Abstract: A method is described of processing image data of pixels to be rendered. In the method, image data representing a pixel to be rendered is provided. Criteria or tests are established for processing the pixel in accordance with binary error diffusion or multibit error diffusion. In response to examination of the pixel in accordance with the criteria, a decision is made as to whether the pixel is to be rendered in accordance with binary error diffusion or multibit error diffusion. The pixel is then rendered in accordance with the decision.

Abstract: An image processing apparatus capable of reducing a nonuniform pitch in the sub scanning direction of an image, caused such as by unstable paper feed of a printer, for example, is formed as described below. An adder adds the density value of one pixel of an input multi-valued image and a diffused error output from an error weighting filter. A comparator compares an output from the adder and a corresponding threshold of a variable threshold matrix, and outputs the result as a binary image. The variable threshold matrix is formed of two sub matrices with a size of 3×3 connected in a main scanning direction, and an average value of thresholds in one sub matrix is larger than another. Accordingly, a line component vertical to the main scanning direction is added in an output image. This line component masks a nonuniform pitch in the sub scanning direction.

Abstract: The present invention relates to an image processing method using the error diffusion method to prevent jumps in a highlight part and darkening in a shadow part at high resolution. The image processing method comprises a step of calculating an average value of density values of N×M (N, M>1) pixels, a step of adding the average value and a diffused quantization error value, a step of quantizing the addition result with a predetermined number of tones, a step of selecting a quantization pattern corresponding to the quantization result, and a step of calculating the diffused quantization error value from the quantization error. The error diffusion algorithm has flexibility in outputting dots. In other words, error diffusion processing is performed in N×M pixel units, and a plurality of quantization patterns are provided, and a quantization pattern is selected based on the quantization result.

Abstract: Thresholding is performed on an inputted pixel value using a corrected threshold value in a thresholding unit, and a binarized pixel value is output. The output is inverted, and from the inverted output the threshold value used for the thresholding is subtracted, and the resultant value is distributed to threshold values used for processing of the surrounding pixels. At this time, an input value is added to the value to be distributed (feedback value). Then, in the thresholding of the next pixel, the input value is subtracted from the distributed value, and the result is subtracted from an initial threshold value to derive a value which becomes a threshold value to be used in the binarization. When the input value changes, there is an effect of canceling out the change so that the edge can be weakened.

Abstract: Image data is encoded using a block consisting of a plurality of pixels as a unit of processing. A statistics section extracts statistical information for each pixel value, from a plurality of encoded blocks adjacent to an encoding target block, at each corresponding position within the respective blocks. An encoding processing section performs encoding on the encoding target block using the statistical information extracted by the statistics section. The encoding processing section comprises a prediction section that predicts a value of an encoding target pixel from the selected reference pixel based on the statistical information, a comparison section that detects an error between the predicted value and the value of the encoding target pixel, and an encoding section that performs entropy encoding on the prediction error.

Abstract: Halftoning by error diffusion, enhanced so as to reduce the presence of structural artifacts in the halftoned output while avoiding an artificial increase in halftoning image noise. Specifically, error diffusion according to the invention divides the input gray level intensity range into different segments for purposes of both thresholding and error diffusion. Different error diffusion threshold masks are applied for each respective segment, and different error diffusion weights are applied for each respective segment, with a decision being made as to whether or not to apply a different threshold mask being based on the local image gradient.

Abstract: A method of sending a facsimile of a document includes diffusing a grayscale image to produce a binary, black-and-white image having on/off image values corresponding to a first spatial resolution. When communicating with a remote facsimile device that supports a lower resolution, the black-and-white image is converted to a lower resolution. To perform this conversion, a scaled value for each image value of the lower-resolution image is calculated by interpolating between neighboring dots of the original black-and-white image. The resulting scaled values are then error diffused to create a black-and-white image.

Abstract: An image processing apparatus that can speed the process without degrading the resolution and gradation of the original error diffusion method includes a product sum calculation unit for calculating a weighted mean error E′avexy leaving out the binarization error of an input pixel Ix−1,y, an adder for adding the calculated result of the product sum calculation unit to Ixy to output I″xy, a multiplier 25 for calculating a diffusion error E′x−1,y, from the binarization error Ex−1,y of Ix−1,y to be error-diffused to Ixy, and a comparator for setting the output pixel Bxy to 1 when E′x−1,y≧Th−I″xy is established and to 0 when not established.

