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Showing papers on "Grayscale published in 1995"


Journal ArticleDOI
TL;DR: Although some numerical measures correlate well with the observers' response for a given compression technique, they are not reliable for an evaluation across different techniques, and a graphical measure called Hosaka plots can be used to appropriately specify not only the amount, but also the type of degradation in reconstructed images.
Abstract: A number of quality measures are evaluated for gray scale image compression. They are all bivariate, exploiting the differences between corresponding pixels in the original and degraded images. It is shown that although some numerical measures correlate well with the observers' response for a given compression technique, they are not reliable for an evaluation across different techniques. A graphical measure called Hosaka plots, however, can be used to appropriately specify not only the amount, but also the type of degradation in reconstructed images.

1,660 citations


Journal ArticleDOI
TL;DR: Two methods for automatically locating text in complex color images that computes the local spatial variation in the gray-scale image, and locates text in regions with high variance are presented.

362 citations


Book
01 Jan 1995
TL;DR: This paper presents two new extraction techniques: a logical level technique and a mask-based subtraction technique, suggesting its suitability for high-speed low-cost applications.
Abstract: The extraction of binary character/graphics images from gray-scale document images with background pictures, shadows, highlight, smear, and smudge is a common critical image processing operation, particularly for document image analysis, optical character recognition, check image processing, image transmission, and videoconferencing. After a brief review of previous work with emphasis on five published extraction techniques, viz., a global thresholding technique, YDH technique, a nonlinear adaptive technique, an integrated function technique, and a local contrast technique, this paper presents two new extraction techniques: a logical level technique and a mask-based subtraction technique. With experiments on images of a typical check and a poor-quality text document, this paper systematically evaluates and analyses both new and published techniques with respect to six aspects, viz., speed, memory requirement, stroke width restriction, parameter number, parameter setting, and human subjective evaluation of result images. Experiments and evaluations have shown that one new technique is superior to the rest, suggesting its suitability for high-speed low-cost applications.

204 citations


Patent
Allen L. Frazier1
09 Jun 1995
TL;DR: In this article, a pixel in the array is analyzed in a transformation (window) to determine the pulse pattern output based on the gray level value of the current pixel and on the grey level values of adjacent vertical (44, 52) and horizontal pixels (46, 50).
Abstract: Gray scale input data (24) are received as an array of pixels, in the native engine resolution, including multi-bit per pixel gray level values. A pixel in the array is analyzed in a transformation (window) (28) to determine the pulse pattern output based on the gray level value of the current pixel (48) and on the gray level values of adjacent vertical (44, 52) and horizontal pixels (46, 50). The pulse pattern output for driving the marking engine (22) in the current pixel location (48) is adjusted by the transformation to produce sub-pixel sized marks (98) of various shapes, sizes, positions, and orientations that, in combination with neighboring marks so produced, provides for the flexible production of marking patterns that contain a number of gray scale levels substantially exceeding the number of gray scale levels contained in the input data (24), and that enhance the simulation of graphic features produced.

98 citations


Patent
22 Feb 1995
TL;DR: In this article, a personal imaging computer system, which is connectable to and operable with a computerized local or wide area network, identifies characters in a document on which the characters are formed.
Abstract: A personal imaging computer system, which is connectable to and operable with a computerized local or wide area network, identifies characters in a document on which the characters are formed. The system scans the document to obtain a gray-scale image of the document, generates a binary image from the gray-scale image by comparing the gray-scale image with the threshold, segments the binary image to locate individual characters within the binary image and to determine the shape of the individual characters, extracts gray-scale image information from the gray-scale image for each such individual character based on the location and shape of the character in the binary image, recognition-processes the extracted gray scale image information to determine the identity of the character, and stores the identity of the character.

87 citations


Book ChapterDOI
13 Sep 1995
TL;DR: This paper considers image rotations and translations and presents algorithms for constructing invariant features and develops algorithms for recognizing several objects in a single scene without the necessity to segment the image beforehand.
Abstract: Invariant features are image characteristics which remain unchanged under the action of a transformation group. We consider in this paper image rotations and translations and present algorithms for constructing invariant features. After briefly sketching the theoretical background we develop algorithms for recognizing several objects in a single scene without the necessity to segment the image beforehand. The objects can be rotated and translated independently. Moderate occlusions are tolerable. Furthermore we show how to use these techniques for the recognition of articulated objects. The methods work directly with the gray values and do not rely on the extraction of geometric primitives like edges or corners in a preprocessing step. All algorithms have been implemented and tested both on synthetic and real image data. We present some illustrative experimental results.

