Abstract: This invention describes a method and apparatus for the increasing the robustness of embedded data. Since many times embedded data is susceptible to removal by an unauthorized person, one preferred embodiment enables an action such that removal of the embedded data provides the attacker no gain. In another preferred embodiment, recording devices are required to embed a registration code in copies, thus aiding in tracing illegal copies. Finally, dynamic locking, including modifying and encrypting the auxiliary data and applicable to all data embedding techniques, is shown to provide this robustness to duplication and modification. The apparatus implements the above two processes with a logic processor and storage unit.

Abstract: An image coding and decoding technology for digital movie or video that provides for error checking within the digital video files. The digital video is coded in a data stream that includes key frames and correspondence data between key frames as well as additional correspondence data between somewhat separated key frames. During decoding, an intermediate image generator generates an intermediate frame or frames by interpolation, based on key frame data and correspondence data file between key frames. If an error detector detects an error in an input coded data stream, an error controller instructs the intermediate image generator to perform an error avoidance processing which may include substituting another key frame for an error-containing key frame or use of the additional correspondence data to create the intermediate key frame or frames for an error-containing correspondence data file, and so forth.

Abstract: Methods, devices and systems for overflow error diffusion in image processing are provided. A method includes calculating error values, em, corresponding to differences between modified intensity values for a number of pixel locations and one or more threshold values, where em represents an error value associated with an mth pixel. The method further includes diffusing a calculated overflow error value associated with each calculated error value, em, to at least one pixel neighbor of the mth pixel location.

Abstract: While powerful in diffusion at one resolution to print photos at a finer resolution, the invention is not thus limited. It defines superpixels (“spels”) for each desired colorimetric level, generates/receives image data, renders by finding levels for image positions, and prints an image using selected spels. One invention aspect finds a randomized value at each found level and uses the value to select the spel from plural ones for each level. Another aspect derives/maintains a randomized-value matrix; and maps a matrix location to an image position, to select a random value at that location and spel for that position. Another uses the value in common for all planes to select a spel for each plane at the found level—compatible spels for different planes, to coordinate color placement in planes. Another controls defining/selecting for a blue-noise property of spels in aggregate. In another, spels defined for a level vary in value to yield nonintegral color quanta.

Abstract: A method to reduce coding artifacts within a discrete decoded picture includes a spatial and/or temporal filtering with respective filter characteristics dependent on an image quality value (Q). Preferably, the spatial filtering includes a deblocking filtering, wherein the deblocking filter operation decreases with an increasing image quality value (Q) and/or the deblocking filtering chooses a image quality value (Q) dependent weighting function for a pixel to be filtered according to an activity of both blocks to which common border said pixel belongs.

Abstract: An implementation of a technology, described herein, for facilitating the recognition of content of digital goods. At least one implementation, described herein, derives a probabilistic mirror distribution of a digital good (e.g., digital image or audio signal). It uses the resulting data to derive weighting factors (i.e., coefficients) for the digital good. Based, at least in part on such weighting factors, it determines statistics of the good and quantizes it. The scope of the present invention is pointed out in the appending claims.

Abstract: A printing method and system thereof are described. The locations in a printed image for a plurality of first color (e.g., cyan) dots and the locations in the printed image for a plurality of second color (e.g., magenta) dots are determined. Locations in the printed image for a plurality of third color dots (e.g., yellow) are then determined. The locations for the third color dots are dependent on the locations of the first color dots and the locations of the second color dots. The decision on where to place third color dots is thus made after, and therefore dependent on, the decisions on where to place first color dots and second color dots. Accordingly, color fluctuations in the printed image are minimized, resulting in superior color smoothness and improving the quality of the printed image.

Abstract: According to the embodiment of the present invention, provided is an image error diffusion method for changing, an error diffusion ratio relative to the each pixel of an image. Further, according to another embodiment of the present invention, in order to generate a half tone image that highly correlates with an original image without losing the characteristics of the image, first, the characteristics of the input image are extracted, and then, the obtained results and input/output information are used to adjust, for each pixel, the diffusion state of a quantization error.

