a ij  near the center of the window and smaller values at greater distance from the center. The values could decrease from a center value with a trend such as linear or Gaussian. The weighting and summing process is performed for each respective vector of each orientation. Summing blocks  615  in the present embodiment perform the summing process for the horizontal vectors and Summing blocks  620  perform the summing process for the vertical vectors. A plurality of sums are produced, denote by Y i  for the horizontal vectors and X i  for the vertical vectors, where i=0 to 4 in the presently illustrated embodiment.  
         [0050]     In some computing architectures it can be advantageous to reduce the number of bits in the weighting and summing process. For instance, when using 8-bit numbers possessing range 0 to 255, and using multiplicative coefficients defined by 8 bits, the resultant product may require 16-bit representation. A sum over the vector of pixels would require an even higher bit representation. Using such a large number of bits to represent results of these intermediate operations can be very costly for real-time, high-speed applications. Further, typical edge identification tasks do not require such a great bit depth. It has been found that it is advantageous as to both cost and speed to reduce the bit depth of these operations. For instance, the weighted sums can be limited to 8 bits of quantization resolution.  
         [0051]     In a subsequent step, the weighted vector sums are received and differences are formed between pairs of sums of neighboring vectors of a particular orientation. In  FIG. 6 , computational blocks  625  and  630  perform differencing for nearest-neighbor rows and nearest-neighbor columns, respectively, to form a plurality of vector-sum differences for each orientation. In  FIG. 6 , the differences are denoted as dy i  for column vectors and dx i  for row vectors, where i=0 to 3. As stated above, the difference step may not be restricted to nearest neighbors, and may be performed between neighboring vectors that are separated by one or more vectors.  
         [0052]     In a further step, a plurality of edge-slope states between the vectors are generated using respective differences between vector sums as input. Determination of the edge-slope states depicted in  FIG. 6  as performed by computational blocks  635  and  640  tests the magnitude and sign of each difference. For each difference, the significance of the edge is determined by comparing the magnitude of that difference to a threshold. A 1 -bit output (states 0 or 1) indicates that the difference is at or above a threshold, thereby indicating significance, or is not at or above the threshold, thereby indicating lack of significance. The thresholds are depicted in  FIG. 6  as t i  where i=0 to 3. These thresholds may be set over a broad range of value and made the same or different for different vector pairs or different vector orientations depending on a particular application. For instance, thresholds may be set low (e.g., 16) when attempting to identify an edge of a gray object, such as a gray typographic character, and may be set high (e.g., 128) when attempting to identify a high contrast edge, like the corner of a black typographic character on a white background. The sign of each difference is also tested and the result is rendered to a 1-bit form indicating a positive or negative slope, where slope of zero could be classified either positive or negative due to the lack of significance of the edge. The edge-slope states are determined for row and column vectors, by computational blocks  635  and  640 , respectively. A plurality of edge-slope states are determined for each orientation.  
         [0053]     An edge encoding block for a given particular orientation receives the edge-slope state and generates a code for the edge state of that orientation. In  FIG. 6 , encoding blocks  645  and  650  provide the encoding of edge states for horizontal and vertical orientations, respectively. The encoding may in one embodiment be performed via a Look-Up Table (LUT) that maps the bits of the plurality of edge-slope states for an orientation to an orientation edge-state code. The  FIG. 6  embodiment illustrates the use of an 8-bit-to-4-bit LUT for that encoding purpose, but it is within the scope of the invention to allow other bit mapping relationship. For instance, use of more vectors or high quantization of vector-sum differences could require more than 8 bits as input and 4 bits output. If only one orientation is employed, this orientation edge-state code is the resulting edge state code of the process. However, if more than one orientation of vectors is employed, the multiple orientation edge-state codes are mapped through an additional encoding process block  655  to arrive at output edge-state code. This encoding may also be performed using a LUT process as will be understood by those skilled in the art.  
