DE68915145T2 - Halftone images with error transfer propagation with a phase shift that changes with time. - Google Patents

Description

The present invention relates to multi-level display systems with display elements having relatively few intensity levels and in particular to the adaptation of these systems for the display of grayscale images.

Flat panel systems such as a binary liquid crystal display (LCD) with elements capable of displaying relatively low intensity values do not have many of the disadvantages found in CRT monitor type display systems. In particular, a binary LCD screen does not require an electron gun or a vacuum tube and can therefore be made much flatter than a TV monitor. An LCD screen has low current and voltage requirements and accordingly dissipates relatively little heat during operation, making it particularly suitable for use in high density and portable systems. The hardware is relatively robust and can display the same image for a very long time without risk of damaging the elements.

However, a cathode ray tube can easily display a relatively wide range of intensity values between a minimum and a maximum intensity value. In fact, the input signal to a cathode ray tube display system is usually an analog intensity signal that is effectively graded due to the noise associated with the signal, which limits finer differentiation of the input signal. The advantage of this ability to finely grade intensity is twofold: First, the display produces a relatively accurate description of the shading of the image. For example, the typical signal-to-noise ratios in video signals, the elements in an analog television set are limited to displaying one of 256 values; this is still a relatively finely graded image, and the displayed value of each element is therefore a relatively good approximation of the part of the image being displayed. In other words, the display has good "grayscale" or "halftone" properties. Secondly, related to the first feature, the display has relatively good spatial resolution. Since the elements can follow the image intensity well, intensity changes between adjacent picture elements are also well represented. Therefore, the spatial resolution of the display is limited primarily by the physical spacing of the elements.

The binary LCD display, and more generally LCD-type displays with elements having relatively few intensity levels, have certain disadvantages that offset the advantages of finely graded display systems. For example, a binary LCD element represents each part of the image by being either on or off. This is poor image reproduction if the image is gray at the location represented. In other words, an LCD display inherently has poor halftone properties. Also related to poor halftone properties, the LCD display also has relatively poor spatial resolution. Since the elements are either on or off, the transition from one image to another must be approximated by having adjacent elements either fully on or fully off. This results in the transition being either too abrupt or too spatially blurred. In the latter case, the displayed image has a resolution that is worse than the spatial spacing of adjacent elements.

According to the state of the art, the task has been considered to provide methods for displaying an input signal which is suitable for systems with display elements with finely graded intensity levels on a screen with elements with relatively coarsely graded intensity levels. As described below, the basic problem addressed by these prior art methods is that the number of intensity levels that a picture element can assume is greater than the number that a display element can assume. Therefore, the method transforms a picture element with a relatively finely graded intensity value into a display element with fewer intensity values. As a result of this transformation, in most cases the intensity value of a display element differs from the intensity value of a picture element.

For example, in the case of a standard television picture displayed on a binary LCD screen, the intensity value of each picture element can take on one of 256 values between a minimum and a maximum intensity value, while the corresponding display element has either the minimum or the maximum value. For a picture element with an intensity between the first and the 256th value, it is in some sense an error to display the picture element with the maximum or minimum value. If the intensity of the picture element corresponds to the 128th value, i.e. lies halfway between the minimum and the maximum intensity values, it is a relatively large error to display the display element with the minimum or maximum intensity. On the other hand, for a picture element whose intensity corresponds to the third value, i.e. lies very close to the minimum value, it is a very small error to display the display element with the minimum intensity.

For many years, processing techniques have been developed that attempt to subjectively display a gray image on a binary element display to address the above problem. These techniques all derive from the premise that the eye combines the intensities of a number of closely spaced elements that are either light or dark and therefore perceives a shade of gray.

US Patent 3,937,878, inventor Judice, describes a technique applied to black and white image display in a binary display system ("dither"); the image to be displayed is divided into a matrix of picture elements, each element corresponding to a corresponding cell of the display. Each display cell is assigned a predetermined threshold value. The threshold values repeat according to a pattern, usually in 16 (4x4) square elements, and are equally spaced between a minimum and a maximum value for the image intensity. If the intensity of a particular picture element is greater than the threshold value assigned to the corresponding display cell, that cell is switched on, otherwise it remains switched off.

In such a system, very dark areas do not exceed even the smallest threshold in the 16 square elements, and therefore the displayed area is dark. Similarly, very bright areas exceed even the largest thresholds, and therefore all 16 square elements are turned on. For areas whose intensity is exactly between completely dark and completely bright, 8 of the 16 thresholds are exceeded, and accordingly 8 elements are turned on and 8 remain dark. The eye summarizes this small area and perceives a shade of gray.

Another method for halftoning by error propagation is described by Fawcett and Schrack in "Halftoning Techniques Using Error Correction", Proceedings of the Society for Information Display, 27(4), pp. 305-308 (1986).

Another method for halftone reproduction by error propagation is described in EP-A-0 264 302.

In the error propagation methods for use in binary display devices, the starting point is again a spatially discretely divided image. The amount by which the display element exceeds or falls below the corresponding intensity value for the image is not simply ignored - as in simple threshold value methods - but is added to or subtracted from geometrically nearby image values, which must later be converted into image elements. In the error propagation methods, halftone reproduction is therefore achieved by adjusting nearby elements in order to compensate for the intensity excess or intensity deficit of a given element.

The present invention takes error propagation one step further by applying the concepts described above to mosaic color displays. In a mosaic color display, the element immediately to the right of a given element does not necessarily have to be the same color as the given element; therefore, the error cannot always be propagated to the element that is physically processed next. For example, in a mosaic of same-color diagonals, the closest unprocessed element of the same color is the element below the element immediately to the right of the given element. Therefore, the error propagation technique applied to these color mosaics distributes the error diagonally across the elements. The technique is more complex to implement in hardware if the elements are processed horizontally according to the standard scanning order of video data. In this case, the error of an element must be stored and reused when the diagonally adjacent element is processed.

A major problem with the state-of-the-art error propagation halftoning techniques is poor performance in dark areas, especially when the display elements have only binary capabilities. As the image becomes dark, the "on" elements become rare and clearly visible individually. Linear or herringbone artifacts can also be observed in the techniques that propagate the error along a single path. Isolated "on" pixels in dark areas degrade image quality far more than isolated "off" pixels in bright areas.

In addition, the techniques developed for black and white images must be specially adapted to be successful when faced with the complications posed by mosaic-like color displays, as described above.