Abstract: A system and method for processing image data converts a pixel of image data having a first resolution to a plurality of subpixels, the plurality of subpixels representing a second resolution, the second resolution being higher than the first resolution. The plurality of subpixels are thresholded to generate a group of subpixel values for each pixel and a threshold error value. It is then determined if the group of subpixel values from the thresholding process produce a pattern containing an isolated subpixel. If the group of subpixel values from the thresholding process produce a pattern containing an isolated subpixel, the group of subpixel vales is modified to produce a pattern without an isolated subpixel. The modification process produces a subpixel error value which is compensated for localized error before being diffused to adjacent pixels.

Abstract: A method and apparatus for recursively optimizing the rate control of a hierarchical subband coding system that offers spatial, quality and/or complexity scalabilities. The rate control method recursively adjusts the quantizer scale for each layer of a subband tree, i.e., a subband decomposed image.

Abstract: A method and system implements screening and a high addressability characteristic into an error diffusion process. A grey level value representing a pixel is received. The grey level value has a first resolution which corresponds to an original input resolution. The grey level value is then screened. A threshold circuit thresholds the grey level value and generates an error value as a result of the threshold. A portion of the error value is diffused to adjacent pixels on a next scanline. The screened grey level value can also be interpolated to generate subpixel grey level values which correspond to a second resolution. The second resolution is higher than the first resolution and corresponds to the high addressability characteristic. The threshold circuit would then threshold the grey level value and generate an error value having a resolution corresponding to the first resolution.

Abstract: A method for color image reproduction that includes an image that is defined by a plurality of pixels. A first array of digital values representing the density and placement of the continuous tone colors contained in each pixel of said image is generated. The first array of digital values is processed so as to derive a separate array of digital multi-level color values representing the density and placement of each color for each of the pixels in the image. The processing generates levels and percentage of ink placements for each level change. In one embodiment, the level and percentage of placement within a level change for each of the pixels is derived using an error diffusion method. The error diffusion method includes digitally processing a separate entry array for each multi-level color value so that for each pixel a separate error diffusion array is generated for a plurality of surrounding pixels.

Abstract: Binary coding is provided to a pixel of multi-grading to produce a bi-gradation image. Two adjacent pixels sandwiching a target pixel are determined. Then density differences between the target pixel and the respective adjacent pixels are found. When at least one of these differences exceeds a given value, the target pixel is considered to be part of the edge. When both of the differences are smaller than the given value, the target pixel is considered out of the edge. In the case of the target pixel belonging to the edge, a threshold value at the binary coding is set at a lower value than that of the case where the target pixel is out of the edge. Through the above procedure, an edge reproducibility of a bi-gradation image can be improved.

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 forming apparatus capable of solving problems experienced in the error diffusion method operates in the following manner. An input pixel value is thresholded by a corrected threshold value, and a binarized pixel value is output. From the output value, the corrected threshold value is subtracted, the result is multiplied by a feedback coefficient &bgr;, and the result is diffused to the threshold values of surrounding pixels. As the threshold value and a scale of the pixel value are changed by the processing unit before thresholding, degree of edge enhancement is controlled.

Abstract: A method generates a one-dimensional dither array having a predetermined number of dither values stored at addresses of the array includes the steps of generating a choice size vector and a choice vector. Initializing an address of the dither array, a dither value, and a counter for indexing the choice size vector and the choice vector to zero. Determining if the dither value is equal to the size of the dither array, and terminating if true, otherwise if false continuing with assigning a step a value that is equal to the size of the dither array divided by a current value of the indexed choice size vector, and assigning an offset a value that is equal to the rounded-down integer value of the step divided by two. Assigning the address, modulus the step, equal to the address, plus the offset, plus the current value of the indexed choice vector multiplied by the step.

Abstract: An image processing apparatus providing a halftoning process such as error diffusion prevents an image contour distortion, as follows: data in an image to be processed is used to partially extend the image to be processed. Then error diffusion or the like is employed to provide a halftoning process. The extension is removed to obtain image data. A dot generation delay can be prevented that would otherwise be introduced such as when an extension-free image is halftoned.