         [0054]     The edge-state code is used in a halftoning processes  660  to direct the halftoning performed at the target pixel. If the edge-identification code indicates that the target pixel is at an appropriate distance from an edge, a halftoning process will be applied that is selected for enhanced edge rendering, as will be described below. If the edge-identification code indicates that the target pixel is not at an edge, a conventional halftoning process will be applied, where the conventional process is that process which is applied within the body of the tinted object.  
         [0055]     An example of a LUT for encoding edge states is given in Table 1. The codes are shown in the table as hexadecimal numbers. In Table 1, the notation used is in reference to horizontal vectors, but concepts embodied by the table are more general. For instance, it is straightforward to interpret the inputs to be from an orientation other than horizontal, such as vertical. Further, the table can be considered an example of a means to produce an orientation edge-state code, or an output edge-state code if only one orientation is to be employed. The notation used as edge state descriptions in Table 1 is explained in Table 2.  
                                                                   TABLE 1                           Row Edge Encoding            Edge Slope States                dY0 &gt;                                           0 1   abs(dY0) &gt; T   dY1 &gt; 0 1   abs(dY1) &gt; T   dY2 &gt; 0 1   abs(dY2) &gt; T   dY3 &gt; 0 1   abs(dY3) &gt; T       means   1 means   means   1 means   means   1 means   means   1 means       Edge       falling   strong   falling   strong   falling   strong   falling   strong   Edge State   State       edge   edge   edge   edge   edge   edge   edge   edge   Description   Code               0   0   0   0   0   0   0   0   Flat   0x0E       0   0   0   0   0   0   0   1   ↑FB   0x00       0   0   0   0   0   0   1   0   Flat   0x0E       0   0   0   0   0   0   1   1   ↓FB   0x01       0   0   0   0   0   1   0   0   ↑B   0x04       0   0   0   0   0   1   0   1   ↑B↑FB   0x02       0   0   0   0   0   1   1   0   ↑B   0x04       0   0   0   0   0   1   1   1   ↑B↓FB   0x0F       0   0   0   0   1   0   0   0   Flat   0x0E       0   0   0   0   1   0   0   1   ↑FB   0x00       0   0   0   0   1   0   1   0   Flat   0x0E       0   0   0   0   1   0   1   1   ↓FB   0x01       0   0   0   0   1   1   0   0   ↓B   0x05       0   0   0   0   1   1   0   1   ↓B↑FB   0x0F       0   0   0   0   1   1   1   0   ↓B   0x05       0   0   0   0   1   1   1   1   ↓B↓FB   0x03       0   0   0   1   0   0   0   0   ↑T   0x08       0   0   0   1   0   0   0   1   ↑T↑FB   0x0F       0   0   0   1   0   0   1   0   ↑T   0x08       0   0   0   1   0   0   1   1   ↑T↓FB   0x0F       0   0   0   1   0   1   0   0   ↑T↑B   0x06       0   0   0   1   0   1   0   1   ↑T↑B↑FB   0x0F       0   0   0   1   0   1   1   0   ↑T↑B   0x06       0   0   0   1   0   1   1   1   ↑T↑B↓FB   0x0F       0   0   0   1   1   0   0   0   ↑T   0x08       0   0   0   1   1   0   0   1   ↑T↑FB   0x0F       0   0   0   1   1   0   1   0   ↑T   0x08       0   0   0   1   1   0   1   1   ↑T↓FB   0x0F       0   0   0   1   1   1   0   0   ↑T↓B   0x0F       0   0   0   1   1   1   0   1   ↑T↓B↑FB   0x0F       0   0   0   1   1   1   1   0   ↑T↓B   0x0F       0   0   0   1   1   1   1   1   ↑T↓B↓FB   0x0F       0   0   1   0   0   0   0   0   Flat   0x0E       0   0   1   0   0   0   0   1   ↑FB   0x00       0   0   1   0   0   0   1   0   Flat   0x0E       0   0   1   0   0   0   1   1   ↓FB   0x01       0   0   1   0   0   1   0   0   ↑B   0x04       0   0   1   0   0   1   0   1   ↑B↑FB   0x02       0   0   1   0   0   1   1   0   ↑B   0x04       0   0   1   0   0   1   1   1   ↑B↓FB   0x0F       0   0   1   0   1   0   0   0   Flat   0x0E       0   0   1   0   1   0   0   1   ↑FB   0x00       0   0   1   0   1   0   1   0   Flat   0x0E       0   0   1   0   1   0   1   1   ↓FB   0x01       0   0   1   0   1   1   0   0   ↓B   0x05       0   0   1   0   1   1   0   1   ↓B↑FB   0x0F       0   0   1   0   1   1   1   0   ↓B   0x05       0   0   1   0   1   1   1   1   ↓B↓FB   0x03       0   0   1   1   0   0   0   0   ↓T   0x09       0   0   1   1   0   0   0   1   ↓T↑FB   0x0F       0   0   1   1   0   0   1   0   ↓T   0x09       0   0   1   1   0   0   1   1   ↓T↓FB   0x0F       0   0   1   1   0   1   0   0   ↓T↑B   0x0F       0   0   1   1   0   1   0   1   ↓T↑B↑FB   0x0F       0   0   1   1   0   1   1   0   ↓T↑B   0x0F       0   0   1   1   0   1   1   1   ↓T↑B↓FB   0x0F       0   0   1   1   1   0   0   0   ↓T   0x09       0   0   1   1   1   0   0   1   ↓T↑FB   0x0F       0   0   1   1   1   0   1   0   ↓T   0x09       0   0   1   1   1   0   1   1   ↓T↓FB   0x0F       0   0   1   1   1   1   0   0   ↓T↓B   0x07       0   0   1   1   1   1   0   1   ↓T↓B↑FB   0x0F       0   0   1   1   1   1   1   0   ↓T↓B   