Display of a video having a higher number of bits per pixel than that available on the display device requires quantization prior to display. Video halftoning performs this quantization so as to reduce visibility of certain artifacts. In many cases, visibility of one set of artifacts is decreased at the expense of increasing the visibility of another set. In this paper, we focus on two key temporal artifacts, flicker and dirty-window-effect, in binary video halftones. We quantify the visibility of these two artifacts when the video halftone is displayed at medium frame rates (15 to 30 frames per second). We propose new video halftoning methods to reduce visibility of these artifacts. The proposed contributions are (1) an enhanced measure of perceived flicker, (2) a new measure of perceived dirty-window-effect, (3) a new video halftoning method to reduce flicker, and (4) a new video halftoning method to reduce dirty-window-effect.
Bit-depth reduction must be performed when the number of bits/pixel (bit-depth) of the original video data is higher than the bit-depth available on the display device. Halftoning is a process that can perform this quantization. The original, full bit-depth video is called the continuous-tone video, and the reduced bit-depth video is called the halftone video. Bit-depth reduction results in quantization artifacts.
Binary halftone videos can suffer from both spatial and temporal artifacts. In the case of binary halftone videos produced from grayscale continuous-tone videos, there are two key temporal artifacts. These temporal artifacts are flicker and dirty-window-effect (DWE). Of these two temporal artifacts, halftone flicker has received more attention in publications on video halftoning [1–5]. Hilgenberg et al. briefly discuss the DWE artifact in . They have, however, not used the term dirty-window-effect to refer to this particular artifact.
The DWE refers to the temporal artifact that gives a human viewer the perception of viewing objects, in the halftone video, through a "dirty" transparent medium, such as a window. The artifact is usually disturbing to the viewer because it gives the perception as if a pattern were laid on top of the actual video. Like other artifacts, dirty-window-effect contributes to a degraded viewing experience of the viewer. Although this artifact is known and has been referred to in the published literature , as far as we know, a quantitative perceptual criteria to assess this artifact has not been published. The artifact has been evaluated qualitatively in .
In contrast to DWE, which is observed due to binary pixels not toggling in enough numbers in response to a changing scene, flicker is typically observed due to too many binary pixels toggling their values in spatial areas that do not exhibit "significant" perceptual change between successive (continuous-tone) frames. Depending on the type of display, flicker can appear as full-field flicker or as scintillations. As a temporal artifact, halftone flicker can appear unpleasant to a viewer. On some devices, it can also result in higher power consumption . Moreover, if the halftone video is to be compressed for storage or transmission, higher flicker can reduce the compression efficiency [2, 3]. Evaluation of flicker has been discussed in [2–5]. Flicker has been referred to as high frequency temporal noise in . A recent approach to form a perceptual estimate of flicker has been discussed in .
For reasons discussed above, it is desirable to reduce these temporal artifacts in the halftone videos. Therefore, perceptual quantitative measures for evaluating these artifacts are desirable. Quantitative assessment of temporal artifacts can facilitate comparison of binary halftone videos produced using different algorithms. Temporal artifact quality assessment criteria can also be combined with the assessment of spatial artifacts to form an overall quality assessment criteria for binary halftone videos. Video halftoning algorithm design can benefit from the temporal artifact evaluation criteria presented in this paper. The perception of temporal artifacts is dependent on the frame-rate at which the halftone video is viewed. For example, for medium frame rate (15 to 30 frames per second) binary halftone videos, flicker between successive halftone frames will correspond to temporal frequencies at which the human visual system (HVS) is sensitive .
In this paper, we present a framework for the quantitative evaluation of the temporal artifacts in medium frame rate binary halftone videos produced from grayscale continuous-tone videos. We utilize the proposed quality assessment framework to design video halftoning algorithms. The proposed contributions of this paper include () an enhanced measure of perceived flicker, () a new measure of perceived dirty-window-effect, () a new video halftoning method to reduce flicker, and () a new video halftoning method to reduce dirty-window-effect.