Abstract: A system is disclosed for error diffusion dithering. The system includes an input for receiving an input matrix representative of image data, and a plurality of processors. The plurality of processors processes the input matrix and provides output data. Each of the processors is in communication with at least a portion of the input matrix. At least one processor processes a portion of the input matrix defined at least in part by a substantially diagonal edge within the image matrix.

Abstract: There is provided an image processing apparatus, operating as described below, employing an error distribution method to perform a halftone process intensively providing dots to achieve high resolution and a high level of tone representation simultaneously. The image processing apparatus, employing the error distribution method to convert an image represented by multiple values into an image provided in binary representation, employs a distribution weighting coefficient to distribute an error caused at a target pixel to a neighboring pixel. The distribution weighting coefficient simply decreases and ultimately attains zero as the distance from the target pixel increases, and the distance extending to attain zero is also set to vary with direction. Such a distribution weighting coefficient allows a halftone process providing dots intensively.

Abstract: A signal transmission system assigns portions of an image or other type of signal to packets so as to provide an approximate equalization of the signal energy across the packets. As a result, the quality of a reconstructed signal in the presence of a given amount of packet loss is substantially the same regardless of the particular packets which are lost. In one possible implementation, the signal is separated into subbands using a cosine-modulated orthonormal filter bank. The subbands are then assigned to packets in accordance with an energy equalization algorithm such that the cumulative energies of the packets are approximately equal. In another implementation, an image signal is scrambled such that pixels in the image are mapped to different spatial positions, thereby producing a whitened image. The whitened image is then separated into subbands, and the subbands are assigned deterministically to the packets. Similar whitening techniques can be also used with non-image signals.

Abstract: A system and method for source coding a signal to localize transmission errors to a set of samples is disclosed. The signal comprises a plurality of signal elements (SEs) with each SE having a plurality of components. The signal is divided into a plurality of data sets with each data set having a set of SEs. Each SE component of a data set is grouped into a plurality of divisions with each SE component having a plurality of bits. The plurality of bits of the SE components are distributed from the plurality of divisions across a generated bitstream. In one embodiment, this is used in the transmission of video signals over a potentially lossy communications channel.

Abstract: An image processor converts pixel data represented with m gradations into pixel data represented with n gradations by using the error diffusion method. The m and n are both given integers and satisfy 2<n<m. Not only the error but also a weight assigning value is added to pixel data to be converted. The weight assigning value is determined according to the values of m and n.

Abstract: The geometric texture and the graininess of an output image are improved in half tone processing using an error diffusion method. An image processing method where half tone processing is performed on input images using an error diffusion method comprising steps of generating a sine wave where the amplitude and the frequency are modulated according to the average value of the target pixel value and the peripheral pixel values, adding the diffused quantization errors, the target pixel value and the sine wave, quantizing the addition result by a predetermined number of grayscale levels, and calculating the quantization errors of the peripheral pixels from the errors by quantization. By applying a disturbance sine wave by the error diffusion method, diffusion errors can be uniformly dispersed, and geometric texture and graininess can be improved.

Abstract: An apparatus and method to convert input image data having a first multivalue to image data having a second multivalue which is less than the first multivalue by using a multi error diffusion technique. An image processing apparatus includes a threshold generating device for generating a plurality of variable thresholds at least based on a characteristic of a target pixel data, wherein a number of the variable thresholds is less than a number of the second multivalue by one. A quantization device is provided to quantize the input image data of the target pixel into the image data having the second multivalue based on the variable thresholds. The variable thresholds are varied in a manner such that predetermined quantized data quantized by the quantization device does not create noticeable banding substantially in a middle density range and does not create noticeable dropout substantially in a high density range.

Abstract: Image quality is improved when monochrome printing by using an image processing method having a monochrome printing mode and a color printing mode for reproducing a gray image using a plurality of colors in a case where the monochrome printing mode is set. The image processing method includes the steps of inputting gray image data, converting the gray image data into color image data composed of a plurality of color components, performing a quantization process to the color image data, and performing an error diffusion process for distributing a quantization error of the color image data to peripheral pixels of an objective pixel in accordance with a direction set for each of the color components.