0x07       0   0   1   1   1   1   1   1   ↓T↓B↓FB   0x0F       0   1   0   0   0   0   0   0   ↑FT   0x0C       0   1   0   0   0   0   0   1   ↑FT↑FB   0x0F       0   1   0   0   0   0   1   0   ↑FT   0x0C       0   1   0   0   0   0   1   1   ↑FT↓FB   0x0F       0   1   0   0   0   1   0   0   ↑FT↑B   0x0F       0   1   0   0   0   1   0   1   ↑FT↑B↑FB   0x0F       0   1   0   0   0   1   1   0   ↑FT↑B   0x0F       0   1   0   0   0   1   1   1   ↑FT↑B↓FB   0x0F       0   1   0   0   1   0   0   0   ↑FT   0x0C       0   1   0   0   1   0   0   1   ↑FT↑FB   0x0F       0   1   0   0   1   0   1   0   ↑FT   0x0C       0   1   0   0   1   0   1   1   ↑FT↓FB   0x0F       0   1   0   0   1   1   0   0   ↑FT↓B   0x0F       0   1   0   0   1   1   0   1   ↑FT↓B↑FB   0x0F       0   1   0   0   1   1   1   0   ↑FT↓B   0x0F       0   1   0   0   1   1   1   1   ↑FT↓B↓FB   0x0F       0   1   0   1   0   0   0   0   ↑FT↑T   0x0A       0   1   0   1   0   0   0   1   ↑FT↑T↑FB   0x0F       0   1   0   1   0   0   1   0   ↑FT↑T   0x0A       0   1   0   1   0   0   1   1   ↑FT↑T↓FB   0x0F       0   1   0   1   0   1   0   0   ↑FT↑T↑B   0x0F       0   1   0   1   0   1   0   1   ↑FT↑T↑B↑FB   0x0F       0   1   0   1   0   1   1   0   ↑FT↑T↑B   0x0F       0   1   0   1   0   1   1   1   ↑↑FT↑T↑B↓FB   0x0F       0   1   0   1   1   0   0   0   ↑FT↑T   0x0A       0   1   0   1   1   0   0   1   ↑FT↑T↑FB   0x0F       0   1   0   1   1   0   1   0   ↑FT↑T   0x0A       0   1   0   1   1   0   1   1   ↑FT↑T↓FB   0x0F       0   1   0   1   1   1   0   0   ↑FT↑T↓B   0x0F       0   1   0   1   1   1   0   1   ↑FT↑T↓B↑FB   0x0F       0   1   0   1   1   1   1   0   ↑FT↑T↓B   0x0F       0   1   0   1   1   1   1   1   ↑FT↑T↓B↓FB   0x0F       0   1   1   0   0   0   0   0   ↑FT   0x0C       0   1   1   0   0   0   0   1   ↑FT↑FB   0x0F       0   1   1   0   0   0   1   0   ↑FT   0x0C       0   1   1   0   0   0   1   1   ↑FT↓FB   0x0F       0   1   1   0   0   1   0   0   ↑FT↑B   0x0F       0   1   1   0   0   1   0   1   ↑FT↑B↑FB   0x0F       0   1   1   0   0   1   1   0   ↑FT↑B   0x0F       0   1   1   0   0   1   1   1   ↑FT↑B↓FB   0x0F       0   1   1   0   1   0   0   0   ↑FT   0x0C       0   1   1   0   1   0   0   1   ↑FT↑FB   0x0F       0   1   1   0   1   0   1   0   ↑FT   0x0C       0   1   1   0   1   0   1   1   ↑FT↓FB   0x0F       0   1   1   0   1   1   0   0   ↑FT↓B   0x0F       0   1   1   0   1   1   0   1   ↑FT↓B↑FB   0x0F       0   1   1   0   1   1   1   0   ↑FT↓B   0x0F       0   1   1   0   1   1   1   1   ↑FT↓B↓FB   0x0F       0   1   1   1   0   0   0   0   ↑FT↓T   0x0F       0   1   1   1   0   0   0   1   ↑FT↓T↑FB   0x0F       0   1   1   1   0   0   1   0   ↑FT↓T   0x0F       0   1   1   1   0   0   1   1   ↑FT↓T↓FB   0x0F       0   1   1   1   0   1   0   0   ↑FT↓T↑B   0x0F       0   1   1   1   0   1   0   1   ↑FT↓T↑B↑FB   0x0F       0   1   1   1   0   1   1   0   ↑FT↓T↑B   0x0F       0   1   1   1   0   1   1   1   ↑FT↓T↑B↓FB   0x0F       0   1   1   1   1   0   0   0   ↑FT↓T   0x0F       0   1   1   1   1   0   0   1   ↑FT↓T↑FB   0x0F       0   1   1   1   1   0   1   0   ↑FT↓T   0x0F       0   1   1   1   1   0   1   1   ↑FT↓T↓FB   0x0F       0   1   1   1   1   1   0   0   ↑FT↓T↓B   0x0F       0   1   1   1   1   1   0   1   ↑FT↓T↓B↑FB   0x0F       0   1   1   1   1   1   1   0   ↑FT↓T↓B   0x0F       0   1   1   1   1   1   1   1   ↑FT↓T↓B↓FB   0x0F       1   0   0   0   0   0   0   0   Flat   0x0E       1   0   0   0   0   0   0   1   ↑FB   0x00       1   0   0   0   0   0   1   0   Flat   0x0E       1   0   0   0   0   0   1   1   ↓FB   0x01       1   0   0   0   0   1   0   0   ↑B   0x04       1   0   0   0   0   1   0   1   ↑B↑FB   0x02       1   0   0   0   0   1   1   0   ↑B   0x04       1   0   0   0   0   1   1   1   ↑B↓FB   0x0F       1   0   0   0   1   0   0   0   Flat   0x0E       1   0   0   0   1   0   0   1   ↑FB   0x00       1   0   0   0   1   0   1   0   Flat   0x0E       1   0   0   0   1   0   1   1   ↓FB   0x01       1   0   0   0   1   1   0   0   ↓B   0x05       1   0   0   0   1   1   0   1   ↓B↑FB   0x0F       1   0   0   0   1   1   1   0   ↓B   0x05       1   0   0   0   1   1   1   1   ↓B↓FB   0x03       1   0   0   1   0   0   0   0   ↑T   0x08       1   0   0   1   0   0   0   1   ↑T↑FB   0x0F       1   0   0   1   0   0   1   0   ↑T   0x08       1   0   0   1   0   0   1   1   ↑T↓FB   0x0F       1   0   0   1   0   1   0   0   ↑T↑B   0x06       1   0   0   1   0   1   0   1   ↑T↑B↑FB   0x0F       1   0   0   1   0   1   1   0   ↑T↑B   0x06       1   0   0   1   0   1   1   1   ↑T↑B↓FB   0x0F       1   0   0   1   1   0   0   0   ↑T   0x08       1   0   0   1   1   0   0   1   ↑T↑FB   0x0F       1   0   0   1   1   0   1   0   ↑T   0x08       1   0   0   1   1   0   1   1   ↑T↓FB   0x0F       1   0   0   1   1   1   0   0   ↑T↓B↑FB   0x0F       1   0   0   1   1   1   0   1   ↑T↓FB   0x0F       1   0   0   1   1   1   1   0   ↑T↓B   0x0F       1   0   0   1   1   1   