Abstract: A method is disclosed for recovering image memory capacity, in relation to an image which has been encoded using a linear transform according to a layer progressive mode into L layers, L being an integer value greater than unity, the L layers being stored in an image memory having a limited capacity. The method comprises defining a Quality Reduction Factor (700), being a positive integer value, identifying at least one of the L layers corresponding to the Quality Reduction Factor, and discarding (702) said at least one of the L layers in progressive order in accordance with the Quality Reduction Factor, thereby recovering said memory capacity.

Abstract: A data driven type processing device has an error diffusion computing unit built therein. An error holding register is provided within the error diffusion computing unit, and is used to successively store and update a value of error information of a pixel that is to be diffused to a neighboring pixel being processed continuously. An error data memory is provided outside the computing unit, and is used to store and update a value of the error information that is to be diffused to another neighboring pixel being processed discontinuously. The error information and the values to be diffused are stored in a packet, and the packet is circulated for operation.

Abstract: An image processing method of quantizing multi-tone image data by an error diffusion method, includes the steps of a) detecting change of the image data; and b) oscillating cyclically in image space a threshold for the quantization in an oscillation range controlled according to the detection result of the step a).

Abstract: An image processing apparatus processes input pixel data and outputs the processed pixel data as output pixel data. The image processing apparatus includes an input reliability calculation section for calculating an input reliability indicating the reliability of the input pixel data, an output reliability calculation section for calculating an output reliability indicating the reliability of the output pixel data, a motion-amount detecting section for detecting the amount of the motion of the input pixel data, a compensation section for compensating the output reliability according to the amount of the motion, and a processing section for processing the input pixel data according to the input reliability and the compensated output reliability and for outputting the output pixel data.

Abstract: Fast transforms that use early aborts and precision refinements are disclosed. When to perform a corrective action is detected based upon testing the incremental calculations of transform coefficients. Corrective action is then performed. The corrective action includes refining the incremental calculations to obtain additional precision and/or aborting the incremental calculations when the resulting numbers are sufficient.

Abstract: In an error diffusion method and an apparatus thereof for a display system capable of preventing errors of pixels of a certain display region for being affected by pixels of other display regions on a PDP (plasma display panel) device or other display devices, the apparatus includes a boundary region recognition unit for recognizing boundaries of displayed regions by a RGB (red, green, blue) input signal and outputting a boundary recognition signal and an error diffusion processing unit for outputting a RGB output signal by computing an error value between a present pixel and surrounding pixels or outputting a RGB output signal by computing only an error value of the present pixel according to the boundary region recognition signal.

Abstract: A method of noise removal from a digital image, especially moiré noise, comprising providing a three-dimensional representation of a at least one image color channel as a surface over the plane of the image, creating a virtual surface patch, placing the surface patch against topography in the three-dimensional surface mapping of the image so that the virtual surface patch intersects topography of the three-dimensional surface with respect to at least some pixels of the image surface region, adjusting the height, tilt and curvature of the surface patch with respect the image surface in order to optimally represent the surface, then estimating a palliative value for the image surface for at least one pixel within the area of the surface patch from the adjustment of the surface patch, and replacing the value of the at least one pixel in the at least one image color channel with the palliative value.

Abstract: An adaptive halftoning method where the difference between a digital image and a filtered digital image is introduced into the system on a pixel by pixel basis is disclosed.

Abstract: A method for estimating a noise characteristic value for a plurality of digital images that are affected by a common noise source includes receiving a plurality of source digital images that are affected by a common noise source, each source digital image including a plurality of pixels; calculating a total number of pixels included in the source digital images; and receiving a predetermined target number of noise estimates to be calculated for the source digital images. The method also includes using the total number of pixels and the predetermined target number of noise estimates to calculate one or more pixel sampling parameters for the source digital images; using the source digital images and the one or more pixel sampling parameters to calculate a predetermined number of noise estimates; and using the noise estimates to calculate a noise characteristic value for the source digital images.

Abstract: A method of image compression comprises the steps of recursively transforming a image using a Discrete Wavelet Transform. This creates a plurality of levels including at least a first level, multiple intermediate levels, and a low-low pass subband of the last level. The transformed image at each level is quantized, and datapacking the quantized image is performed. The step of datapacking further includes, encoding of the first level using adaptive run length of zero cofficients; encoding of the intermediate levels using run-length coding of zero coefficients and a predetermined two-knob huffman table for non-zero coefficients and encoding of the low-low pass subband using a low frequency packing algorithm.