Abstract: A method and system implements a high addressability characteristic into an error diffusion process. A histogram of the image is generated and the actual background and black reference values are determined. A gray level value representing a pixel is received. The gray level value has a first resolution which corresponds to an original input resolution. The gray level value is interpolated to generate subpixel gray level values which correspond to a second resolution. The second resolution is higher than the first resolution and corresponds to the high addressability characteristic. A threshold circuit thresholds the interpolated gray level value and generates an error value as a result of the threshold using the determined background and black reference values. The error value has a resolution corresponding to the first resolution. A portion of the error value is diffused to adjacent pixels on a next scanline.

Abstract: An image processing system uses probability error diffusion, and is implemented using a variety of devices capable of reproducing image data including color photo-copy machines, color facsimiles, color printers, black and white printers, and digital printers. The image processing system is employed in a multi-functional peripheral capable of performing several functions. The image processing system identifies which channels in a printing device will print a pixel, and applies error diffusion to those channels. The image processing system determines characteristics of the pixel and subsequently calculates a pixel placement probability, and then applies the error diffusion to the pixel placement probability. Error diffusion may also be applied to a difference between the pixel placement probability and a print probability.

Abstract: A multi-level input image is divided into blocks, each of which is quantized to a bi-level output block. A single quantization error value is calculated for each block, and distributed over neighboring blocks that have not yet been processed. Blocks containing abrupt changes in image content are preferably converted by comparing each picture element individually with a threshold value. Blocks not containing abrupt changes are preferably quantized by comparing the average value of the block with multiple threshold values to determine a multi-level block output value, from which a predetermined pattern of bi-level picture elements is generated.

Abstract: Minimum density pixels are always turned OFF. Maximum density pixels are always turned ON. The binary conversion errors obtained along the main scanning direction based on the maximum and minimum density pixels are subjected to modification processes with using the correction value “a”. Thus, binary conversion errors are gradually converted into the non-uniform value pattern IE[pos]. Accordingly, uniform conversion errors will not be distributed to pixels along each main scanning line. The leading edge S of the middle density region will not receive uniform conversion errors. Turned-On pixels will be generated properly non-uniformly, thereby preventing occurrence of any undesirable textures.

Abstract: An image processing apparatus comprises an error diffusion processing section 10 for performing error diffusion processing with quantization levels of three or above on image data x(i, j) for producing an output; and a second error diffusion processing section 20 for performing error diffusion processing with quantization levels of three or above on the data outputted from the first error diffusion section 10 for outputting image data y(i, j). Quantization levels of three or above of the quantizer 22 in the error diffusion processing section 20 are determined to be desired value. Quantization levels of three or above of the quantizer 12 in the error diffusion processing section 10 are determined to be levels each between each neighboring two of the quantization levels of the quantizer 22, the minimum level of the image input data x(i, j) and the maximum level of the image input data x(i, j).

Abstract: An image processing apparatus includes a threshold value processing circuit subjecting a correction value with respect to an input image data to a threshold value process and outputting an output image data, a subtracting circuit outputting an error signal based on a difference between the correction value and the output image data, an error filter distributing, as a distributing error data dependent on a value of a diffusion matrix, the error signal to neighborhood pixels of a target pixel within the input image data, and a correction circuit multiplying a coefficient to the input image data or the output image data.

Abstract: Error diffusion halftoning in which error diffusion coefficients and/or thresholds vary, and preferably vary based on output error or on image source data plus accumulated error. Varying error diffusion coefficients and/or thresholds is observed to reduce printed artifacts. Preferably, a look-up table is provided, which may be based on output error or based on image source data plus accumulated error, and which directly provides error values for diffusion by adding to adjacent pixels, and which further may provide printer output data.

Abstract: An image processing apparatus including an input unit for inputting multi-valued input image data, a quantization unit for quantizing the input image data input by the input unit into output image data having a number of levels which is smaller than that of the input image data, and a correction unit for correcting a quantization error which occurs during a quantization process of the quantization unit, the correction unit correcting the quantization error by diffusing an error amount into input image data which have not yet been quantized by the quantization unit, wherein the correction unit periodically varies the error amount to be diffused into the input image data within a range of values up to and including the quantization error.