The rest of the paper is organized as follows. Flicker and dirty-window-effect in binary halftone videos are discussed in detail in Section 2. Section 3 presents the proposed technique to assess temporal artifacts. Section 3 also presents halftoning algorithms that reduce temporal artifacts based on the proposed quality assessment techniques. The paper concludes with a summary of the proposed contributions in Section 4.
2. Flicker and Dirty-Window-Effect
As discussed in the previous section, dirty-window-effect refers to the temporal artifact that causes the illusion of viewing the moving objects, in the halftone video, through a dirty window. In medium frame-rate binary halftone videos, the perception of dirty-window-effect depends primarily on both the continuous-tone and the corresponding halftone videos. Consider two successive continuous-tone frames and their corresponding halftone frames. Assume that some objects that appear in the first continuous-tone frame change their spatial position in the second, successive, continuous-tone frame, but the corresponding halftone frames do not "sufficiently" change in their halftone patterns at the spatial locations where the continuous-tone frames changed. When each of the two halftone frames is viewed independently, it represents a good perceptual approximation of its corresponding continuous-tone frame. However, when the two halftone frames are viewed in a sequence, if the change in their binary patterns does not "sufficiently" reflect the corresponding change in the continuous-tone frames, the halftone video can suffer from perceivable dirty-window-effect. DWE should not be visible if the successive continuous-tone frames are identical.
We now present an example to illustrate the point discussed in the paragraph above. For this illustration, each frame of the standard caltrain sequence  was independently halftoned using Ulichney's 32-by-32 void-and-cluster mask . Figures 1 and 2 show the first continuous-tone frame and first halftone frame, respectively, of the caltrain sequence. Figures 3 and 4 show the second continuous-tone frame and second halftone frame, respectively. Figure 5 shows the absolute difference of the first two (grayscale) continuous-tone frames. The brighter regions in this figure represent spatial locations where the two successive frames differed in luminance. Figure 6 shows the absolute difference image of the halftone frames depicted in Figures 2 and 4. The dark pixels in this image are the pixels that have identical values in the, successive, halftone frames. Note that locations of some of these dark pixels overlap with locations that represent change of scene (due to moving objects or due to camera motion) in Figure 5. These are the spatial locations where perception of DWE is very likely in the halftone video. This was found to be the case when we viewed the halftone sequence at frame rates of 15 and 30 frames-per-second (fps). For comparison, Figure 7 shows absolute difference of the first two frames halftoned using Gotsman's technique , which is an iterative halftoning technique. It can be seen by comparing Figures 6 and 7 with Figure 5 that Gotsman's method  produces less DWE than the frame independent void-and-cluster method. This was our observation when these videos were viewed at frame rates of 15 fps and 30 fps.
Now, consider a scenario where the values of grayscale pixels within a (spatial) region of a continuous-tone frame are close to the values of the corresponding pixels in the next (successive) continuous-tone frame. If such is the case, one would expect the corresponding binary halftone frames to have similar pixels values as well. However, it is possible that although each of the corresponding binary halftone frame is perceptually similar to its continuous-tone version, when viewed in a sequence the two successive halftone frames toggle their pixel values within the same spatial region. This can result in the perception of flicker.
Assessment of halftone flicker has traditionally been done by evaluating difference images [2, 5]. In this approach, absolute pixel-by-pixel difference between two successive halftone frames is evaluated. The resulting binary image, called the difference image, shows locations where pixels toggled their values. Figure 8 illustrates flicker in two successive frames of a halftone video. This technique is feasible for evaluating flicker, if only a few difference images are to be looked at. This technique will prove to be not feasible for videos with large number of frames. The technique is also not objective, since visual inspection of the difference image is required. Moreover, higher flicker will be depicted with this technique whenever there is a scene change in the video. This should be considered a false positive. At a scene change, the binary patterns are expected to change quite a bit to reflect the scene change. This does not mean higher flicker. At a scene change, temporal masking effects of the HVS also need to be taken into account . Hsu et al. proposed a method based on the difference image technique to provide a quantitative assessment of flicker for the entire halftone sequence . They have called their assessment measure average flicker rate (AFR), which they compute by adding the "on" pixels in the absolute difference image and then dividing the resulting sum by the total number of pixels in the frame. AFR is evaluated for all adjacent pairs of halftone frames and plotted as a function of frame number to give the flicker performance of the entire video. In this paper, for the evaluation of halftone flicker, we modify the approach proposed in .