1   1   ↑T↓B↓FB   0x0F       1   0   1   0   0   0   0   0   Flat   0x0E       1   0   1   0   0   0   0   1   ↑FB   0x00       1   0   1   0   0   0   1   0   Flat   0x0E       1   0   1   0   0   0   1   1   ↓FB   0x01       1   0   1   0   0   1   0   0   ↑B   0x04       1   0   1   0   0   1   0   1   ↑B↑FB   0x02       1   0   1   0   0   1   1   0   ↑B   0x04       1   0   1   0   0   1   1   1   ↑B↓FB   0x0F       1   0   1   0   1   0   0   0   Flat   0x0E       1   0   1   0   1   0   0   1   ↑FB   0x00       1   0   1   0   1   0   1   0   Flat   0x0E       1   0   1   0   1   0   1   1   ↓FB   0x01       1   0   1   0   1   1   0   0   ↓B   0x05       1   0   1   0   1   1   0   1   ↓B↑FB   0x0F       1   0   1   0   1   1   1   0   ↓B   0x05       1   0   1   0   1   1   1   1   ↓B↓FB   0x03       1   0   1   1   0   0   0   0   ↓T   0x09       1   0   1   1   0   0   0   1   ↓T↑FB   0x0F       1   0   1   1   0   0   1   0   ↓T   0x09       1   0   1   1   0   0   1   1   ↓T↓FB   0x0F       1   0   1   1   0   1   0   0   ↓T↑B   0x0F       1   0   1   1   0   1   0   1   ↓T↑B↑FB   0x0F       1   0   1   1   0   1   1   0   ↓T↑B   0x0F       1   0   1   1   0   1   1   1   ↓T↑B↓FB   0x0F       1   0   1   1   1   0   0   0   ↓T   0x09       1   0   1   1   1   0   0   1   ↓T↑FB   0x0F       1   0   1   1   1   0   1   0   ↓T   0x09       1   0   1   1   1   0   1   1   ↓T↓FB   0x0F       1   0   1   1   1   1   0   0   ↓T↓B   0x07       1   0   1   1   1   1   0   1   ↓T↓B↑FB   0x0F       1   0   1   1   1   1   1   0   ↓T↓B   0x07       1   0   1   1   1   1   1   1   ↓T↓B↓FB   0x0F       1   1   0   0   0   0   0   0   ↓FT   0x0D       1   1   0   0   0   0   0   1   ↓FT↑FB   0x0F       1   1   0   0   0   0   1   0   ↓FT   0x0D       1   1   0   0   0   0   1   1   ↓FT↓FB   0x0F       1   1   0   0   0   1   0   0   ↓FT↑B   0x0F       1   1   0   0   0   1   0   1   ↓FT↑B↑FB   0x0F       1   1   0   0   0   1   1   0   ↓FT↑B   0x0F       1   1   0   0   0   1   1   1   ↓FT↑B↓FB   0x0F       1   1   0   0   1   0   0   0   ↓FT   0x0D       1   1   0   0   1   0   0   1   ↓FT↑FB   0x0F       1   1   0   0   1   0   1   0   ↓FT   0x0D       1   1   0   0   1   0   1   1   ↓FT↓FB   0x0F       1   1   0   0   1   1   0   0   ↓FT↓B   0x0F       1   1   0   0   1   1   0   1   ↓FT↓B↑FB   0x0F       1   1   0   0   1   1   1   0   ↓FT↓B   0x0F       1   1   0   0   1   1   1   1   ↓FT↓B↓FB   0x0F       1   1   0   1   0   0   0   0   ↓FT↑T   0x0F       1   1   0   1   0   0   0   1   ↓FT↑T↑FB   0x0F       1   1   0   1   0   0   1   0   ↓FT↑T   0x0F       1   1   0   1   0   0   1   1   ↓FT↑T↑FB   0x0F       1   1   0   1   0   1   0   0   ↓FT↑T↑B   0x0F       1   1   0   1   0   1   0   1   ↓FT↑T↑B↑FB   0x0F       1   1   0   1   0   1   1   0   ↓FT↑T↑B   0x0F       1   1   0   1   0   1   1   1   ↓FT↑T↑B↓FB   0x0F       1   1   0   1   1   0   0   0   ↓FT↑T   0x0F       1   1   0   1   1   0   0   1   ↓FT↑T↑FB   0x0F       1   1   0   1   1   0   1   0   ↓FT↑T   0x0F       1   1   0   1   1   0   1   1   ↓FT↑T↓FB   0x0F       1   1   0   1   1   1   0   0   ↓FT↑T↓B   0x0F       1   1   0   1   1   1   0   1   ↓FT↑T↓B↑FB   0x0F       1   1   0   1   1   1   1   0   ↓FT↑T↓B   0x0F       1   1   0   1   1   1   1   1   ↓FT↑T↓B↓FB   0x0F       1   1   1   0   0   0   0   0   ↓FT   0x0D       1   1   1   0   0   0   0   1   ↓FT↑FB   0x0F       1   1   1   0   0   0   1   0   ↓FT   0x0D       1   1   1   0   0   0   1   1   ↓FT↓FB   0x0F       1   1   1   0   0   1   0   0   ↓FT↑B   0x0F       1   1   1   0   0   1   0   1   ↓FT↑B↑FB   0x0F       1   1   1   0   0   1   1   0   ↓FT↑B   0x0F       1   1   1   0   0   1   1   1   ↓FT↑B↓FB   0x0F       1   1   1   0   1   0   0   0   ↓FT   0x0D       1   1   1   0   1   0   0   1   ↓FT↑FB   0x0F       1   1   1   0   1   0   1   0   ↓FT   0x0D       1   1   1   0   1   0   1   1   ↓FT↓FB   0x0F       1   1   1   0   1   1   0   0   ↓FT↓B   0x0F       1   1   1   0   1   1   0   1   ↓FT↓B↑FB   0x0F       1   1   1   0   1   1   1   0   ↓FT↓B   0x0F       1   1   1   0   1   1   1   1   ↓FT↓B↓FB   0x0F       1   1   1   1   0   0   0   0   ↓FT↓T   0x0B       1   1   1   1   0   0   0   1   ↓FT↓T↑FB   0x0F       1   1   1   1   0   0   1   0   ↓FT↓T   0x0B       1   1   1   1   0   0   1   1   ↓FT↓T↓FB   0x0F       1   1   1   1   0   1   0   0   ↓FT↓T↑B   0x0F       1   1   1   1   0   1   0   1   ↓FT↓T↑B↑FB   0x0F       1   1   1   1   0   1   1   0   ↓FT↓T↑B   0x0F       1   1   1   1   0   1   1   1   ↓FT↓T↑B↓FB   0x0F       1   1   1   1   1   0   0   0   ↓FT↓T   0x0B       1   1   1   1   1   0   0   1   ↓FT↓T↑FB   0x0F       1   1   1   1   1   0   1   0   ↓FT↓T   0x0B       1   1   1   1   1   0   1   1   ↓FT↓T↓FB   0x0F       1   1   1   1   1   1   0   0   ↓FT↓T↓B   0x0F       1   1   1   1   1   1   0   1   ↓FT↓T↓B↑FB   0x0F       1   1   1   1   1   1   1   0   ↓FT↓T↓B   0x0F       1   1   1   1   1   1   1   1   ↓FT↓T↓B↓FB   0x0F                  
 