Abstract: This invention produces a realistic defocused image, without using traditional ray tracing technique, by correctly converting the scale of original pixels to the linear scale of amount of light and summing up defocused disks of every pixel in an original image. The result of this process is bright and sparking defocused disks of bright spots previously only possible with rays tracing technique and completely missing in conventional imaging software. This invention enables a personal user to create defocused images in order to create and increase the sense of field depth, which is an important part of daily photographic and imaging work. The input image can be scanned data from photographic films, data from digital cameras, or computer generated images after three-dimensional rendering.

Abstract: An image processing apparatus for quantizing image data indicative of a density gradation level of a constituent pixel of an image into a discrete value on the basis of quantization levels of a number smaller than the maximum density gradation level and not smaller than two.

Abstract: Image sharpening is performed by applying variable contrast stretching to pixels of interest in a digital image. For each pixel of interest, the amount of contrast stretching is a function of minimum and maximum intensity values in a local pixel neighborhood.

Abstract: Digital watermarks are embedded in image data (102)in order to enable authentication of the image data and/or replacement of rejected portions of the image data. Authentication codes are derived by comparing selected discrete cosine transform (DCT) (104) coefficients within DCT data (106) derived from the original, spatial-domain image data. The authentication codes thus generated are embedded in DCT coefficients (612) other than the ones which were used to derive the authentication codes. The resulting, watermarked data can be sent or made available to one or more recipients who can compress or otherwise use the watermarked data. Image data derived from the watermarked data—e.

Abstract: A lower-bit replacement means of an information addition means replaces lower 3 bits of an 8-bit image signal with 3 bits of an image area separation signal, and outputs an 8-bit conversion image signal. A lower-bit extraction means of an information extraction means extracts lower 3 bits of the 8-bit conversion image signal and outputs an image area separation signal as additional information. On the other hand, as regards image information, the conversion image signal input to the information extraction means is output as it is, as an image signal.

Abstract: An edge enhancement method and an edge enhancement apparatus in digital image scalar-up circuit are provided. A band-pass filtering process is performed to an input image pixel in multiple directions to generate multiple sum-of-border values which are summed up to generate an overall sum-of-border value. A first gain and a second gain are provided according to the overall sum-of-border value. A high-pass filtering process and a low-pass filtering process are performed to the input image pixel to obtain border and plain components which are multiplied by the first gain and second gain, respectively. The gained border component and plain component are summed and added to the original pixel to obtain a new pixel.

Abstract: A picture-encoding apparatus provided by the present invention includes a wavelet transformation unit for carrying out wavelet transformation on an input picture to generate wavelet-transformation coefficients, a bit-plane encoding-pass-generating unit for spreading the wavelet-transformation coefficients over bit-planes, an arithmetic encoding unit for carrying out an arithmetic encoding process in an encoding pass, a rate control unit for controlling an encoded-data quantity of the generated arithmetic code so as to achieve a target encoded-data quantity, a header-generating unit for generating a header, a packet-generating unit for generating a packet by addition of the header to the arithmetic code experiencing control of the encoded-data quantity executed by the rate control unit, and an encoded-code-stream-truncating means for truncating an encoded-code stream completing processing through all the encoding passes by discarding a rear portion of the stream so as to make an encoded-data quantity of the st

Abstract: A method and apparatus for enhancing the contrast of an image, where pixels of the image having a brightness less than a mean brightness of the image are transformed in accordance with a first straight-line function, and pixels having a brightness greater than the mean brightness of the image are transformed in accordance with a second straight-line function. Variable slope factors of the two straight-line functions are determined by an analysis of the brightness distribution of the transformed output image. The pixels, thus transformed, produce the contrast-enhanced output image.

Abstract: Methods and apparatus for digital data array edge enhancement are disclosed. A local data window containing a data sample s is selected. Minimum and maximum sample values, max and min, are located within the window, and an edge deflection value ed is defined to have a value between max and min. A diffusion quantity is then calculated to move the value of s towards max, if s is greater than ed, or towards min, if s is smaller than ed. This approach has advantages over gradient-based edge-enhancement, including simplicity, convergence speed, and stability.