3. Proposed Technique
In this section, we propose a framework that can be utilized to evaluate temporal artifacts in medium frame-rate binary video halftones. We assume that each frame of the halftone video is a good halftone representation of the corresponding continuous-tone frame. This is, for example, the case when each continuous-tone frame is halftoned independently to produce the corresponding halftone frame. The proposed quality evaluation framework also depends on the continuous-tone video from which the halftone video has been produced. Therefore, our quality assessment measure is a full-reference (FR) quality assessment measure. Before we proceed with the presentation of the proposed framework, we describe some observations about binary halftone videos as follows.
Flicker and dirty-window-effect in a binary halftone video represent local phenomena. That is, their perception depends on both the temporal and spatial characteristics of the halftone video. Thus, flicker or DWE may be more observable in certain frames and in certain spatial locations of those frames. In our observation, the perception of DWE is higher if the moving objects (or regions) are relatively flat. This means that moving objects with higher spatial frequencies (or with higher degree of contrast) are less likely to cause the perception of DWE. Similarly, the perception of flicker is higher if the similar corresponding spatial regions of two successive halftone frames have higher low spatial frequency (or low contrast) content. It is interesting to note that for still image halftones, it has been reported that the nature of dither is most important in the flat regions of the image . This phenomenon is due to the spatial masking effects that hide the presence of noise in regions of the image that have high spatial frequencies or are textured.
Due to temporal masking mechanisms of the human visual system (HVS) [11, 13], the perception of both flicker and DWE might be negligible at scene changes.
Flicker and DWE are related. Reducing one artifact could result in an increase of the other. If halftone pixels toggle values between halftone frames within a spatial area that does not change much between continuous-tone frames, flicker might be observed at medium frame rates. If they do not toggle in spatial areas that change between successive frames or exhibit motion, DWE might be observed. To minimize both artifacts, a halftoning algorithm should produce halftone frames that have their pixels toggle values only in spatial regions that have a perceptual change (due to motion, e.g.) between the corresponding successive continuous-tone frames. Certain halftoning algorithms produce videos that have high DWE but low flicker. An example is a binary halftone video produced by using ordered-dither technique on each grayscale continuous-tone frame independently. Similarly, there are halftoning algorithms that produce videos with high flicker but low DWE. An example is a binary halftone video produced by halftoning each grayscale continuous-tone frame independently using Floyd and Steinberg  error diffusion algorithm.
The observations discussed above are reflected in the design of the framework for evaluation of temporal artifacts, which we introduce now. To facilitate the clarity of presentation, we utilize the notation introduced in . We adapt that notation for the current context and have described it in Table 1. Please refer to the notation in Table 1 regarding the terminology used in the rest of this paper.
Let be the total number of frames in . Let be the total number of pixel rows in each frame of , and let be the total number of pixel columns in each frame of .
3.1. Halftone Dirty-Window-Effect Evaluation
It has been explained in the previous section that dirty-window-effect may be observed if, between successive frames of a halftone video, the halftone patterns do not change sufficiently in response to a changing scene in the continuous-tone video. Based on our observations on DWE, note that is a function of , , and . Therefore,
For the halftone frame, we also define perceived average dirty-window-effect as
Perceptual dirty-window-effect Index DWE of a halftone video is defined as
Dirty-window-effect performance of individual halftone frames can be represented as a plot of against frame number. The DWE performance of the entire halftone video is given by the single number DWE, the Perceptual DWE Index. The framework introduced thus far is quite general. We have not described the form of the function in (1). We have also not described how to calculate the arguments of this function. We provide these details next.