         [0056]    
       
         
               
             
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                   
               
               
                 Notation used in Table 1. 
               
             
          
           
               
                 Notation 
                 Meaning 
               
               
                   
               
               
                 FT 
                 Far Top, indicates a significant edge between rows 0 and 1 
               
               
                 T 
                 Top, indicates a significant edge between row 1 and 2 
               
               
                 B 
                 Bottom, indicates a significant edge between rows 2 and 3 
               
               
                 FB 
                 Far Bottom, indicates a significant edge between rows 3 and 4 
               
               
                 ↑ 
                 indicates edge slope increases in the direction of increasing 
               
               
                   
                 row number 
               
               
                 ↓ 
                 indicates edge slope decreases in the direction of increasing 
               
               
                   
                 row number 
               
               
                 Flat 
                 Flat, indicates absence of a significant edge 
               
               
                   
               
             
          
         
       
     
         [0057]     To understand the codes used in the table consider the following examples. The edge state description ⇑B⇑FB having code 0x02 refers to a significant increasing-value edge between rows  2  and  3  and a significant increasing-value edge between rows  3  and  4 . ⇑T⇓B⇓FB having code 0x00 refers to a significant increasing edge between rows  1  and  2 , a significant decreasing edge between rows  2  and  3 , and a significant decreasing edge between rows  3  and  4 . Since each of FT, T, B, and FB can be in one of 3 states in this table (increasing, decreasing, not significant), 81 states are possible requiring 7 bits of coding. Practically, not all of these states are important to real edge-identification applications. It has been found that 4 to 6 bits can encode the useful states for most applications. Table 1 provides a 4-bit example.  
         [0058]     As stated above, more than one orientation of vectors may be employed, and the multiple orientation edge-state codes can be mapped at block  655  through an additional encoding process to arrive at an output edge-state code. To understand the multiple orientation aspect of this embodiment of the invention, consider the application of finding a corner pixel. In particular, assume that we wish to indicate that a corner covers pixels p 33 , p 34 , p 43 , p 44 , and the edge identification processor is employing horizontal vectors (rows) and vertical vectors (columns). The definition of the vertical edge states are analogous to the horizontal states, with FL (Far Left), L (Left), Right (Right), FR (Far Right) being analogous to FT, T, B, FB respectively. A corner covering p 33 , p 34 , p 43 , p 44  would result in the codes for ⇑B (0x04) and ⇑R (0x04), from the row-edge encoding table and the column edge-encoding table, respectively. When these two codes are received by an encoder for multiple orientations, a code would be generated for the p 33 -p 34 -p 43 -p 44 -type corner. An example of a table for encoding an overall edge state from orientation edge states is given below in Table 3. In this example, the table coverts 4 bits from the horizontal codes and 4 bits from the vertical codes to 8 bits for an overall edge state code. Due to the equality of input and output bits in this example, the table can be rather straightforward, in that we can construct the output as a concatenation of the input bits.  
                                 TABLE 3                           An example of a table encoding an overall edge state       from orientation edge states.                Horizontal Edge   Vertical Edge   Overall Edge           State Code   State Code   State Code                       0x00   0x00   0x00           0x00   0x01   0x01           0x00   0x02   0x02           0x00   0x03   0x03           0x00   0x04   0x04           0x00   0x05   0x05           0x00   0x06   0x06           0x00   0x07   0x07           0x00   0x08   0x08           0x00   0x09   0x09           0x00   0x0A   0x0A           0x00   0x0B   0x0B           0x00   0x0C   0x0C           0x00   0x0D   0x0D           0x00   0x0E   0x0E           0x00   0x0F   0x0F           0x01   0x00   0x10           0x01   0x01   0x11           0x01   0x02   0x12           0x01   0x03   0x13           0x01   0x04   0x14           0x01   0x05   0x15           0x01   0x06   0x16           0x01   0x07   0x17           0x01   0x08   0x18           0x01   0x09   0x19           0x01   0x0A   0x1A           0x01   0x0B   0x1B           0x01   0x0C   0x1C           0x01   0x0D   0x1D           0x01   0x0E   0x1E           0x01   0x0F   0x1F           0x02   0x00   0x20           0x02   0x01   0x21           0x02   0x02   0x22           0x02   0x03   0x23           0x02   0x04   0x24           0x02   0x05   0x25           0x02   0x06   0x26           0x02   0x07   0x27           0x02   0x08   0x28           0x02   0x09   0x29           0x02   0x0A   0x2A           0x02   0x0B   0x2B           0x02   0x0C   0x2C           0x02   0x0D   0x2D           0x02   0x0E   0x2E           0x02   0x0F   0x2F           0x03   0x00   0x30           0x03   0x01   0x31           0x03   0x02   0x32           0x03   0x03   0x33           0x03   0x04   0x34           0x03   0x05   0x35           0x03   0x06   