The present invention provides a processing method and system in which color images having regions of elements with relatively finely graduated intensity values are displayed on a mosaiced color LCD-type display having display elements with relatively few intensity values. The method of displaying an image according to the invention includes the basic error propagation method for mosaiced color displays described above. As previously described, if the mosaiced color display is patterned so that diagonal rows consist of single color elements, this method propagates the error diagonally between the elements. However, the basic method assumes the "error" propagated to the first element in the diagonal to be zero, or more generally a temporarily fixed, position-independent constant. By an additional feature of the method according to the present invention, called "pixel offset", an "error" is propagated to the first element in the diagonal row, which changes with each new image or frame processed. The "error" propagated into the first element in the diagonal row is also called the "default value". More precisely, the "error" propagated into the first element of each diagonal increases incrementally with each frame processed until the "error" becomes greater than the maximum value for the intensity of the elements. At this point, the propagation starts again by subtracting the maximum value.

In the case of the binary display, the incremental increase in the predictive error value associated with each diagonal results in the spatial drift of "on" elements on the diagonals. This spatial drift of the "on" elements on the diagonals is the "pixel offset"; the result is the perception of a halftone display, since the time-integrated total of the displayed images, if all predicates are equally probable, approaches the exact gray tone image as the number of displayed images increases. If the processing is fast enough that the eye can summarize a number of displayed images of the same input image, the display perceived by the current display approaches the actual gray tone of the input image.

The present invention also achieves color halftone reproduction of the displayed image, which is subjectively a high quality representation of the image. In addition, the present invention uses the rapid succession of displayed images to achieve the subjective high quality halftone reproduction of the display.

In addition, the present invention eliminates artifacts through pixel offset error propagation. Instead of necessarily assigning an element the display intensity corresponding to the "On" state when its image intensity value plus its error value exceeds a threshold value, in the binary case, the displayed pixel is turned on only if there are fewer than a certain number of "off" elements since the last "on" element. Even if the element remains "off" due to the number of previous "off" diagonal elements, it is still considered "on" for the purpose of determining later elements in the diagonal.

FIG. 1 is a flow chart of the processing method according to the present invention.

FIG. 2 is a schematic diagram showing the mapping of picture elements in row 1 to display elements in row 1.

FIG. 3 is a schematic diagram of a standard mosaic color display with like-colored diagonals drawn through each display element.

FIG. 4 is a schematic diagram of a mosaic color image in which the elements are labeled according to the same-color diagonal.

FIG. 5 is a horizontal schematic representation of the mapping process of the m-th diagonally labeled row of the representation according to the present invention.

FIG. 6 is a diagram showing the relative intensity values of the picture elements, the display elements and the threshold levels of the process.

FIG. 7 is a diagram showing relative intensity values as in FIG. 6, where the picture elements on a standard television display can assume one of 256 intensity values, and where the display elements on a binary LCD display can assume one of two intensity values.

FIG. 8 is a diagram showing relative intensity values as in FIG. 6 and also schematically shows the imaging process of a picture element with intensity value I(m,n).

FIG. 9 is a schematic diagram showing the actual physical processing of elements related to the diagonal matrix designations according to the present invention.

FIG. 9A is a schematic diagram showing how, in an actual physical embodiment, the value E is propagated from one element to the diagonally adjacent element.

FIG. 10 is a block diagram of an embodiment of the present invention.

FIG. 10A is a block diagram of another embodiment of the present invention.

FIG. 11 is a schematic diagram showing a change of the preselected error value for the first element in row m for sequentially processed images.

Detailed description of a preferred embodiment of the present invention

The present invention improves on the prior art by using error propagation in mosaic color displays and by systematically varying the error associated with the first element of each diagonal row on which that error is propagated in a mosaic display with same-color diagonals. The systematic variation of the error propagated to the first element in the diagonal "Error" - synonymous with the default value - in the binary case results in the pixel offset or spatial displacement of "on" elements on the diagonal, whereby the integral of display images of a sequence of images or frames over time approaches the actual gray tone of the input images. In addition, artifacts are eliminated by suppressing isolated bright pixels surrounded by dark areas. Although the following description focuses on the case of a diagonal mosaic, the present invention is not limited to mosaics with a pattern of same-colored diagonals.

The present invention addresses two issues: (1) halftoning in mosaic color displays using error propagation and (2) halftoning using pixel shifting. In order to describe the present invention, certain introductory terms related to error propagation need to be described in some detail.

(a) Detailed description of introductory terms related to error propagation techniques

Any error propagation method, including the present invention, can be represented by the flow chart in Fig. 1. Referring to Fig. 1, a portion of an image 2 is shown and divided into an image matrix 4 of matrix elements 6 having discrete intensity values. The matrix indices 1 and p maintain the spatial relationship between image matrix and image. The values of the image matrix elements can be assigned, for example, from a spatially and amplitude graded version of a CRT video signal.

The intensity value of each input matrix element 6 is proportional to the intensity of the brightness of the corresponding region of the displayed image 2. The intensity value associated with each image matrix element is discrete and finite, and the number of intensity values displayed is relatively large considering the number of possible intensity values of the display described below. The number of discrete intensity values that each image element can assume is defined as q.

The intensity values of the image matrix are then converted by a processor 8 into a display matrix 10, with each matrix element 12 of the display having an intensity value. Each matrix element 12 of the display has a spatially corresponding image matrix element 6; therefore, the intensity value of each display element is mapped one-to-one from the intensity of the corresponding image matrix element 6 plus an error value described below.

The number of intensity values that each display element can assume is discrete and divided into steps and is denoted by r. As described above, the present invention applies when the number of intensity values that the display element can assume is less than the number of intensity values that the picture elements can assume; accordingly, the value of r is less than q. Therefore, the method transforms the relatively finely graded intensity value of a picture element into a display element with a smaller number of intensity values. In the case of a standard television picture being displayed on a binary LCD screen, the picture element intensity can assume one of 256 intensity values, while the corresponding display element can assume one of two values (on or off).

Referring to Fig. 2, a schematic representation of one of the horizontal lines, namely line 1, of the image and display elements of Fig. 1. The arrows show that the mapping according to the present invention is one-to-one between the corresponding matrix elements. The processor 8 of Fig. 1 (not shown in Fig. 2) here operates in real time. Such real time processing by the processor 8 is not a necessary prerequisite for the term "error" propagation to apply to the display method, but this characteristic is a preferred embodiment. That is, the processor maps the intensity of one pixel to the intensity value of a display element before the intensity value of the next pixel reaches the input of the processor. If the processor mapped at a slower rate than the input rate of the pixel intensity values, the processor would have to store the backlogged values before processing, which is known in the art as "frame storage." Therefore, in Fig. 2, the intensity value of the first pixel in row 1 is mapped to the corresponding display element before the intensity value of the second pixel reaches the processor. The same applies to the remaining sequence of elements from line 1 and all lines. Thus, the displayed image corresponds temporally to the original image, which was fed to the processor as a temporal sequence of image intensity values.