85 citations


Proceedings ArticleDOI
23 Oct 1995
TL;DR: The extended perceptual model accounts for: (1) contrast sensitivity as a function of spatial frequency, mean luminance and spatial extent, (2) luminance masking, and (3) contrast masking.
Abstract: The goal of numerous digital image processing algorithms is to reproduce an image as accurately as possible given some specific restrictions. For example, in digital image halftoning, a gray scale version of an image needs to be approximated by a high spatial resolution binary image. Likewise, lossy image compression seeks to reconstruct an image from a minimally coded description of the original. In these and many other applications, image fidelity is determined by the human observer; hence, the effectiveness of the algorithm is measured by the extent to which reproduction errors are visible. As a result, a model that predicts human perceptual sensitivity to image distortion is beneficial to both the design and evaluation of many such image processing algorithms. This summary briefly describes an extension of our work on perceptual image distortion. Our extended perceptual model accounts for: (1) contrast sensitivity as a function of spatial frequency, mean luminance and spatial extent, (2) luminance masking, and (3) contrast masking.

76 citations


Journal ArticleDOI
TL;DR: The integrated function Algorithm for binarization of gray level document images is improved by smoothing, a new print pixel identification strategy, and a postprocessing step removing false print objects.

73 citations


Journal ArticleDOI
TL;DR: This paper proposes a new method for the direct extraction of topographic features from gray scale character images by computing the directions of principal curvature efficiently and prevented the extraction of unnecessary features.
Abstract: Optical character recognition (OCR) traditionally applies to binary-valued imagery although text is always scanned and stored in gray scale. However, binarization of multivalued image may remove important topological information from characters and introduce noise to character background. In order to avoid this problem, it is indispensable to develop a method which can minimize the information loss due to binarization by extracting features directly from gray scale character images. In this paper, we propose a new method for the direct extraction of topographic features from gray scale character images. By comparing the proposed method with Wang and Pavlidis' method, we realized that the proposed method enhanced the performance of topographic feature extraction by computing the directions of principal curvature efficiently and prevented the extraction of unnecessary features. We also show that the proposed method is very effective for gray scale skeletonization compared to Levi and Montanari's method. >

72 citations


Patent
18 Jul 1995
TL;DR: In this article, a method of displaying characters on a pixel oriented grayscale display device having a predetermined pixel resolution employing parametric, geometric glyph descriptors is disclosed, which supports a client process that passes a request for a particular font and a physical character height for the displayed characters as well as the physical resolution expressed in pixels for unit length.
Abstract: A method of displaying characters on a pixel oriented grayscale display device having a predetermined pixel resolution employing parametric, geometric glyph descriptors is disclosed. The process supports a client process that passes a request for a particular font and a physical character height for the displayed characters as well as the physical resolution expressed in pixels for unit length. A character space height value in pixels is determined and compared to selected values to determine whether the character space height in physical pixels falls into one of three distinct ranges. If within the smallest range, no hinting or grid fitting is performed and the physical pixel coordinates of a scaled glyph descriptor are scan converted using subpixel coordinates. The on subpixels within each pixel are counted to provide a grayscale value for illuminating that particular pixel. If the character space height is in the highest range, the same process is performed after the scaled glyph descriptor is hinted to physical pixel boundaries. Character space heights in the mid range are hinted to the physical pixel boundary but scan converted using a conventional scan converter for the physical pixel space. The on pixels that result from this scan conversion are then illuminated to the maximum grayscale value while off pixels from the conversion are left off. The values of the variables that define the ranges are user selectable and may be varied in response to other parameters.

69 citations


Journal ArticleDOI
TL;DR: A cryptographic scheme for encrypting 2-D gray scale images by using a large family of fractals based on a transposition of the image elements implemented by a generator of 2- D hierarchical scanning patterns, derived from a parailel algorithm implementing the creation of the family of scanning patterns.
Abstract: We present a cryptographic scheme for encrypting 2-D gray scale images by using a large family of fractals. This scheme is based on a transposition of the image elements implemented by a generator of 2-D hierarchical scanning patterns producing a large subset of the (n2)! possible orders defined on a 2-0 image of n x n elements. Each pattern defines a distinct order of pixels and can be described by an expression, which is considered as the key of the transposition. This transposition cipher can easily be combined with various substitution ciphers, producing efficient product ciphers operating on pictorial data. Two such ciphers are constructed and their effects on real gray value images are shown. Encryption and decryption algorithms are derived from a parailel algorithm implementing the creation of the family of scanning patterns.