Abstract: To eliminate artifacts resulting from the quantization of images by means of an error diffusion process, a determination is made whether a current pixel being processed is within a shadow or highlight region of an image. If so, a dot of a complementary value is placed in the region only if a distance constraint between the current pixel and neighbor dots is satisfied. If the distance constraint is not satisfied, the placement of the dot is postponed. The distance constraint is based upon the grayscale level of the current pixel. A road map for determining the distance to other dots is defined in a manner such that it expands further from the location of the current pixel as the grayscale value of that pixel approaches the extreme limits of the grayscale range. As a result, a homogenous distribution of dots in highlight and shadow regions of an image is produced.

Abstract: A method and system implements a dynamic error diffusion process. A grey level value representing a pixel is received. An image segmentation circuit determines an image characteristic of the pixel being processed. A threshold circuit thresholds the grey level value (pixel) and generates an error value as a result of the threshold process. A portion of the error value is diffused to adjacent pixels on a next scanline. The distribution of this error value is dynamic in that different sets of weighting coefficients are used based the image characteristic of the processed pixel. One set of coefficients are utilized in processing a pixel having a first image characteristic, and a second set of coefficients are utilized in processing a pixel having a second image characteristic.

Abstract: When gradation values of an original image are converted, a pixel data read unit reads out a piece of pixel data, and a pixel data conversion unit converts the gradation value of the piece of pixel data. A condition judging unit decides whether a pixel corresponding to the piece of pixel data satisfies a predetermined condition, and a data conversion correction unit corrects by a stochastic process the conversion performed by the pixel data conversion unit when the condition judging unit decides that the piece of pixel data satisfies the predetermined condition.

Abstract: A method and apparatus are disclosed which permit halftoning of pixels in an image based upon the relative repulsive forces between a current pixel being halftoned and preferably all previous pixels that have been halftoned. Such arrangements give improved halftoned image quality, at least for some images, compared to that obtained from error diffusion or dithering.

Abstract: A non-causal error diffusion technique that is capable of gray image signals into binary image signals to prevent the occurrence of visible correlated patterns and/or artifacts. In the non-causal error diffusion method, transformation errors produced when great gray level sets of image signals for a certain pixel are transformed into reduced gray level sets of image signals are reflected to the image signals for pixels at non-causal locations with respect to the certain pixel.

Abstract: An image processing apparatus detects, in step 1, whether or not differences between currently supplied image data and image data of a previous pixel are more than a predetermined value m, and identifies a border of a computer-created image or a natural image, where a brightness level differs from the remaining area of the image, when the differences are more than the predetermined value m. Conversely, when the differences are less than the predetermined value m, the image processing apparatus checks, in step 2, whether image data at a pixel before and a pixel two before the current pixel are identical with respect to the color components constituting the color image. When the differences are not all zero, it is checked whether or not the image data at a pixel before the current pixel and the image data at the current pixel are all zero. When the image data are not identical, the color image is identified as being a natural image.

Abstract: An image processing system in which a computer image is halftoned by halftoning a current pixel using error diffusion, with a halftoned output value of the current pixel being determined using errors derived from substantially all previously halftoned pixels of the image. Output error values are determined for each pixel, and are acted upon by an error diffusion mask of geometrically reducing values. In certain instances, previously halftoned pixels are divided into two or more groups to obtain a desired contribution from previously halftoned pixels.

Abstract: A system and method to print grey scale or color images using fewer colors of ink than in the original image. This method distributes the error made at each point (due to the embodied approximation) to the neighbors of that point while obtaining some chosen predetermined patterns for several colors kor grey levels. Getting these predetermined patterns and essentially predetermined patterns for all colors in turn reduces the anisotropic algorithmic artifacts, suppresses edge over-enhancement and allows for good performances on patches of uniform and almost uniform colors or grey levels.