The sequential processing of all the elements of the 1 lines in Fig. 1 therefore results in the display of image 2 on screen 10 as a sequence of elements 12 with varying intensity values. As an extension, a sequence of images divided into picture elements such as elements 6 in Fig. 1 could be processed sequentially, thereby displaying on the screen a nearly simultaneous sequence of displayed images 10. The display would then change at the same speed, thereby displaying a moving image. The frequency of the input image is defined as the frame rate. Since Since each input image is simply another sequence of intensity values corresponding to the picture elements of the image, it follows from the above description of processing speed that the frame rate is designed so that an entire image is physically processed and displayed before the picture elements of the next frame arrive for processing.

Note that a "frame" represents a "picture" and consists of picture elements with intensity values. In addition, a "new" frame may consist of the same input signals as the previous frame if a display is periodically refreshed for a constant picture.

(b) Detailed description of the basic error propagation technique for mosaic color displays

Referring to Fig. 3, the pixel pattern of a mosaic color display with the same color diagonals is shown. The R corresponds to the red pixels, G to the green pixels and B to the blue pixels. The colors correspond to the primary colors. An analog input signal, or an input signal which has an amplitude with fine steps due to its inherent limitation in terms of signal-to-noise ratio, is usually continuous in time and consists of superimposed signals for each of the three primary color intensities representing the respective region of the analog image. For each discrete spatial subdivision of the input image, ie the temporal subdivision of the input signal and the assignment of a corresponding intensity value to each time interval, there are therefore three separate input amplitudes corresponding to the intensity level of the primary colors of the analog image in the region spatially corresponding to the display element. These three input intensity values are of course separate, but due to the inherent limitation of the signal-to-noise ratio discussed above is divided into fine steps.

Mapping intensity values of color images to display intensity values is therefore not as simple as in the case of monochrome display. The present invention provides two methods for treating an image intensity value consisting of three primary intensity values to be mapped to a display intensity value consisting of a primary color. The first method effectively neglects the image intensity values of the two primary colors that do not correspond to the primary color of the display element. This method is advantageous when the spatial resolution is primarily of interest. The second method effectively temporarily divides temporally adjacent image intensity values into groups of three, averages the image intensity value for each primary color over the three intervals, and transfers the averaged image intensity value for each primary color to the display element that spatially corresponds to one of the image intensity values with the appropriate primary color. This method is advantageous when the exact shade of gray is more important than the spatial resolution.

The present invention includes both methods of treating the input image signal. Since the invention is generally applicable, it is most convenient for the following explanation to assume that the input signal has previously been processed according to one of the two methods described above, so that a finely divided image intensity value with a color corresponding to the basic color of the spatially corresponding display element is to be mapped onto this display element. At present, the same mapping concepts described above with reference to Figs. 1 and 2 can be applied to map a color image represented by a matrix of picture elements with color intensities I(m,n) onto to map a matrix of display elements with color intensities D(m,n), where I(m,n) must now be imagined as the resulting image intensity value of a single primary color, determined according to one of the two methods described above.

In Fig. 3 it can be seen that parallel single-color diagonals can be drawn through all the elements of the mosaic. In Fig. 3 the diagonals are numbered from the bottom left, m=1, up the left side of the mosaic and then lengthways up. In the top left corner the diagonals are numbered so that m=100 is the diagonal in the top left corner. Of course the mosaic-like color display can have a greater or lesser height and 100 was chosen for example purposes only.

Fig. 4 shows an image matrix with matrix elements related to the monochrome pixel diagonals of the mosaic color display of Fig. 3. Since the error propagation method for mosaic color displays perfected by the present invention propagates diagonally between pixels, it is convenient to refer to the matrix of image and display elements diagonally. Therefore, the elements of the "matrix" in Fig. 4 are not arranged in orthogonal rows and columns as in standard matrices. Moreover, each diagonal does not necessarily have the same number of elements as other diagonals. Therefore, it is most convenient to refer to diagonals in Fig. 4 and related figures, with the elements of each diagonal numbered from 1 to n total and designated by n. However, due to the similarities of the elements designated as in Fig. 4 to a standard matrix, the terminology of matrixes will be used in the description. Accordingly, each diagonal is numbered and is the first index of the matrix, and each element of the diagonal is "top" to "bottom" and is the second index of the matrix.

Fig. 4 therefore shows the diagonal rows numbered m, and the elements in the diagonal are numbered from top to bottom with n = 1, 2, .... A part of the picture elements are labeled i(number of the diagonal, position in the diagonal) or i(m,n). The second element in the 98th diagonal is, for example, labeled i(98,2). Note that not all diagonals have the same number of elements; for example, row 1 has only one element, while row 5 has 5 elements. The maximum number of elements in a row, ntotal, is therefore a function of m. As discussed above, each picture element i(m,n) has an associated intensity value I(m,n).

Not shown in Fig. 4 is an identical display matrix with matrix elements d(m,n) that are labeled diagonally just like the image elements in Fig. 4. In addition, each display element d(m,n) is assigned a display intensity value D(m,n) associated with it.

It is noted here and discussed further below that the physical implementations typically process the elements in horizontal rows. Since the error propagates diagonally in the method of the present invention, where the mosaic has diagonals of the same color, the processor must be able to store the error of an element while intermediate elements in the horizontal rows are processed and recall the error when the diagonally adjacent element is ready for processing.

Referring to Fig. 5, the m-th diagonal rows of a colored mosaic image and display matrix are shown as horizontal rows. The lines between the image and display elements represent the one-to-one relationship between image and display matrix elements.

A picture element i(m,n) has an intensity value I(m,n) of q possible values. The display element d(m,n) has an intensity value D(m,n) of r possible values. As described above, the possible number of image intensity values that I(m,n) can assume is greater than the number of display intensity values that D(m,n) can assume. In other words, q > r. The r display intensity values are defined as A1, A2, ..., Ar; thus D(m,n) can be A1, A2, ..., or Ar.

To properly appreciate the present invention, consider the following simple mapping from picture element intensities I(m,n) to display element intensities D(m,n) for each matrix element: Between each of the r display intensity values A1, A2,..., Ar there is a threshold T1, T2 T(r-1); therefore, T1 is between A1 and A2, T2 is between A2 and A3, Tx is between Ax and Ax+1, and T(r-1) is between Ar-1 and Ar. If a picture intensity value I(m,n) is greater than Tx but less than T(x+1), then the display intensity value is D(m,n) = A(x+1). At the limits, if I(m,n) < T1, then D(m,n) = A1, and if I(m,n) ≥ T(r-1), then D(m,n) = Ar.

Fig. 6 shows the relative relationship between the q possible intensity values that I(m,n) can assume, the r possible display values D(m,n) lying between A1 and Ar, and the r-1 threshold values TI, T2 T(r-1). The intensity values I(m,n) are normalized to the range of values between 0 and 1. It can be seen that the g possible image intensity values that each image element can assume are much more numerous than the r possible display intensity values D(m,n) that each display element can assume. In other words, the image elements have Relatively finely graduated intensity values compared to the display elements.