Journal ArticleDOI
TL;DR: The proposed GSHT with a gray-scale image as the direct input removes this shortcoming, requiring neither preprocessing nor postprocessing step in detecting bands in agray- scale image.

Proceedings ArticleDOI
21 Apr 1995
TL;DR: An automatic method of face feature detection using a method called edge pixel counting, which utilized the edge information to estimate the face feature positions in the first frame of a moving facial image sequence, using a variable size face feature template.
Abstract: Detection and tracking of facial features without using any head mounted devices may become required in various future visual communication applications, such as teleconferencing, virtual reality etc. In this paper we propose an automatic method of face feature detection using a method called edge pixel counting. Instead of utilizing color or gray scale information of the facial image, the proposed edge pixel counting method utilized the edge information to estimate the face feature positions such as eyes, nose and mouth in the first frame of a moving facial image sequence, using a variable size face feature template. For the remaining frames, feature tracking is carried out alternatively using a method called deformable template matching and edge pixel counting. One main advantage of using edge pixel counting in feature tracking is that it does not require the condition of a high inter frame correlation around the feature areas as is required in template matching. Some experimental results are shown to demonstrate the effectiveness of the proposed method.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Patent
Joseph Shu1
11 Oct 1995
TL;DR: In this paper, an adaptive filtering and thresholding arrangement provides a set of error filters (930A-C) having different sizes and associated weighted coefficients for diffusing quantization errors among neighbouring pixels in predetermined tonal areas of an image to achieve a smooth halftone image quality.
Abstract: An adaptive filtering and thresholding arrangement provides a set of error filters (930A-C) having different sizes and associated weighted coefficients for diffusing quantization errors among neighbouring pixels in predetermined tonal areas of an image to achieve a smooth halftone image quality. Each error filter circuit is optimally applied to a particular pixel area depending upon the grayscale tone of that area and the desired output print resolution. The arrangement further provides for the addition of "noise" errors to threshold values at selected input image pixel ranges and at the intersection of two differently filtered areas to eliminate visible pattern distortion.

Patent
05 Oct 1995
TL;DR: In this paper, a method and apparatus for processing a greyscale input of an image, particularly of a shipping label, into a binary output image in which foreground information is segmented from the background information and contrasts between adjacent regions having different background densities are obliterated is described.
Abstract: A method and apparatus for processing a greyscale input of an image, particularly of a shipping label, into a binary output image in which foreground information is segmented from the background information and contrasts between adjacent regions having different background densities are obliterated is described. A neuron employing a 5 x 5 input neighborhood having a unique neuron activation function is shown. No explicit line process is employed. Output is biased toward a particular one of the output values by employing non-linear feedback as a function of both the grey scale value for the pixel corresponding to the label site being updated and the most recent value of the label site. The otherwise strong contribution from a gradient term in the energy function is suppressed by a shunting inhibition when the shunting inhibition function detects that the pixel lies on or near a boundary between adjacent regions of differing background intensities.

Patent
14 Jul 1995
TL;DR: In this paper, a sensor assembly consisting of three separate rows of optical sensors is used for color and gray scale scanning, where two of the rows have color filters and one is unfiltered (receptive to white light).
Abstract: A sensor assembly and an optical image color scanner using the sensor assembly. The sensor assembly is of the type having three separate rows of optical sensors. Two of the three sensor rows have color filters and one is unfiltered (receptive to white light). For gray scale scanning, only the unfiltered (white) sensor row is used, thereby maximizing the speed of gray scale scanning. For color scanning, three color values are computed as a linear transformation of values from the two filtered and one unfiltered values. The linear transformation may be as simple as subtracting signals from the two filtered sensor rows from the signal from the unfiltered (white) sensor row. For color scanning, memory buffers are required for two of the three sensor output signals. For highest accuracy in color scanning, the exposure time for the white sensor row is reduced relative to the exposure time for the two filtered sensor rows. An optional white channel bandpass filter (passing all wavelengths within the human visual range and rejecting wavelengths outside the human visual range) provides improved accuracy if the light source has significant wavelengths outside the human visual range.