Abstract: Tone dependent plane dependent error diffusion halftoning takes into account multiple color planes, such as cyan and magenta, when determining the placement of a dot in any of the color planes. The combined tones of the correlated color planes is used to determine the threshold levels against which the combined tones and the accumulated errors for the correlated color planes is compared. Further, tone dependent error weightings are determined based on the combined tones of the correlated color planes. The tone dependent error weightings are used to diffuse the final accumulated errors for each color plane. A prerendered mid-tone bitmap may be used to break up any structured patterns that occur in the mid-tones. Using this technique, printed dots of two or more colors are dispersed so as to avoid noticeable clumping of dots of two or more colors to provide a more uniform pattern and to avoid the unintentional overlapping of colors. This technique can be used to augment any existing error diffusion method.

Abstract: In accordance with the present invention a method of and a system for enhancing image quality of a coded digital video signal representative of at least one frame in a digital video system are provided. The method comprises the steps of creating a usefulness metric identifying a limit to sharpness enhancement to be applied to the coded digital video signal, defining local spatial features in the frame, and identifying a frame type for the frame. The usefulness metric created in the creating step is: UME = 1 - M * ( 1 + q_scale N ) 2 * q_scale num_bits max ? ( q_scale num_bits ) wherein UME is the usefulness metric, q_scale is a quantization scale for a macroblock, num_bits is a number of bits to encode a luminance block, max is a function representing a maximum value for the frame, and M and N are scaling factors.

Abstract: A method and system for processing an image based on noise appearance in the image, includes the steps of and means for: forming a noise table representing noise magnitude vs. intensity of the image; providing a plurality of potential image processing paths, each path having at least one image transform; modifying the noise table according to the image transform(s) in the at least one image processing path to produce an output noise table, generating a noise metric from the output noise table, said noise metric representing the noise appearance of the image processed by the at least one image processing path; selecting one of the plurality of potential image processing paths based on the noise metric; and applying the selected image processing path to the image.

Abstract: Image defects in a digital image are reduced by a process comprising: providing a digital image data set in the form of a matrix of pixels; selecting a sub-matrix comprising at least a 5×5 matrix of pixels; identifying a pixel within the sub-matrix to be treated as a central pixel; determining a value for at least one optical property in the central pixel; selecting at least four pixels around the central pixel as averaging pixels, at least two of the averaging pixels being in a position in the sub-matrix that is not adjacent the position in the matrix of the central pixel; determining a value for the at least one optical property for the at least four averaging pixels; averaging the values for the at least one optical property for more than one of the at least four averaging pixels to provide an average treatment value for the central pixel; assigning the average treatment value for the central pixel to the central pixel; and storing the average treatment value assigned to the central pixel.

Abstract: A system and method for eliminating absent or poor quality video sections from a video recording, such as a second generation of video recording. Synchronizing pulses associated with a video signal to be recorded are analyzed to determine whether a video signal is present and, further, to determine whether the video signal is not distorted (i.e., non-trick play mode). A recording device is selectively paused in response to the absence of a valid video signal or the presence of a video signal that is distorted, of poor quality or otherwise not worth recording.

Abstract: In order to reduce time required to perform error diffusion processing on one line of image data, one line of multi-tone image data 100 is divided into two or more segments of image data 102 and 103 with an overlapped region 101 provided across the boundary. The two or more segments of image data 102 and 103 are subjected to error diffusion to create binary image data 104 and 105 corresponding to the divided image data 102 and 103, respectively. Then the binary image data 104 and 105 are merged to form binary data 106 corresponding to the original image data of one line. Upon merging the binary image data, binary data b2 obtained from the divided image data 102 located upstream of the line before divided in the direction in which the error diffusion processing progresses is used as binary data corresponding to the overlapped region.

Abstract: A method is presented for marking high-quality digital images with a robust and invisible watermark. It requires the mark to survive and remain detectable and authenticatable through all image manipulations that in themselves do not damage the image beyond useability. These manipulations include JPEG “lossy” compression and, in the extreme, the printing and rescanning of the image. The watermark also has the property that it can detect if the essential contents of the image has changed. The first phase of the method comprises extracting a digest or number N from the image so that N only (or mostly) depends on the essential information content, such that the same number N can be obtained from a scan of a high quality print of the image, from the compressed form of the image, or in general, from the image after minor modifications (introduced inadvertently by processing, noise etc.). The second phase comprises the marking.