There is an error associated with the mapping described above, which is a basic characteristic of the number of display intensity values r being less than the number of image intensity values q. Figure 7 shows the case where the picture elements can assume one of 256 possible intensity values, as in a television screen, and the display elements can assume one of two possible intensity values, as in a binary LCD display. In this case, q=256, r=2, A1=0, A2=1, and T1 is chosen to be, for example, 0.50. The dashed lines show that all image intensity values between 1 and 256 are displayed with an intensity of 0 or 1. Therefore, the mapping process results in the display element being too bright for image intensity values between 129 and 255 and too dark for image intensity values between 2 and 128.

This error is inherent in any system that maps a relatively finely graded intensity value to a relatively coarsely graded intensity value, which is not necessarily binary. Figure 8 is a zoomed-in view of the possible intensity values near the xth possible image intensity value. The xth and (x+1)th possible image intensity values lie between the thresholds Ty and T(y+1); therefore, if the image intensity value I(m,n) had one of these intensity values, the display element's intensity value D(m,n) would have a mapped intensity value A(y+1) according to the simple algorithm above. On the other hand, the (x-1)th possible image intensity value lies between Ty and T(y-1); according to the simple mapping algorithm, a picture element with intensity level x-1 would have a displayed intensity value Ay.

From Fig. 8 it can be seen that if the picture element has the x-th intensity level, the displayed intensity D(m,n) = A(y+1) is greater than the intensity of the picture element by the amount denoted by z1. Similarly, if the picture element has the (x-1)-th intensity level, the displayed intensity D(m,n) = Ay is smaller than the intensity of the picture element by the amount denoted by z2.

The present invention takes this imaging error into account by means of an error propagation method. Error propagation generally relates to the correction of the intensity values of neighboring display elements due to the over-reproduction or under-reproduction of the image intensity I(m,n) by the intensity D(m,n) of the display. The over-reproduction or under-reproduction resulting from the imaging is the "error" that is passed on to the next image element. The n-th element of the m-th row is generally referred to as (m,n) and is used equivalently to i(m,n). The error passed on to the (m,n)-th element of the matrix is E(m,n).

In an error propagation method in which the error is propagated to the next element in the m-th line, i.e. from the (m,n-1)-th element to the (m,n)-th element, the amount of the over-intensity or under-intensity reproduction resulting from the mapping of the intensity I(m,n-1) of the picture element to D(m,n-1) is subtracted from or added to the intensity I(m,n) of the picture element before I(m,n) is mapped to the intensity D(m,n) of the display element using the mapping method described above.

For example, consider the mapping of the intensity value I(m,1) of the first image element in the m-th row to the intensity value D(m,1) of the corresponding display element. Since - as described above - there are more possible image intensity values q than possible display intensity values r, D(m,1) is normally larger or smaller than I(m,1) by some amount. If this error is passed on to the second element in the m-th row, then E(m,2) = I(m,1) - D(m,1). Note that E(m,2) is negative if the intensity value of the display is larger than the intensity value of the image, and vice versa. Therefore, if there is an excess of display intensity, it is passed on as a negative number, and if there is a deficiency of intensity, it is passed on as a positive number.

If we now consider the mapping of the intensity I(m,2) of the second image element of the m-th line to the intensity D(m,2) of the corresponding display element, the method maps the sum of the intensity I(m,2) of the image element and the propagated error E(m,2) to the intensity D(m,2) of the display element. In other words, the excess or the lack of displayed intensity of the first element is subtracted or added to the intensity value of the second image element before it is mapped to the intensity value of the second display element.

The pixel intensity value I(m,2) plus the propagated error E(m,2) mapped to the display element intensity value is defined as the "corrected pixel intensity value" of the second pixel in the m-th row. The excess or deficiency of displayed intensity over the corrected intensity value is propagated to the next element. In other words, E(m,3) = [I(m,2) + E(m,2)] - D(m,2). In addition, the corrected pixel intensity value, I(m,3) + E(m,3), of the third element is mapped to the intensity value D(m,3) of the corresponding display element.

The remaining elements of the m-th row are mapped analogously. Therefore, for the n-th element of the m-th row, the corrected pixel intensity value I(m,n) + E(m,n) is mapped to the intensity value D(m,n) of the corresponding display element. The propagated error value is E(m,n) = [I(m,n-1) + E(m,n-1)] - D(m,n-1).

(c) Detailed description of the pixel offset

Referring again to the first picture element in row m, i(m,1), in Fig. 5, it was assumed that there was no error value E(m,1) or - which is equivalent - E(m,1) = 0. The present invention further provides a system in which the error value E(m,1) is arbitrarily chosen between 0 and the maximum value that the intensity value of an image can assume. According to the invention, the corrected intensity value of the first element, I(m,1) + E(m,1), is transferred to the corresponding display element D(m,1). Furthermore, the error that is passed on to the second element of the m-th row is the corrected intensity value of the first element minus the intensity value of the corresponding display element or E(m,2) = [I(m,1) + E(m,1)] - D(m,1).

The processing of each element in each row by the inventive pixel offset feature is formally carried out in the same way. For each n-th element, I(m,n) + E(m,n) is mapped to D(m,n). Also, E(m,n) = [I(m,n-1) + E(m,n-1)] - D(m,n-1), except for E(m,1), whose value is chosen.

In the pixel offset method, the value of the default error E(m,1) changes with each frame processed, regardless of whether the image changes from frame to frame or not. More precisely, the value of the default error increases incrementally at each diagonal with each frame processed until until it reaches or exceeds the maximum value of the element intensity, in which case it is reinitialized by subtracting the maximum value. In mosaic-type color displays with diagonals of the same color, the incremental increase in the error associated with the first element of each diagonal results in the spatial displacement of "on" elements on the diagonals in the case of binary display. If all the default errors are equally probable, the total of the displays integrated over time will approach the exact grayscale image as the number of images displayed increases. If processing is so fast that the eye summarizes a number of displayed images for the same input image, the display perceived by means of the current image will thus approach the actual halftone of the input image.

The present invention can therefore be summarized as a method according to claim 1.

Although the above discussion and the following considerations focus primarily on a mosaic-type color display with same-colored diagonals, the invention is not so limited. The invention is well suited to displays with same-colored rows or columns as well as other variations such as a hexagonally coordinated pattern, provided the elements are denoted by the matrix notation (m,n), where m denotes the element groupings for processing based on the particular matrix pattern and n denotes the processing order of the elements of the m-th group.

In addition, the order of the input signals does not necessarily have to correspond to the mapping order of the elements; ie, the mapping process does not have to be in real time. For example, the input signals of a frame can be stored in a memory matrix and can be accessed in the Order of processing by the respective procedure.