0x36           0x03   0x07   0x37           0x03   0x08   0x38           0x03   0x09   0x39           0x03   0x0A   0x3A           0x03   0x0B   0x3B           0x03   0x0C   0x3C           0x03   0x0D   0x3D           0x03   0x0E   0x3E           0x03   0x0F   0x3F           0x04   0x00   0x40           0x04   0x01   0x41           0x04   0x02   0x42           0x04   0x03   0x43           0x04   0x04   0x44           0x04   0x05   0x45           0x04   0x06   0x46           0x04   0x07   0x47           0x04   0x08   0x48           0x04   0x09   0x49           0x04   0x0A   0x4A           0x04   0x0B   0x4B           0x04   0x0C   0x4C           0x04   0x0D   0x4D           0x04   0x0E   0x4E           0x04   0x0F   0x4F           0x05   0x00   0x50           0x05   0x01   0x51           0x05   0x02   0x52           0x05   0x03   0x53           0x05   0x04   0x54           0x05   0x05   0x55           0x05   0x06   0x56           0x05   0x07   0x57           0x05   0x08   0x58           0x05   0x09   0x59           0x05   0x0A   0x5A           0x05   0x0B   0x5B           0x05   0x0C   0x5C           0x05   0x0D   0x5D           0x05   0x0E   0x5E           0x05   0x0F   0x5F           0x06   0x00   0x60           0x06   0x01   0x61           0x06   0x02   0x62           0x06   0x03   0x63           0x06   0x04   0x64           0x06   0x05   0x65           0x06   0x06   0x66           0x06   0x07   0x67           0x06   0x08   0x68           0x06   0x09   0x69           0x06   0x0A   0x6A           0x06   0x0B   0x6B           0x06   0x0C   0x6C           0x06   0x0D   0x6D           0x06   0x0E   0x6E           0x06   0x0F   0x6F           0x07   0x00   0x70           0x07   0x01   0x71           0x07   0x02   0x72           0x07   0x03   0x73           0x07   0x04   0x74           0x07   0x05   0x75           0x07   0x06   0x76           0x07   0x07   0x77           0x07   0x08   0x78           0x07   0x09   0x79           0x07   0x0A   0x7A           0x07   0x0B   0x7B           0x07   0x0C   0x7C           0x07   0x0D   0x7D           0x07   0x0E   0x7E           0x07   0x0F   0x7F           0x08   0x00   0x80           0x08   0x01   0x81           0x08   0x02   0x82           0x08   0x03   0x83           0x08   0x04   0x84           0x08   0x05   0x85           0x08   0x06   0x86           0x08   0x07   0x87           0x08   0x08   0x88           0x08   0x09   0x89           0x08   0x0A   0x8A           0x08   0x0B   0x8B           0x08   0x0C   0x8C           0x08   0x0D   0x8D           0x08   0x0E   0x8E           0x08   0x0F   0x8F           0x09   0x00   0x90           0x09   0x01   0x91           0x09   0x02   0x92           0x09   0x03   0x93           0x09   0x04   0x94           0x09   0x05   0x95           0x09   0x06   0x96           0x09   0x07   0x97           0x09   0x08   0x98           0x09   0x09   0x99           0x09   0x0A   0x9A           0x09   0x0B   0x9B           0x09   0x0C   0x9C           0x09   0x0D   0x9D           0x09   0x0E   0x9E           0x09   0x0F   0x9F           0x0A   0x00   0xA0           0x0A   0x01   0xA1           0x0A   0x02   0xA2           0x0A   0x03   0xA3           0x0A   0x04   0xA4           0x0A   0x05   0xA5           0x0A   0x06   0xA6           0x0A   0x07   0xA7           0x0A   0x08   0xA8           0x0A   0x09   0xA9           0x0A   0x0A   0xAA           0x0A   0x0B   0xAB           0x0A   0x0C   0xAC           0x0A   0x0D   0xAD           0x0A   0x0E   0xAE           0x0A   0x0F   0xAF           0x0B   0x00   0xB0           0x0B   0x01   0xB1           0x0B   0x02   0xB2           0x0B   0x03   0xB3           0x0B   0x04   0xB4           0x0B   0x05   0xB5           0x0B   0x06   0xB6           0x0B   0x07   0xB7           0x0B   0x08   0xB8           0x0B   0x09   0xB9           0x0B   0x0A   0xBA           0x0B   0x0B   0xBB           0x0B   0x0C   0xBC           0x0B   0x0D   0xBD           0x0B   0x0E   0xBE           0x0B   0x0F   0xBF           0x0C   0x00   0xC0           0x0C   0x01   0xC1           0x0C   0x02   0xC2           0x0C   0x03   0xC3           0x0C   0x04   0xC4           0x0C   0x05   0xC5           0x0C   0x06   0xC6           0x0C   0x07   0xC7           0x0C   0x08   0xC8           0x0C   0x09   0xC9           0x0C   0x0A   0xCA           0x0C   0x0B   0xCB           0x0C   0x0C   0xCC           0x0C   0x0D   0xCD           0x0C   0x0E   0xCE           0x0C   0x0F   0xCF           0x0D   0x00   0xD0           0x0D   0x01   0xD1           0x0D   0x02   0xD2           0x0D   0x03   0xD3           0x0D   0x04   0xD4           0x0D   0x05   0xD5           0x0D   0x06   0xD6           0x0D   0x07   0xD7           0x0D   0x08   0xD8           0x0D   0x09   0xD9           0x0D   0x0A   0xDA           0x0D   0x0B   0xDB           0x0D   0x0C   0xDC           0x0D   0x0D   0xDD           0x0D   0x0E   0xDE           0x0D   0x0F   0xDF           0x0E   0x00   0xE0           0x0E   0x01   0xE1           0x0E   0x02   0xE2           0x0E   0x03   0xE3           0x0E   0x04   0xE4           0x0E   0x05   0xE5           0x0E   0x06   0xE6           0x0E   0x07   0xE7           0x0E   0x08   0xE8           0x0E   0x09   0xE9           0x0E   0x0A   0xEA           0x0E   0x0B   0xEB           0x0E   0x0C   0xEC           0x0E   0x0D   0xED           0x0E   0x0E   0xEE           0x0E   0x0F   0xEF           0x0F   0x00   0xF0           0x0F   0x01   0xF1           0x0F   0x02   0xF2           0x0F   0x03   0xF3           0x0F   0x04   0xF4           0x0F   0x05   0xF5           0x0F   0x06   0xF6           0x0F   0x07   0xF7           0x0F   0x08   0xF8           0x0F   0x09   0xF9           0x0F   0x0A   0xFA           0x0F   0x0B   0xFB           0x0F   0x0C   0xFC           0x0F   0x0D   0xFD           0x0F   0x0F   0xFE           0x0F   0x0F   0xFF                      
 