Abstract: When a subject pixel has been turned OFF, an accumulated error value is calculated based on binary conversion. Then, the sum of the accumulated error value and the binary conversion error for the subject pixel is compared with a predetermined value. When the sum is less than the predetermined value, the binary conversion error for the subject pixel is multiplied with a coefficient so that the absolute value of the binary conversion error is decreased. Then, the absolute-decreased error is distributed to unprocessed neighboring pixels according to an error distribution matrix. Then, the binary conversion error for the subject pixel is stored in a working memory as a binary conversion error for the s-th pixel to be used in the process of the next pixel.

Abstract: A multi-level printer is controlled to selectively enhance each pel, based on an error diffusion process. However, each channel (e.g., RGB red, green and blue color channels; Lab luminance, red direction and blue direction channels; or other suitable channel division) is processed individually according to a suitable kernel to provide a multi-color image. The printer is capable of providing a plurality of "actual" levels of enhancement to a pel for any particular channel. The "desired" image defines a "desired" level of enhancement for each pel in each channel. Correlation bins are defined for each actual level of enhancement for associating each "desired" level of enhancement for each pel in each channel with an actual level of enhancement. An error value based upon the selected actual level of enhancement and the desired level of enhancement is diffused to the neighboring pels according to a kernel.

Abstract: A vector error diffusion system for quantizing pixel value in color images, which initially determines whether any pixel should be white or colored, and subsequently determines whether the pixel should be a primary color, a secondary color or black.

Abstract: An image processing device has an error distribution unit, and a multiplier. The error distribution unit carries out an error distribution operation to artificially increase the number of shades to be displayed on a display. The multiplier multiplies an input signal by a multiplication coefficient, so that the input signal is separated into display data and error data along a bit boundary and the error distribution operation is carried out on the input signal. Further, a semiconductor integrated circuit has a dither pattern generator, an adder, and an error distribution unit. The dither pattern generator stores a plurality of dither patterns in advance and receives an input image signal, the adder receives the input image signal and a pattern signal from the dither pattern generator, and the error distribution unit carries out an error distribution operation on the output of the adder. Therefore, the image processing device can realize a smooth display characteristic for the entire range of input shades.

Abstract: A dither method converts multi-bit grey level pixel values into an image array of binary level pixel values, wherein the image array is arranged as a raster of scan lines.

Abstract: The invention relates to the halftoning of grey values of pixels obtained by a photoelectric scanning of an image. The grey values of the pixels for processing are thresholded, the quantisation error which occurs in these circumstances being added to the grey value of an adjacent yet to be thresholded and situated in a first or second direction of the image. The selection of a pixel in the first or second direction is determined in these conditions by the differences in grey values of not more than two pixels arranged in both directions and situated in the vicinity of the thresholded pixel. The pixel is preferably selected in the direction in which the smallest difference in grey value is encountered, i.e. not in the direction of the grey value gradient but exactly perpendicularly to it. It has been found that the edge transitions can be reproduced most sharply in this way.

Abstract: An image data processing apparatus is described that prevents the quality of image data from being degraded by pixel quantity conversion. The apparatus includes an analog processor, a quantity converter and a binarization converter. The analog processor quantizes each of the analog element data to generate multiple-state element data, The quantity converter changes the number of plural pieces of multiple-state element data in one line to generate quantity-converted element data. The quantity converter averages at least two adjacent pieces of multiple-state element data to generate an average value as one piece of new multiple-state element data. The quantity converter further selectively outputs the new multiple-state element data and original multiple-state element data as the quantity-converted element data. The binarization converter binarizes the quantity-converted element data to generate binary element data.

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: Error diffusion algorithms such as the celebrated Floyd Steinberg error-diffusion algorithm are high-performance halftoning methods in which quantization errors are diffused to "future" pixels. Originally intended for grayscale images, they are traditionally extended to color images by error-diffusing each of the three color planes independently (separable error-diffusion). Adding a design rule which is based on certain characteristics of human color perception to the error-diffusion paradigm results in a color halftoning algorithm having output of considerably higher quality when compared to separable error-diffusion. These benefits are achieved by adding the Minimum Brightness Variation Criterion (MBVC) to the design rules of color error-diffusion halftoning methods. Halftone values are constrained to be vertices of a Minimum Brightness Variation Quadruple (MBVQ) associated with each pixel of the color image being processed.