The error propagation method for the same-color diagonal display does not necessarily have to propagate the error from one display element directly to the diagonally adjacent element. A simple extension of the method described above would split the error of one display element and distribute it among a number of adjacent elements in the diagonal. Therefore, when processing the nth element of the mth row, the error value E(m,n) would be equal to the sum of a certain percentage of the errors of a number of previous elements in the mth row. For example, the value of E(m,n) may be equal to ½ the sum of the corrected intensities of the previous two elements in the row minus their corresponding display elements. Similarly, E(m,n) would be equal to ½[I(m,n-1) + E(m,n-1)] - D(m,n-1)] + ½[[I(m,n-2) + E(m,n-2)] - D(m,n-2)].

By further extension, the error E(m,n) could be distributed over a number of nearby elements, which do not necessarily have to be on the m-th diagonal. When processing the n-th element in the m-th row, the error value E(m,n) would therefore be equal to the sum of a certain percentage of the errors of a number of nearby, preceding elements in the m-th, (m+3)-th, (m+6)-th, etc. diagonals, since these diagonals have the same color as the (m,n)-th element of the display with single-color diagonals. For example, the value for E(m,n) may be equal to ½[[I(m,n-1) + E(m,n-1)] - D(m,n-1)] + ½[[I(m+3,n+2) + E(m+3,n+2)] - D(m+3,n+2)], where the element (m+3, n+2) is an immediately previously processed element with the same color as the (m,n)th element.

The method according to claim 2 is provided for the "multi-element" and "multi-branching" methods just described.

Note that the propagation coefficients of this method, K(m,m',n,j), are zero except for those few pixels from which an error is propagated.

It should also be noted that the above formulations are not limited to mosaics with same-colored diagonals, but can be applied equally well to mosaics made of other patterns. The elements must of course be denoted by the matrix notation (m,n), where in denotes the element groupings for processing based on the respective mosaic pattern and n denotes the processing order of the elements of the m-th group.

Figure 9 relates the diagonally labeled rows of the matrix model to the horizontal processing of a typical physical embodiment. The diagonal row in Figure 9 corresponds to one of the same color diagonals of the mosaic color display on which the error is propagated in the present invention. It will be seen that the first pixel in the mth diagonal row is the first element physically processed in the horizontal row in which it lies. Since E(m,1) is preselected as described above, the physical process maps I(m,1) + E(m,1) to the corresponding display element D(m,1), not included in Figure 9. The physical process then maps the pixel in the horizontally adjacent position to the (m+1,1)-th element since the electronic signals of the image and display, as mentioned above, typically correspond to a standard raster display. The physical processing continues until the last pixel in the horizontal row is processed and then, starting with pixel (m-1,1), begins with processing the next horizontal row. Only then is the picture element (m,2), the second element in the m-th diagonal row, physically processed.

From the above explanation and from Fig. 9, it is clear that the number of elements in a horizontal line are processed in the physical implementation between adjacent elements in a diagonal row. Therefore, the physical implementation must have means for storing and accurately accessing the value [I(m,1) + E(m,1)] - D(m,1) = E(m,2) so that it can map I(m,2) + E(m,2) after processing a number of intermediate picture elements. One way to accomplish this storage is to have a line buffer with a storage capacity equal to the number of elements in a horizontal line. Since the error must also be propagated to and from the intermediate elements in the horizontal line as they also lie on other diagonal rows, a line buffer the size of a horizontal line is well suited to this function.

The line buffer accomplishes this in a manner analogous to the operation of a FIFO shift register having a size equal to the number of elements in a horizontal row. Referring to Figure 9A, the resulting value E(m,2) of the element 21 being processed is loaded into a buffer 20 before beginning to process the horizontally adjacent element 22. As each of the intermediate elements 23-28 in the scan order is processed, the value of E(m,2) shifts toward the output 30 of the buffer 20 as data corresponding to the error of the intermediate elements 23-28 is input to and output from the buffer 20. When the second element 29 of the m-th diagonal row must be physically processed, the value E(m,2) is available at the output 30 of the buffer 20 where it can be accessed for processing. After processing the resulting error E(m,3), which is propagated to the next element in the m-th row (not shown), is input to buffer 20. While Fig. 9A shows a display with seven intermediate elements, the above analogy applies to displays with more or fewer horizontal elements.

Referring to Fig. 10, an embodiment of the present invention is shown. The embodiment propagates the error in accordance with the method of the invention and has means for storing the error while processing intermediate elements. Since the order of the input and output signals corresponds to the order in standard raster scans from left to right and top to bottom, it is now easiest to think of the elements designated (l,p) as corresponding to the horizontal rows and vertical columns of picture elements. In summary, the intensity value I(l,p) of the picture element designated (l,p) is entered by the input means 42. If l=1 or p=1, then the element is at the top of a diagonal row according to the current naming of the elements, and the error value E(l,p) must be entered in accordance with the present invention. To do this, the default buffer 52 is accessed and E(l,p) is retrieved. If the element under consideration is not located at the top of a diagonal row, i.e. l&ne;1 and p&ne;1, the associated error E(l,p) is retrieved from the error storage means 48. Regardless of how E(l,p) was obtained, it is added to I(l,p) in processing means 50. The means 46 for determining the threshold value is addressed with the sum I(l,p) + E(l,p) and decides between which of the r-1 threshold values described above the sum I(l,p) + E(l,p) lies. The associated threshold value is used by the processing means 50, which outputs the value of a display intensity D(l,p) to the output means 44 according to the threshold value. Due to the horizontal and vertical designation of the elements, the element i(l+1, p+1) is diagonal to i(l,p). Therefore, the processing means 50 also stores the value E(l+1, p+1) = [I(l,p) + E(l,p)] - D(l,p) in the error storage means 48.

The error storage means may be a line buffer having a size equal to the number of vertical columns of the picture elements.

The above method can be applied to a device that generally propagates the error diagonally and is not limited to the specific mapping method described above. The device works with any method of determining D(l,p) based on I(l,p) and E(l,p) and does not necessarily have to use the threshold method of the present invention. Furthermore, the device works with any value of E(l+1 p+1) determined from I(l,p), E(l,p) and D(l,p).

More specifically, the specific embodiment comprises a device according to claim 13.

It also follows that the output means of this device is connected to a display with a colour mosaic pattern, each element of which can assume the intensity values A1, A2, ..., Ar.

An alternative embodiment of the device propagates the error to more than one adjacent element on the diagonal or other diagonals. This device comprises means according to claim 14.

In this embodiment, the partial error storage means could be a number of line buffers.