Patent
27 Dec 1995
TL;DR: In this paper, a self-luminous display panel driving system is presented, where one field of a composite video signal is divided into N sub-fields, and the luminance of each pixel is set by pixel data.
Abstract: In a self-luminous display panel driving system, one field of a composite video signal is divided into N sub-fields, and the luminance of each pixel is set by pixel data. The pixel data comprises N bits corresponding to the number of the sub-field. The present pixel data of a pixel is compared with the prior pixel data of the same pixel. A change between the bit data of the highest luminance and the bit data of a luminance of one digit lower is detected. An inter-frame change signal is produced when a change is detected. In response to the inter-frame change signal, the present pixel data is corrected so as to change the sub-field of the present pixel data.

Proceedings ArticleDOI
11 Aug 1995
TL;DR: It is shown in the paper that using the dynamics comes down to measuring the persistence of image minima when processing the image via a increasing family of contrast filters, and a symmetrical equivalent for the dynamics is defined and an efficient technique of computation is proposed.
Abstract: Image extrema are often used for locating the structures present in an image. Their extraction and their selection is a classic image segmentation preprocessing problem. One of the most powerful morphological tools for selecting significant extrema in a grayscale is to use their dynamics. However, a drawback of this technique is that minima and maxima (the dark and light structures they point out) are processed independently. We show in the paper that using the dynamics comes down to measuring the persistence of image minima (resp. maxima) when processing the image via a increasing (resp. decreasing) family of contrast filters. This principle can be generalized to any increasing family of morphological filters by reconstruction and leads to a general method for valuating image minima with respect to any criterion: size, shape, contrast. This proposition is still true for families of alternating filters whose main characteristic is to have a self dual behavior. In this paper we concentrate on this point. A symmetrical equivalent for the dynamics is defined and an efficient technique of computation is proposed. One of its key concept is a merging tree of extrema. The usefulness of this notion in image segmentation applications is also illustrated.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Dissertation
01 Jan 1995
TL;DR: The essential scale-space causality property for local extrema of a signal under this operation is proved and it is shown that structuring functions from the "elliptic poweroids" lead to favourable dimensionality and semi-group properties.
Abstract: This thesis develops and demonstrates an original approach to scale-space theory. A new scale-space theory based on a unified multiscale morphological dilation-erosion smoothing operator is presented. The essential scale-space causality property for local extrema of a signal under this operation is proved. This result holds for signals on $\IR\sp2$ and higher dimensions and for negative as well as positive scales. When applied to grayscale images we show that structuring functions from the "elliptic poweroids" lead to favourable dimensionality and semi-group properties. Paraboloids, in particular, allow efficient computation of the scale-space, and such an algorithm is presented. The generalised frequency response of this signal smoother, which is similar to that of a Butterworth filter (with an amplitude dependent corner frequency), is obtained. The filter is statistically characterised by obtaining second-order statistical properties of the output signal with independent and identically distributed uniform noise input. Similar scale-space results are obtained for the multiscale morphological closing-opening operator, and we show that the resulting scale-space fingerprints are identical to those of the dilation-erosion. To demonstrate the utility of the new theory, we present an approach for the recognition of multiple 3-D objects in range data via the local matching of surfaces. In this approach the reduced morphological scale-space fingerprint is used as the primitive for matching. The resulting recognition process is invariant to translation, rotation, limited scaling, and partial occlusion. The results of the proposed object recognition method showing the recognition of a scene containing nine faces at various positions, angles and scales is presented. In a second demonstration we show the recognition of eight mountains in a digital elevation map.