We now describe a particular instantiation of the framework introduced before. , , , and constitute the maps/images , , , and , respectively. To evaluate in (1), we need the (local) contrast map of , , dissimilarity map between continuous-tone frames and , , and the similarity map between the successive halftone frames and , . We derive from the Structural Similarity (SSIM) Index Map  evaluated between the continuous-tone frames and . We will denote this derived measure by . We scale to have its pixels take values between 0 and 1 inclusive. For the dissimilarity map, we set
For the similarity map, we set
where represents the point spread function (PSF) of the HVS and represents absolute difference image for successive halftone frames and . We are assuming that the HVS can be represented by a linear shift-invariant system  represented by . For the evaluation of , we utilize Nasanen's model  to form a model for HVS. The pixel values of the map are between 0 and 1 inclusive. We want to represent an image that has pixels with values proportional to the local contrast content. Using , we want to give higher weight to spatial regions that are relatively "flat." We approximate the calculation of high local contrast content by computing the local standard deviation. In this operation, each pixel of the image is replaced by the standard deviation of pixels in a local window around the pixel. The filtered (standard deviation) image is then normalized (via pixel wise division) by the mean image, which is also computed by replacing each pixel by the mean value of pixels in a local window around the pixel. This gives us . is further normalized to have pixel values between 0 and 1 inclusive. With these maps defined, we define (1) as
Observe that . This instantiation of the DWE assessment framework is depicted in Figure 9. In Figure 9, K, P, and R each has a value of 1. L, Q, and S have each a value of 1. The "Artifact Map" is . Each of its pixels, , is a product of three terms. At pixel location , the first term measures the local dissimilarity between the successive continuous-tone frames. A higher value of the first term, , will mean that the successive frames have a lower structural similarity in a local neighborhood of pixels centered at pixel location . This will in turn assign a higher weight to any DWE observed. This reflects the fact that the "local" scene change should result in higher perception of DWE if the halftone pixels do not change "sufficiently" between the successive frames. The second term, , depends on the number of pixels that stayed the same in a neighborhood around (and including) pixel location . It gives us a measure of perceived DWE due to HVS filtering. Since the HVS is modeled as a low-pass filter in this experiment, will have a higher value, if the "constant" pixels form a cluster as opposed to being dispersed. The third term, , measures the low contrast content in a local neighborhood centered at . A higher value of this term will result in higher value of perceived DWE. This is to incorporate spatial masking mechanisms of HVS. This term can also be viewed as representing the amount of low spatial frequency content. We incorporate the effect of scene changes by setting to zero. This is where scene change detection comes into play. This accounts for temporal masking effects. Note that between successive continuous-tone frames and , a very low average value of can indicate a change of scene. Any scene change detection algorithm can be utilized, however. For the results reported in this paper, we determined scene changes in the videos through visual inspection and manually set to zero at frames where a scene change is determined to have occurred.
3.2. Experimental Results on DWE Assessment
We first discuss the DWE evaluation results on the standard caltrain sequence . Figure 10 shows the dissimilarity map . In this map/image, the brighter regions depict the areas where the first two frames of the caltrain sequence are structurally dissimilar. These are the regions where DWE is likely to be observed, if the corresponding halftone pixels do not "sufficiently" change between the successive halftone frames. Figure 11 shows . In this map, the luminance of a pixel is proportional to the local normalized standard deviation in the image. Therefore, brighter regions in this image correspond to areas where DWE is less likely to be observed, if the corresponding halftone pixels do not "sufficiently" change between the successive halftone frames.
The caltrain sequence  was halftoned using three techniques. The first halftone sequence was formed by using ordered-dither technique on each frame independently. The threshold array was formed by using a void-and-cluster mask . The second sequence was formed by halftoning the sequence using Gotsman's technique . The third halftone sequence was formed by halftoning each frame independently using Floyd and Steinberg  error diffusion. Figure 12 depicts plotted as a function of frame number. According to this plot, the ordered-dither halftone sequence has highest DWE. Gotsman's technique has relatively lower DWE, whereas the error diffusion based halftone sequence has the lowest DWE. These results are consistent with our visual inspection observations when the sequence was played back at frame rates of 15 fps and 30 fps.