More generally, the device receives signals in one sequence - not necessarily in the sequence of a standard grid - and maps them according to another sequence. The device then requires a memory matrix 54 between the input means 42 and the processing means 50, as shown in Fig. 10A. This device therefore comprises:

(a) input means receiving a plurality of intensity-coded signals I(l,p) corresponding to a position on the image, where l comprises integers from 1 to ltotal and ltotal denotes groups of elements for processing, p comprises integers from 1 to ptotal and denotes the elements in the l-th group according to their processing sequence, ptotal is a function of l, each intensity-coded signal I(l,p) corresponding to at least one of q image intensity values, where q is at least equal to three;

(b) matrix storage means in which the intensity values of the input image of an entire frame can be stored and accessed;

(c) output means for sequentially outputting a plurality of intensity-coded signals D(l,p) corresponding to the position of the intensity values I(l,p) of the input image, each intensity-coded display signal D(l,p) corresponding to one of r display intensity values A1, A2, ..., Ar ordered by amplitude, where r is an integer less than q and Ax is the x-th display intensity value;

(d) partial error storage means for storing partial error values PE(l,l',p,p') corresponding to an intensity-coded signal I(l,p) obtained from the elements (l',p');

(e) a default buffer means for maintaining a preselected error value E(l,p) corresponding to a number of intensity-coded signals processed;

(f) a processing means for mapping the intensity-coded signals I(l,p) to the intensity signal D(l,p) at the output by

(1) retrieving a value I(l,p) from the matrix storage means;

(2) Fetch the value E(l,p) from the preset buffer if l = 1 or p = 1;

(3) if l ≠ 1 or p ≠ 1, fetch the values PE(l,l',p,p') for all l' and p' from the partial error storage means and sum up the values of PE(l,l',p,p') to obtain E(l,p);

(4) Determine the value D(l,p) based on the values of I(l,p) and E(l,p);

(5) Sending the value D(l,p) to the output device;

(6) Calculate the partial error values PE(a,l,b,p), where (a,b) are the elements to which the error of (l,p) is propagated;

(7) Storing the partial error values PE(a,l,b,p) for all (a,b) in the partial error storage means.

The above device can be applied to mosaic-like color patterns that differ from those with same-colored diagonals, as long as the elements are denoted by the matrix notation (l,p), where l represents groups of elements that are processed based on the particular mosaic pattern of the screen, and p represents the processing sequence of the elements within the group.

In the following discussion, the designations correspond as before to the diagonals of the same-color diagonal mosaic. In other words, in is one of m total single-color diagonals of a mosaic color display, and n is the nth element from the top of the diagonal. Again, the focus is on the same-color diagonal mosaic for example purposes, and the invention applies to mosaic color patterns in general.

For each diagonal row, E(m,1) corresponds to a picture element that is at the physical edge of the picture. There is no need to propagate an error from a previous element because element (m,1) starts a diagonal row. Therefore, as described previously, E(m,1) is selected for each of the diagonal rows. The value can be the same or different for all of the diagonal rows. It can also be changed from picture to picture.

The consequence of changing the error value for the first element E(m,1) of the m-th row on consecutive frames processed by the present invention is that D(m,n) for all of them will change to any or all of them. Referring to Figure 11, the "row" is drawn horizontally, but as in previous figures, the diagonal row m may correspond to a mosaic-like color display or generally to any mosaic pattern. It is assumed that the two particular frames are identical, or that at least the m-th row is the same on the two consecutive frames. In this description, it is further assumed that E(m,1) alternates on consecutive frames between two values between the minimum and maximum values of the image intensity. Since the values of E(m,1) are different, the errors propagated to the subsequent diagonal element will generally be different, since the error associated with the (m,n)th element E(m,n) = I(m,n-1) + E(m,n-1) - D(m,n-1) and the values of I(m,n) between pixels are assumed to be equivalent. Furthermore, the mapping of the display element values D(m,n) at corresponding pixels of the two identical frames may differ, since D(m,n) is mapped from the corrected intensity value I(m,n) + E(m,n) of the nth element and E(m,n) is different at the two identical frames. It is therefore clear that a change in E(m,1) for all in may result in changes in any or all D(m,n).

The alternation of the intensity value D(m,n) of the n-th display element between two intensity values in consecutive identical frames is perceived as an average of the two intensities, provided that the alternation is fast enough. If the threshold is approximately halfway between the two possible display intensity values, then a picture element with an intensity value I(m,n) close to the Threshold is not well represented by either of the two adjacent display intensity values. Alternating between the two adjacent display intensity values, which is more likely with the present method, results in a perceived intensity approximately equal to the threshold or the intensity value of the pixel. Furthermore, for those pixels whose intensity I(m,n) does not border a threshold, a change in E(m,1) is less likely to result in a change in display intensity between successive frames. This is also a good result because I(m,n) is relatively close to a possible display intensity level Ax when it is not near a threshold and because it is well represented by the mapping to Ax.

The above description can be extended so that the error value of the first element E(m,1) of the m-th line changes between more than two values within the range of possible image intensity values for successive frames. As the number of values that E(m,1) can assume with each frame increases, the average intensity D(m,n) of each display element in a sequence of identical frames approaches the intensity value I(m,n) of its corresponding picture element. In other words, if 1000 identical frames were processed and displayed, with E(m,1) chosen randomly for each frame, and if the 1000 frames were processed in such a short time that the eye could not detect a display change, then the display would be perceived as identical to the frame in all respects, especially in grayscale reproduction.

While the above is the fundamental basis for the present invention, the processing speed is not at a stage where such a large number of frames at a rate that is imperceptible to the eye. If E(m,1) were to change between 1000 values for the same frame at today's processing speeds, the eye, instead of perceiving the average of the intensities, would detect the resulting intensity changes of the individual display elements in row m. The specific embodiments described below represent attempts to reconcile the following two conflicting requirements: changing E(m,1) for successive frames to achieve a more accurate display intensity over time, while not changing E(m,1) so much as to detect the changes in the displayed picture elements over time for the same input frame.

In one embodiment of the invention, the error value E(m,1) of the first element in the m-th row for each m is initially unrelated to the value for any other in. Each E(m,1) has an initial value between 0 and the maximum intensity value of the image. For each frame, E(m,1) increases incrementally with each m. If E(m,1) is equal to or exceeds the maximum intensity value of the image, this maximum value is subtracted and the process continues.

In a more specific embodiment of the invention, the display elements can only assume one of two possible intensity values, ie in the general notation above, r=2. A1 and A2 are normalized to 0 and 1 respectively, and T1 is chosen to be ½. The image intensity values correspond to the input values of a television set and can assume one of 256 values between normalized intensity values 0 and 1. For each image, E(m,1) for each m is initially arbitrarily chosen to be either 0 or 0.5. For subsequent images, E(m,1) changes between 0 and 0.5 for each m. This leads to qualitatively good halftone reproduction and is therefore a preferred embodiment.