         [0059]      FIG. 7  shows an example digital image  700  and a resultant image plane of codes  720  as produced by an edge identification process  710  as diagrammatically illustrated in  FIG. 6 . The image  700  is a square of pixels each possessing a value of 255 within a field of pixels each possessing a value of 0. The image is input to the edge identification process  710  to produce edge identification codes, each shown in hexadecimal form in the image plane of codes  720 . As can be seen in the example, the codes  720  differentiate inside edge, outside edge, vertical edge, horizontal edge, and positions about a corner. This edge information can be used to direct tinted edge enhancement.  
         [0060]     Below, we describe the halftoning process that is directed by the edge-identification code to perform a halftoning process for the enhancement of tinted edge or a conventional halftoning process.  
         [0061]     The overall halftoning processes utilizes edge-identification codes and a step of halftoning that applies halftoning to edge pixels in a different manner than the halftoning applied to the interior region of the tint or image segment. In rendering the edge pixels it is preferred to use a halftone that is related to the interior halftone by some number of common spatial frequency harmonics. A halftone that is related by common harmonics will avoid the undesirable phenomenon of beats between halftones, which would result in a lower frequency “beaded” appearance at the edge. Examples of common-harmonic screening for an edge may include, but are not limited to, (1) the same screen with different tone reproduction characteristics, (2) the same screen angles and frequencies with a different spot function, possibly phase shifted, (3) a dot screen whose frequency vectors can be generated by the frequency vectors of the interior screen, (4) a line screen whose frequency vectors can be generated by the frequency vectors of the interior screen. It should be noted that for any of the harmonically related screens the phase and amplitude of the edge halftones are parameters that can be optimized for a given marking process and edge orientation (position and angle). Additional insight in harmonically related halftones maybe be found in U.S. application Ser. No. 10/909,627 incorporated by reference above. Examples of rendering edge borders with common harmonic screens are shown in  FIGS. 3, 4 ,  7 ,  9 , 11  &amp;  12 .  
         [0062]     As depicted in  FIG. 8  there is shown a pixel border  800  provided for segment  801  as is delineated by lines  802  and  803 . In the example shown in  FIG. 8 , the contone level for the edge border pixels  800  is boosted by some predetermined amount, resulting in a dilation of the halftone dots. By using the existing (interior) halftone, the beating of two different halftones is avoided while enabling partial compensation for the dot erosion/deletion at the edges, thereby producing sharper tinted fonts and line-art. Similar to existing CRM (Contone Rendering Module) outlining methods, selection of the boost levels is a delicate tradeoff. Boosting that is too conservative results in excessive edge dot erosion, and overly aggressive boosting gives rise to objectionably dark outlines at the segment edges. The compensation (boost) level can be empirically determined from calibration prints that are visually inspected for quality and subsequently implemented in a lookup table (LUT). The boost levels will in general be a function of the original edge levels and surrounding contone levels. The boost level can be separation independent utilizing a 1-dimensional TRC (Tone reproduction Curve) for each color separation, for example four TRC&#39;s for conventional cyan, magenta, yellow, black printing. Or in but one possible alternative, the boost levels can involve utilization of cross-separation terms such as with four, 4-Dimensional-to-1-Dimensional look-up tables for color-separation printing.  
         [0063]     The boosting method has the particular advantage of versatility, since it is TRC driven—the boost TRC&#39;s can be computed off line. Another advantage is separate boost TRC&#39;s can be constructed for each halftone. This is important since edge xerographics can be highly dependent on the halftone frequency and angle, and thus provide different edge erosion characteristics. One exemplary approach uses a single edge boost TRC for each separation (for each halftone), with the edge compensation applied only for tinted text/line-art segments that get overlaid against a white background. In an experiment using this method with the appropriate boost TRC chosen, the text/line sharpness rivaled an existing CRM (Contone Rendering Module) outlining algorithm, and in some cases exceeded it.  