Patent
Douglas N. Curry1
05 Jun 1995
TL;DR: In this paper, a method for generating halftone image cells based on grayscale image data values is described, where each of the cells is formed from serpentine dot patterns.
Abstract: An apparatus and method for producing a halftone image which generates halftone cells based on grayscale image data values. Each of the halftone cells is formed from serpentine dot patterns. The serpentine dot patterns form two separate arcs. The halftone cells are written onto a recording medium to produce the halftone image. Rotation of the halftone cells allows data to be encoded within each of the halftone cells without varying the tone of the image. The tone of the image may be controlled by selectively varying a thickness of the arcs within the halftone

Journal ArticleDOI
TL;DR: A new approach to grayscale font generation improves on the fuzzy characters produced by existing methods by incorporating the expertise of type designers into rules for character-outline weight and phase control.
Abstract: A new approach to grayscale font generation improves on the fuzzy characters produced by existing methods by incorporating the expertise of type designers into rules for character-outline weight and phase control. The method we propose for synthesizing high-contrast grayscale characters relies on the set of visual rules that type designers have derived from their many years of manual design. We call our grayscaling method 'perceptually tuned font generation', because it is based on human perception-that of both the designer and the reader. >

Patent
24 May 1995
TL;DR: In this paper, a method for charging select pixel elements of an active matrix liquid crystal display to gray scale voltage levels is described, and the pixel elements in each enabled row which are to be charged to the first grey scale voltage level are selected.
Abstract: A method of and apparatus for charging select pixel elements of an active matrix liquid crystal display to gray scale voltage levels is disclosed. Which of the pixel elements of the display are to be charged to a first gray scale voltage level is determined. During a scan of the row conductors for the first gray scale voltage level, pixel elements in each enabled row which are to be charged to the first gray scale voltage level are selected. After completion of the scan for the first gray scale voltage level, all of the selected pixel elements in the display are simultaneously charged to the first gray scale voltage level.

Patent
21 Sep 1995
TL;DR: In this paper, the structure of pixel electrode constituting a pixel element of a liquid-crystal display device employing the capacitively coupling driving method and driving method for the device are described.
Abstract: The structure of pixel electrode constituting a pixel element of a liquid-crystal display device employing the capacitively coupling driving method and driving method for the device are described. The field of view angle at the main viewing direction is increased and the grayscale graduation reversal is eliminated through a procedure of sequentially increasing or decreasing, at each scanning busline, the value of compensating potential at a time when a potential being applied to the gate terminal of the switching element shifts from ON potential to OFF potential, to be applied on an adjacent scanning busline to which the storage capacitance is formed, by setting each of the values of storage capacitance ratio and parasitic capacitance ratio different through making each of the values of storage capacitance and parasitic capacitance formed between the plural pixel electrodes and respective switching elements within one pixel element different to each other.

Proceedings ArticleDOI
09 May 1995
TL;DR: A Bayesian approach for segmenting a sequence of gray-scale images to obtain a binary sketch and achieves accurate rendering of the lip and eye movements and preserves the main characteristics of the face, so that it is easily recognizable.
Abstract: We present a Bayesian approach for segmenting a sequence of gray-scale images to obtain a binary sketch. We extend a 2-D algorithm to video sequences. The 2-D algorithm is an adaptive thresholding scheme that uses spatial constraints and takes into consideration the local intensity characteristics of the image. We model the segmentation distribution as a 3-D Gibbs random field. We add temporal constraints and temporal local intensity adaptation to ensure a smooth transition of the segmentation from frame to frame. For computational efficiency as well as performance we use a multi-resolution approach. We also consider several suboptimal implementations to reduce the delay as well as the amount of computation. We tested the performance of the algorithm on head and shoulders video sequences. The algorithm achieves accurate rendering of the lip and eye movements and preserves the main characteristics of the face, so that it is easily recognizable.

Patent
07 Jun 1995
TL;DR: In this article, a system for performing edge enhancement of mixed low-resolution image files employs a binarization and sorting unit to sort data that is indicative of binary data from the mixed low resolution image input file.
Abstract: A system for performing edge enhancement of mixed low resolution image files employs a binarization and sorting unit to sort data that is indicative of binary data from the mixed low resolution image input file. The sorted binary data is then supplied to a binary data edge enhancement processor for edge enhancement processing. The output from the binary data edge enhancement processor unit is supplied to a data merger unit along with the original image data. The data merger unit determines whether the original image data was part of a gray-scale image. If the data merger determines the original data is part of a gray-scale image, the original data is supplied as the output of the processing system. If the data merger determines that the original data is binary image data, the output from the binary edge enhancement processor unit is supplied as the output of the processing system.