The advantage of the pixel offset feature of the invention can be illustrated by considering a uniformly dark (non-black) area of the analog image processed according to the above embodiment. Assuming that the intensity of the pixels is less than T1 (or ½), most of the display elements are turned off. If the default error of the mth row is E(m,1) = 0, the error gradually accumulates in the elements in row m until I(m,n) + E(m,n) is greater than T1, and the (m,n)th element is "turned on". However, I(m,n) + E(m,n) is only marginally greater than T1 or ½, while D(m,n) = 1; therefore the error propagated to the (m,n+1)th element is approximately -½. Consequently, there are many "off" pixels in line in addition to (m,n), since the error must add up to more than ½ so that another element is "on". This results in few "on" elements on line m with the same distance.

If E(m,1) were changed to E(m,1) = ½ on the next frame, the "on" elements of the display would be equidistant between the "on" elements of the previous display. This is because all elements of the previous frame with a summed error of zero would now have an error of ½, resulting in an "on" pixel, while those earlier "on" elements with a summed error of ½ would have an error of 0, resulting in an "off" pixel.

If E(m,1) varied between 0 and ½ for consecutive identical images, the present invention would therefore result in a uniform temporal and spatial shift of "On" pixels on the m-th row, with the eye seeing the spatial and temporal average of the "On" elements instead of a few, stationary "On" elements on a black background, namely the result of the time-constant default case.

In another method, the same parameters are chosen as in the embodiment just described. However, E(m,1) is initially chosen randomly between 0 and 1 for each m. On successive frames, E(m,1) for each m alternates between its initial value and either (i) a value that is half the initial value if the initial value is greater than or equal to ½, or (ii) a value that is half the initial value if the initial value is less than ½.

Another feature of the present invention is a technique for suppressing artifacts that is unique to the present invention. Other grayscale rendering techniques in the art are known to eliminate artifacts, but they cannot use pixel offsetting. Artifacts include scattered, isolated "on" pixels in display areas where the image is dark. These "on" pixels are clearly perceived individually and degrade the displayed image quality. Such artifacts are a natural consequence of the error propagation technique of the present invention. This is because the error value of neighboring elements increases even in image areas with an intensity well below the first threshold T1 as the error is propagated to subsequent elements. Eventually, the corrected intensity value of the nth element, E(m,n) + I(m,n), exceeds T1, resulting in D(m,n) = A2 or a bright display pixel in a uniformly dark image area.

The present invention eliminates these artifacts by maintaining a record variable C of when the last display element in the series was displayed with an intensity greater than A1. If (1) the display element under consideration is to be imaged with an intensity A2 using the nominal processing algorithm of the present invention and (2) the record shows that more display elements with an intensity value A1 than a preselected number N have been processed since the last element with an intensity value greater than A1, then the display element is imaged with an intensity value A1 instead of A2. If both conditions are not met, then the display element under consideration is imaged with an intensity A2, which is the result of the nominal processing algorithm of the present invention.

Of course, the counter C is reset every time the display element is displayed or should have been displayed using the nominal algorithm with an intensity greater than A1. Likewise, the counter C is reset when the display element under consideration starts a new line. It should be emphasized that in the removal of artifacts, all processing is done in a manner as described in detail above. The artifact removal feature adds a final decision as to whether the display element is displayed with A1 or A2.

Other side aspects of the present invention suggest themselves. For example, in one embodiment, the intensity values of the display are equidistant from each other and the threshold values are equidistant from adjacent intensity values.

The pixel-shift error propagation technique could also be used for black-and-white displays. Then it would not be necessary to propagate the error diagonally, since horizontally adjacent elements are black or white. The error could be propagated horizontally and the elements could be labeled such that m corresponds to the horizontal rows and n to the vertical columns. Therefore, all i(m,1), i.e. the elements where the error is preselected, would form the first vertical column of the image.

Claims (19)