         [0064]     Another class of edge screens useful in addressing the present problem utilizes frequency components that are rotated or flipped about an axis. For example, when using a 170 cpi 15° interior screen, an edge screen rotated by 45° may be beneficial, such as a 240 cpi 60° screen. There is some potential for image quality improvement based on this teaching in combination with U.S. Publication No. 2003/0058474, herein incorporated by reference in its entirety, where screens used at two different orientations were found to solve a different halftone jaggy problem.  
         [0065]      FIG. 9  depicts an example of harmonically related halftones applied to the image segment pixel border  800  where the angles and frequencies employed in the border  300  are rotated 45°, and the frequency increased by the square root of two (√2). In  FIG. 10 , a schematic of a dot screen pair as provided for  FIG. 9  is illustrated. In  FIG. 10 , the low frequency dot screen has a frequency f and an angle α. The high frequency dot screen has a frequency √2 ×f, and an angle of alpha plus 45 degrees (α+45°). The fundamental frequency of the low frequency screen is shown as dark circles. In the high frequency screen those same dots are shown with additional dots placed midway between the dark dots. The two screens have common frequency components, i.e., matched harmonics. As will be appreciated by those skilled in the art, the edge quality is thus improved with the halftone provided in  FIGS. 9 and 10 , especially for lighter text, compared to the image rendered using non-harmonically related halftones. The frequency vector diagram for this configuration is shown in  FIG. 11 .  FIG. 11  shows that the fundamental frequency of the high frequency screen is the same as the first harmonic of the low frequency screen, with the fundamental low frequency being displaced 45° from the first harmonic.  
         [0066]      FIG. 12  schematically depicts harmonically related halftones applied to the image border  800  as per the disclosure where the angles and frequencies employed in the border  800  are frequency doubled. The segment  801  and border  800  employ using two halftone screens with matched harmonics in which the fundamental halftone frequencies of the adjacent halftone dot screens have an integer multiple frequency relationship and the same phase angles. In the image in  FIG. 12 , the border  800  is printed using a dot screen having a fundamental frequency of 212 cpi and angle of 45°. (Note that cpi is defined here as cycles per inch. This could be used as a measure of frequency for line screens or dot screens, but is typically limited in use to dot screens.) The segment  801  is printed using a dot screen having a fundamental frequency of 106 cpi and angle of 45°. The harmonics of the screens are matched, and thus do not produce objectionable beats at their boundary  802 . Note that the frequency of the border halftone screen  800  is 2 times the frequency of the segment halftone screen  801 .  FIG. 13  diagrams how the fundamental frequency vectors for the 212 cpi border at 45° are matched to second harmonics of the 106 cpi segment.  
         [0067]      FIG. 14  schematically depicts harmonically related halftones applied to the image border as per the disclosure where the angles and frequencies employed in the border area  800  are a line screen aligned with one frequency vector of the halftone in segment  801 . The rendering as embodied here is with a dot screen having a fundamental frequency of 170 cpi and angle of 45° for the segment  801  and 170 LPI at 135° line screen for the border  800 . (Note that LPI means lines per inch. Although some experts in the field of halftoning use these units for a measure of frequency for either line screens or dot screens, its use is limited herein to line screens for clarity of discussion.)  FIG. 15  shows the frequency vector diagram for this configuration with the 170 LPI line screen aligned with one axis of the 170 cpi halftone at 45°. Further, it may be desirable that line screen type for the border area  300  to be at a higher frequency multiple than the dot screen.  FIG. 16  provides depiction of harmonically related halftones applied to the image border as per the disclosure above where the angles and frequencies employed in the border are at 2× or a double frequency line screen.  
         [0068]     As will be appreciated by one skilled in the art, the above discussion assumed orthogonal halftone screens because it was simpler to describe the concepts using the assumption that the fundamental frequencies of a dot screen were the same in both directions and the angles between those frequencies were related by 90°. Some halftone screens are constructed based on non-orthogonal cells. The concept of the desirability of matched harmonics still applies. The only difference is that the design must account for the different frequency vectors, and not assume they are the same in both directions.  
         [0069]     The claims, as originally presented and as they may be amended, encompass variations, alternatives, modifications, improvements, equivalents, and substantial equivalents of the embodiments and teachings disclosed herein, including those that are presently unforeseen or unappreciated, and that, for example, may arise from applicants/patentees and others.