Proceedings ArticleDOI
14 Aug 1995
TL;DR: The authors extend the topographic analysis method, so that characters and lines can be extracted from gray scale map images where methods using only the information in the binary image fail.
Abstract: There is a large number of documents, including hand-printed maps, where useful information is lost if binarization is performed on the scanned image before further processing. For such documents, methods which utilize the gray scale values must be used in order to extract as much of the available information as possible. Topographic analysis has been used in the literature to recognize characters directly in the gray scale images. The authors extend the topographic analysis method, so that characters and lines can be extracted from gray scale map images where methods using only the information in the binary image fail.

Patent
31 Mar 1995
TL;DR: In this paper, a wide viewing angle liquid crystal display and a method of operating the same are disclosed, each of a plurality of pixel elements of the display have individually driveable first and second pixel sub-elements.
Abstract: A wide viewing angle liquid crystal display and method of operating the same are disclosed. Each of a plurality of pixel elements of the display have individually driveable first and second pixel sub-elements. A desired average gray scale intensity for a first pixel element is determined. First and second drive voltages are determined as a function of the desired average gray scale intensity for the first pixel element. The first drive voltage is provided to the first pixel sub-element to drive it to a first gray scale intensity. The second drive voltage is provided to the second pixel sub-element to drive it to a second gray scale intensity. The average gray scale intensity for the first pixel element, which is a function of the first and second gray scale intensities, has reduced viewing angle dependence.

Patent
07 Jun 1995
TL;DR: In this paper, an improved error diffusion method for incorporating into a halftoning algorithm for processing gray scale images to counterpart binary images was proposed, which adopts a tone scale function to process the input gray scale image before proceeding with the error diffusion processing.
Abstract: An improved error diffusion method for incorporating into a halftoning algorithm for processing gray scale images to counterpart binary images. The improved error diffusion method adopts a tone scale function to process the input gray scale image before proceeding with the halftoning (error diffusion) processing in order to improve the image darkening problem caused by the conventional error diffusion method and a noise correction process to eliminate the background noises resulted from the accumulated error of the conventional error diffusion method. The proceeding of the tone scaling process and the halftoning process are parallel with the correction process so that errors generated in either one will not affect the other.

Patent
21 Dec 1995
TL;DR: In this paper, a time-domain graphic synthesis method and apparatus form M single-bit patterns of length N to convert multiple-bit grayscale pixel data into single bit binary display signals.
Abstract: A time-domain graphic synthesis method and apparatus form M single-bit patterns of length N to convert multiple-bit grayscale pixel data into single-bit binary display signals. M designates the number of gray levels to be displayed. N specifies a selected pattern size for usage in converting gray levels into perceived grayscale pixel data and advantages are gained if N is defined to be a prime number. Each of the N-bit binary patterns identifies a particular gray shade and each pattern, by definition, includes a plurality of ones and zeros. The ratio of the number of ones in an N-bit pattern to the total number N defines a relative intensity for that N-bit pattern. The relative intensity is indicative of and corresponds to the particular gray shade. The M single-bit patterns of length N are applied to a display which stores multiple-bit grayscale pixel data so that the column location of a pixel is converted to modulo-N form to designate one of the N bits of the pattern. Furthermore, for successive rows of the display, the column location of a pattern is progressively shifted or rotated with respect to a pixel. The shifting is modulo-N shifting and the amount of shifting is selected so that all N column locations are selected for N successive rows of the display. By applying the N-bit patterns in this manner, processing of all elements of the display includes processing of a matrix of adjacent N×N-bit squares. Processing of consecutive time frames of the display also includes shifting or rotating on a frame-by-frame basis, generating a repetitive pattern of N frames.

Patent
25 Aug 1995
TL;DR: In this paper, a linear matrix logic structure is used to generate gray scale shading for monochromatic and color displays using frame rate control modulation for intensity shading for each pixel, which does not require any memory for storing phase tiling matrices or frame modulation pattern sequences.
Abstract: An LCD controller for use e.g. in a portable computer provides gray scale shading for both monochromatic and color displays using frame rate control modulation for intensity shading for each pixel. The gray scale shading process and circuit do not require any memory for storing phase tiling matrices or frame modulation pattern sequences; both of these instead are generated in real time using a linear matrix logic structure. Use of linear matrix operations also allows generation of various phase shifts of frame modulation pattern sequences to provide a better image on the display. In addition to providing programmable 4, 8, or 16 intensity levels, the present method and apparatus provide that vertically, horizontally or diagonally adjacent pixels on the display never have the same phase in the same frame, and in addition that the pixel display drivers are uniformly loaded.