1. An error propagation method for processing image elements and displaying an image, comprising the following steps: a) providing an image comprising a plurality of picture elements i(m,n), where m comprises integers from 1 to mtotal, n comprises integers from 1 to ntotal, ntotal is a function of m, each picture element i(m,n) has an intensity I(m,n) equal to at least one of q image intensity values, where q is at least equal to three, each pair of numbers (m,n) indicates the position of a picture element on the display plane, and adjacent numbers m or n correspond to adjacent positions; b) providing a display comprising a plurality of display elements d(m,n), each of which has a position corresponding to the position of the picture element i(m,n), and each display element d(m,n) is capable of emitting light with an intensity D(m,n) equal to one of r display intensity values A1, A2 Ar sorted by amplitude, where r is an integer less than q and Ax is the intensity value of the x-th display element; c) defining r-1 thresholds, (T1, T2 ...T(r-1)), where Tx is the x-th threshold; d) Defining an error value E(m,n) for each m and n, where E(m,n) = I(m,n-1) + E(m,n-1) - D(m,n-1) and where E(m,1) for m = 1 to mtotal for each processing of an image independently of neighboring display positions is preselected, and where E(m,1) for m = 1 to mtotal changes at the same rate as that of the frame; e) providing many temporally consecutive images at a constant frame rate, each image being processed and displayed once per frame period, the perceived image being formed by a sequence of temporally consecutive displayed images, and displaying the display pixel d(m,n) for m = 1 to mtotal and for each m for n = 1 total with an intensity (i) D(m,n) = A1, if I(m,n) + E(m,n) ≤ T1, (ii) D(m,n) = Ar if I(m,n) + E(m,n) ≥ T(r-1), or (iii) for r > 2 and T1 ≤ I(m,n) + E(m,n) < T(r-1) D(m,n) = Ax, where x is the value between 2 and r-1 that satisfies the condition T(x-1) ≤ I(m,n) + E(m,n) < Tx. 2. Method according to claim 1, wherein step d) is replaced by the following step: d) Define an error value E(m,n) for each m and n, where where (i) m' is in the range of the designations for the mtotal element groupings for processing, while j for each element in the element group m' lies in the range of the ntotal designations; (ii) K(m,m',n,j) is a propagation coefficient for the error propagation from i(m',j) to i(m,n); (iii) E(m,1) for m = 1 to mtotal is preselected each time an image is processed, independently of adjacent display positions, and E(m,1) for m = 1 to mtotal changes at the same rate as that of the full image. 3. A method according to claim 1 or 2 for suppressing artifacts caused by consecutive picture elements with intensity levels close to the lowest display intensity value A1, comprising the following additional steps: Define a counter variable C and a suppression constant N; for each considered m and n: (i) Setting C=N if n=1, (ii) Displaying the display element intensity value D(m,n) with an intensity value A1 if C< 0 and d(m,n)=A2, (iii) (A) Set C=N if I(m,n) + E(m,n) ≥ T1 (B) Set C=C-1 if I(m,n) + E(m,n) < T1. 4. A method according to any one of claims 1 to 3, wherein the image from the input signal is supplied to a cathode ray tube display, the input signal comprises three superimposed Analog signals corresponding to the intensity of the respective primary color of the image, and the display is carried out by elements for three colors arranged in a mosaic-like color pattern, and wherein I(m,n) is the discrete intensity value of the picture element of the same color of the corresponding display element, wherein I(m,n) is determined from the analog signal of the image area corresponding to the display element d(m,n), wherein the image area is the picture element i(m,n). 5. A method according to claim 4, wherein the display is a mosaic color display with same color diagonals and the display elements d(m,n) correspond to the n total elements in each of the m total same color diagonals of the display, the picture elements i(m,n) also being labeled diagonally to the image to spatially correspond to the display elements d(m,n), the image being one of many temporally consecutive images at a constant frame rate and the image being displayed once for each frame period, displaying a sequence of temporally consecutive, possibly identical images that vary at the frame rate. 6. The method of claim 5, wherein E(m,1) is the same for all m in each of the consecutive images. 7. A method according to claim 6, wherein r = 2, A1 = 0, T1 = A2/2 and the value of E(m,1) for all m alternates with the frame speed between 0 and T1, wherein some or all of the display panel elements D(m,n) have different display intensity values in successive, identical images. 8. A method according to claim 5, wherein the value of E(m,1) for each m in each one of the successive images delivered at the constant frame rate is unrelated to E(m,1) for all others in, where E(m,1) for all m lies between A1 and Ar. 9. A method according to claim 8, wherein r = 2, A1 = 0, T1 = A2/2 and the values of E(m,1) for all in alternate with the frame speed between two values at a distance A2/2 within the range between 0 and A2. 10. The method of claim 5, wherein E(m,1) alternates between two different values for all in each consecutive image. 11. The method according to claim 10, wherein r = 2 and E(m,1) for all in alternates between 0 and T1. 12. Method according to one of claims 1 to 11, wherein the intensity values of the display, (A1, A2,...Ar), have equal distances from each other and the threshold values (T1, T2,..., T(r-1)) between adjacent intensity values have equal distances from each other. 13. Apparatus for displaying an image and processing image elements according to the method of claim 1, comprising: a) an input means (42) which receives in a standard scanning order from left to right and from top to bottom a plurality of intensity-coded input signals I(l,p) corresponding to a plurality of pixels i(l,p) each corresponding to an image position where l comprises integers from 1 to ltotal and corresponds from top to bottom to the ltotal horizontal rows of a raster scan, p comprises integers from 1 to ptotal and corresponds from left to right to the ptotal vertical columns of a raster scan, each intensity-encoded signal I(l,p) corresponding to at least one of q image intensity values, where q is at least equal to three; (b) an output means (44) for the sequential output of a plurality of intensity-coded signals D(l,p) corresponding to a plurality of display elements d(l,p), each display element d(l,p) corresponding to the position of the picture element i(l,p) and each intensity-coded display signal D(l,p) corresponding to one of r display intensity values A1, A2,..., Ar ordered by amplitude, where r is an integer less than q and Ax is the intensity value of the x-th display element; (c) error storage means (48) for storing the error value E(l,p) corresponding to an intensity-coded signal at the input; (d) a default buffer (52) for maintaining a preselected error value E(l,p) corresponding to a number of intensity-coded signals at the input; (e) a processing means (50) for converting the intensity-coded signal I(l,p) at the input to the intensity-coded signal D(l,p) at the output by 1) Retrieving the value I(l,p) from the input means; 2) Get the value E(l,p) from the prefix buffer if l = 1 or p = 1; 3) Fetch the value E(l,p) from the error storage means if l ≠ 1 and p ≠ 1; 4) Determine the value D(l,p) based on the values of I(l,p) and E(l,p); 5) Sending the value D(l,p) to the output device (44); 6) Calculate the value E(l+1, p+1) based on I(l,p), D(l,p) and E(l,p); 7) Storing E(l+1, p+1) in the error storage means (48) 14. Apparatus according to claim 13 for displaying an image and for processing image elements according to the method of claim 2, wherein features (c), (e3), (e6) and (e7) in claim 13 are replaced by the following features: c) partial error storage means (48) for storing partial error values PE(l,l',p,p') = K(l,l',p,p') x [I(l',p') - E(l',p')] corresponding to an intensity-coded signal I(l,p) from elements at the input; e) (3) if l ≠ 1 and p ≠ 1, fetching the values PE(l,l',p,p') from the storage means (48) for Partial error and summing the fourth of PE(l,l',p,p') to obtain E(l,p); (6) Calculate the partial error values PE(a,l,b,p) where (a,b) includes all elements to which the error of (l,p) is propagated; (7) storing the partial error values PE(a,l,b,p) for all (a,b) in the partial error storage medium (48). 15. Apparatus according to claim 13 or 14, wherein the image is supplied from the input signal to a video screen with a cathode ray tube, the input signal comprises three superimposed analog signals corresponding to the intensity of the respective primary color of the image, and the display is carried out by elements for three colors arranged in a mosaic-like color pattern, and wherein I(l,p) is the discrete intensity value of the same-color picture element of the corresponding display element, wherein I(l,p) is determined from the analog signal of the image area corresponding to the display element d(l,p), wherein the image area is the picture element i(l,p). 16. Apparatus according to claim 15, wherein the display is a mosaic color display with same color diagonals and the display elements d(l,p) correspond to the ptotal elements in each of the ltotal same color diagonals of the display, where ptotal is a function of l, the image elements i(l,p) also being labeled diagonal to the image to spatially correspond to the display elements d(l,p). 17. Device according to one of claims 13 to 16, wherein the processor further comprises means (46) for determining threshold values to determine whether an intensity-encoded signal corresponds to an intensity greater than any or all of the r-1 thresholds T1, T2, ..., T(r-1), where Tx is the x-th threshold. 18. Device according to claim 17, wherein the processing means (50) sums the values E(l,p) and I(l,p), accesses the means (46) for determining threshold values and determines the value D(l,p) to (i) D(l,p) = A1 if the means (46) for threshold determination determines that I(l,p) + E(l,p) < T1 (ii) D(l,p) = Ar if the means (46) for threshold determination determines that I(l,p) + E(l,p) ≥ T(r-1) or (iii) D(l,p) = Ax if r> 2 and T1&le;I(l,p) + E(l,p) < T(r-1) where x is the value between 2 and r-1 determined by the threshold determining means (46) that satisfies the condition T(x-1) &le; I(l,p) + E(l,p) < Tx. 19. Device according to one of claims 13 to 18 for suppressing artifacts caused by successive pixels whose intensity levels are close to the lowest display intensity value A1, wherein a counter variable C and a suppression constant N are defined and the processing means (50) further performs the following for each input intensity value of a pixel: (i) Setting C=N if p=l, (ii) if C< 0 and D(l,p) = A2, output of the intensity value A1 to the output means for the intensity value D(l,p) of the display element, (iii) Setting C=N if I(l,p) + E(l,p) ≥ T1, (iv) Set C=C-1 if I(l,p) + E(l,p) < T1.