3.3. Validation of the DWE Assessment Framework
In this section, we present our results on the validation of the DWE assessment framework. To establish the validity of the DWE assessment framework, we modified Gotsman's technique  such that our DWE assessment criteria were incorporated while generating the halftone sequence. This resulted in reduction of DWE in most halftone sequences. We briefly describe Gotsman's method to generate a halftone video . Gotsman's method is geared towards reducing flicker in halftone videos. The first frame of the halftone video is generated by independently halftoning the corresponding continuous-tone frame. This is done via an iterative technique which requires an initial halftone of the image as the initial guess (or the starting point). The initial halftone of the image is iteratively refined, via toggling the bits, until a convergence criterion is met. The technique results in achieving a local minimum of an HVS model-based perceived error metric. For the first halftone frame, the initial guess or the starting point can be any halftone of the first continuous-tone frame. The starting point of each subsequent frame is taken to be the preceding halftone frame. This causes each subsequent frame to converge to a halftone which has a lot of pixels that do not toggle (with respect to the preceding halftone frame), particularly when there is no scene change. This results in producing halftone frames that are temporally better correlated than those generally produced using a frame-independent (or intraframe) approach. Our modification to this technique is as follows. The first halftone frame is generated independently, just like in Gotsman's original technique. However, unlike Gotsman's technique , the initial guess for a subsequent frame is not taken to be the preceding halftone frame in its entirety. Instead, we only copy certain pixels from the previous frame. In particular, to determine the initial guess of a frame (other than the first frame), we produce a frame-independent halftone of the corresponding continuous-tone frame using a void-and-cluster mask . Then certain pixels of this frame that meet a criteria, to be described next, are replaced by pixels from the previous halftone frame. What pixels from the previous frame need to be copied is determined based on our DWE assessment technique. For the halftone frame (), , if a pixel location in the initial halftone is such that , then the pixel from the preceding halftone frame is copied into the initial halftone frame. Here is a threshold that controls the amount of dirty-window-effect reduction. With , we produced the caltrain halftone and compared it with Gotsman's technique. Figure 13 depicts the reduction in perceived DWE due to our modification of Gotsman's algorithm. Evaluation via visual inspection confirmed the reduction in perceived DWE. Table 2 shows more results for comparison of DWE Index, DWE, evaluation for five different sequences . The number of frames reported in Table 2 is for 30 fps playback. Thus, Table 2 gives DWE for 30 fps playback. For the modified method, . Two points can be concluded based on the results reported in the table. For most sequences, improvement in the perception of DWE due to modified Gotsman's method is marginal. This was the case during our visual evaluation of the sequences. One exception to this was the caltrain sequence. This observation reinforces the fact that perception of DWE is content dependent. It is interesting to note that the modified Gotsman's method actually produced the football sequence with a slightly higher DWE. This is due to the fact that in the modified Gotsman's method, it is the content of the initial frame halftone that is controlled via the modified method. However, since the method iteratively improves the halftone frame, there is no explicit control on how the halftone frame changes subsequently, and there is a possibility for a scenario like this.
3.4. Halftone Flicker Evaluation
The development of framework for halftone flicker evaluation will parallel the approach, utilized above, for the evaluation of DWE, since flicker and DWE are related artifacts. The development presented below is based on the framework proposed in . Based on our discussion on flicker above, we note that is a function of , , and . Thus,
For the halftone frame, Perceived Average Flicker is defined as
Perceptual Flicker Index of a halftone video is defined as
Perceived Average Flicker can be plotted (against frame number) to evaluate flicker performance of individual halftone frames. Perceptual Flicker Index gives a single number representing flicker performance of the entire halftone video. Next, we present a particular instantiation of the framework discussed thus far.