Abstract: The present invention is directed toward correcting a corrupted image of an object to remove the effects of smearing or misdirected flux in the image, wherein the image comprises one or more dimensions and has a plurality of image elements. The method of the present invention comprises the steps of: a) sampling portions of the image of the object at unequal intervals, the intervals being selected to effect an implicit weighting of the samples corresponding to a predetermined weighting function; b) summing the implicitly weighted samples to create an approximation to a weighted integral; c) repeating steps a)-b) to compute weighted integrals associated with each of the plurality of image elements thereby to obtain a correction to the image. The present invention is also implemented as a computer readable medium for controlling a computer to implement the steps of the method and in apparatus form.

Abstract: An image processing system includes an image input unit having a plurality of image input channels; a parallel image data processing unit that receives image data from the image input channels of the image input unit, divides the image data received into a plurality of divided data, each divided data including data in a number that is less than a predetermined number, and processes in parallel the divided image data; and a sequential image data processing unit that sequentially processes the divided image data output from the image parallel data processing unit while switching the divided image data for the image input channels.

Abstract: A method for adjusting the lightness/darkness of a binary halftone image includes receiving digital image data defining a binary halftone image in terms of a plurality of light pixels having a first value and a plurality of dark pixels having a second value. If the binary halftone image is to be lightened, the first value for each light pixel is moved in a direction away from the second value by a select amount so that it lies outside of the valid dynamic range. If the binary halftone image is to be darkened, the second value for each dark pixel is moved in a direction away from the first value by a select amount so that it lies outside of the valid dynamic range. Error diffusion is then performed on the binary halftone image to move all pixel values into the dynamic range. In the case of lightening the image, the error diffusion operation converts some dark pixels to light pixels. In the case of darkening the image, the error diffusion operation converts some light pixels to dark pixels.

Abstract: Error diffusion is performed upon input image data. In one aspect, multiple error diffusion processing elements perform error diffusion on a selected pixel in parallel. In another aspect, the error diffusion logic is integrally formed with a fast local memory in the same electronic device, such as an ASIC. The error data produced by the error diffusion logic for a pixel is buffered in the fast local memory until it is to be used by the error diffusion logic on other pixels. In still another aspect, a first-in-first-out (FIFO) buffer regulates or buffers the color image data between the output of a color conversion system, such as a colorant lookup table, and the input an error diffusion processing element. In yet another aspect, the error diffusion logic has tagging logic that produces and stores an indicator, either in the output data stream itself or in a separate area, to indicate whether a raster contains printable data.

Abstract: When a color image is input, a histogram is generated for each primary color, and a luminance value having the highest frequency is obtained. Next, a luminance value that will become a background candidate is decided in the neighborhood of the luminance value having the highest frequency for each primary color. A value equal to or larger than the decided luminance value is defined to be a background candidate. Additionally, a background color is decided within a background candidate luminance area. By replacing the pixels within the background candidate luminance area with the decided background color, a reverse-side visible portion is removed while maintaining the appearance of the background.

Abstract: Optimally determined halftoning algorithms are applied to tone values by selecting among combinations of at least two algorithms that best address the tradeoff between output quality and rendering performance. Input tone values are scrutinized and matched with the algorithm combination that processes the associated tone values in a manner that increases performance (including data compressibility) without sacrificing output quality. The selection process is computationally simple and fast. Reliability is ensured because the combinations of halftoning algorithms are tabulated as a result of analysis of test samples of the printed output.

Abstract: A continuous-tone image data is converted to a bi-level image data by halftoning conversion, then the bi-level image data i.e. binary image data is compressed by compressing means including predictive coding and image data compressing. These operations are done in a image coding apparatus. In this apparatus, when the continuous-tone image is converted into bi-level image data in halftoning so that predictions of predictive coding become strong. As a result, halftoning conversion is performed within a scope of binary image-coding-rules. This permits to produce a binary data easy to compress. Compressing a binary data in a low distortion quality and at a high compression rate is achievable through a method of image coding, and by an image coding apparatus of the present invention. Also a recording medium including a program carrying out this method is obtainable.

Abstract: Disclosed are two novel techniques for digital color halftoning with green-noise stochastic dither patterns generated by homogeneously distributing minority pixel clusters. The first technique employs error diffusion with output-dependent feedback such that the overlapping of pixels of different colors can be regulated for increased color control. The second technique uses a green-noise mask which is a dither array designed to create green-noise halftone patterns. The green-noise mask is constructed to also regulate the overlapping of different colored pixels. As is the case with monochrome image halftoning, both techniques are tunable, allowing for large clusters in printers with high dot-gain characteristics, and small clusters in printers with low dot-gain characteristics.

Abstract: A binary image generating method and apparatus using location information of minority pixels. A modified input pixel value u(m, n) is calculated by adding a value obtained by filtering an error value e(m, n) of a previous binary pixel to a currently input continuous tone pixel value i(m, n). An ideally optimum distance dopt(i(m, n)) between the currently input continuous tone pixel value i(m, n) and a minority pixel is calculated. A minimum distance dm between the input pixel and minority pixels is calculated using location information of the minority pixels at minimum distances from binary pixels adjacent to the input pixel. A threshold value t(m, n) is calculated using the ideally optimum distance dopt(i(m, n)) and the minimum distances dm for the currently input continuous tone pixel value i(m, n). The threshold value t(m, n) is compared with the modified input pixel value u(m, n) to determine a binary pixel value b(m, n) of the input pixel.

Abstract: A display apparatus is composed of a pseudo gray level data processor generating pseudo gray level data having m bits based on input gray level data having n bits. The pseudo gray level data processor includes a state variable generator generating a state variable data having n−m bits, based on lower n−m bits of the input gray level data, an adder calculating a sum of the lower n−m bits of the input gray level data and the state variable data to output a carry bit representative of carry-over of the sum, and a pseudo gray level data calculator generating the pseudo gray level data based on the input gray level data and the carry bit.

Abstract: A method for implementing error diffusion on a plasma display panel (PDP) comprises the steps of performing an anti compensation process on a received video signal of the PDP; diffusing an error generated by a first one of a plurality of pixels to a plurality of adjacent pixels; absorbing errors generated by the plurality of adjacent pixels by the first pixel; and multiplying each of a plurality of numeric weightings and the error of each of the adjacent pixels to obtain an error function of the first pixel. This is effected in a cost effective while simple addition circuit for solving the problem of low level contouring in PDP due to insufficient gray scale of video signal in low gray scale.

Abstract: An error adding portion adds together input multi-tone image data and peripheral error information. An adding/subtracting portion adds to or subtracts from multi-tone image data calculated by the error adding portion, a random number in a matrix prepared for each set of pixels of the input multi-tone image data. A quantizing portion quantizes multi-tone image data calculated by the adding/subtracting portion into image data, the number of bits of which image data being smaller than the number of bits of the multi-tone image data calculated by the adding/subtracting portion. An error calculating portion calculates an error based on the multi-tone image data calculated by the error adding portion and the image data quantized by the quantizing portion. An error storing portion stores the error calculated by the error calculating portion for each peripheral pixel.

Abstract: Error addition section 201 generates correction data by adding correction value Emo and correction value E1 to the input data. Binary processing section 202 converts the correction data to binary data to generate output data. Binary error calculation section 203 calculates binary error E based on the correction data and output data. Propagation coefficient judgment section 204 judges propagation coefficients K1 to K4. Propagation error operation section 205 operates on binary error E and propagation coefficients K1 to K4 to calculate correction value E1 and correction value Emi. Error memory 206 temporarily stores correction value Emi, and outputs it to error addition section 201 when the pixel data to be corrected is input.

Abstract: A method and apparatus for multi-level color error diffusion employs semi-vector quantization. When operating on image data comprising three color separations, the method employs a vector quantization for the two separations with the most visually perceptive color output to generate a multi-level output pixel for each separation based on the sum and a difference of the input pixel values for the two separations. The method generates multilevel output pixels for the third color separation using scalar error diffusion.

Abstract: A system for simulating grayscales in a digital printer, such as an ink-jet printer, exploits a modified error diffusion technique. When a datum for a particular pixel in an image is 0, the datum is substituted with a low-level artificial datum such as 4 on a scale from 0 to 255. The addition of the artificial datum in the error diffusion algorithm avoids artifacts caused by the presence of large number of zeros in the error diffusion algorithm.

Abstract: A method for enhancing printing quality to process the picture and textual data in an image properly such that both the picture and textual data can be clearly printed. The inventive method can treat the image data to be printed in a real time fashion and while the entire image data is not required. In the inventive method, the difference of gray level is reallocated by error diffusion method to render the edge more smooth and clear.