, , , and constitute the maps/images , , , and , respectively. Therefore, to evaluate in (7), we need the local contrast map of , , similarity map between continuous-tone frames and , , and the dissimilarity map between the successive halftone frames and , . We set to be a map based on the Structural Similarity (SSIM) Index Map  evaluated between the continuous-tone frames and . This will be denoted by . is scaled to have its pixels values between 0 and 1 inclusive. For the dissimilarity map, we set
where represents the point spread function (PSF) of the HVS. This is based on the assumption that the HVS can be represented by a linear shift-invariant system  represented by . can have its pixels take values between 0 and 1 inclusive. is evaluated exactly as in the case of DWE, already described in Section 3.1. We define (7) as
Note that . This instantiation of the flicker assessment framework is depicted in Figure 9. In Figure 9, K, Q, and R each have a value of 1. L, and S have each a value of 0. P has a value of 1. The "Artifact Map" is . has the form described in . We do evaluate differently in this paper. For clarity, we repeat the description of as provided in . is a product of three terms. At pixel location , the first term measures the local similarity between the successive continuous-tone frames. A higher value of the first term, , will mean that the successive frames have a higher structural similarity in a local neighborhood of pixels centered at pixel location . This will in turn assign a higher weight to any flicker observed. This is desired because if the "local" scene does not change, perception of any flicker would be higher. The second term, , depends on the number of pixels that toggled in a neighborhood around (and including) pixel location . It gives us a measure of perceived flicker due to HVS filtering. Since the HVS is modeled as a low pass filter in this experiment, will have a relatively higher value, if the pixel toggles form a cluster as opposed to being dispersed. The third term, , measures the low contrast content in a local neighborhood centered at . A higher value of this term will result in higher value of perceived flicker. Finally, we incorporate the effect of scene changes by setting to a low value (zero, e.g.), if a scene change is detected between continuous-tone frames and . This is to account for temporal masking effects. For the results reported in this paper, we (manually) determined scene changes in the videos through visual inspection and manually set to zero whenever a scene change is determined to have occurred between successive continuous-tone frames and .
3.5. Experimental Results on Flicker Assessment
Now we discuss the flicker evaluation results on the standard trevor sequence . This sequence was halftoned using three techniques. The first halftone sequence was formed by using ordered-dither technique on each frame independently. The threshold array was formed by using a void-and-cluster mask . The second sequence was formed by halftoning the sequence using Gotsman's technique . The third halftone sequence was formed by halftoning each frame independently using Floyd and Steinberg  error diffusion. Figure 14 depicts plotted as a function of frame number. As you can see on this plot, the error diffusion-based halftone sequence has higher flicker relative to the other two compared halftone sequences. Authors' visual evaluation of the sequences played back at frame rates of 15 fps and 30 fps revealed highest flicker in the sequences generated using Floyd and Steinberg  error diffusion.
3.6. Validation of the Flicker Assessment Framework
To validate the flicker assessment framework proposed in this paper, we will utilize the flicker assessment framework to modify an existing video halftoning algorithm. If this modification results in improvement of perceived flicker at medium frame rates, then the proposed framework is valid. This is the case as will be shown next. We modify frame-independent Floyd and Steinberg error diffusion algorithm to reduce flicker. As described before, frame-independent Floyd and Steinberg error diffusion (FIFSED) algorithm halftones each frame of the continuous-tone video independently using Floyd and Steinberg error diffusion  algorithm for halftone images. The general set up for image error diffusion is shown in Figure 16. In this system, each input pixel, from the continuous tone image, to the quantizer is compared against a threshold to determine its binary output in the halftoned image. We modify FIFSED and introduce frame-dependence in the algorithm. The modified algorithm will be called frame-dependent Floyd and Steinberg error diffusion (FDFSED) algorithm. To make the algorithm frame-dependent (or interframe), we will incorporate threshold modulation for flicker reduction. The idea of threshold modulation to reduce flicker was originally conceived by Hild and Pins , and later used in . FDFSED works as follows. The first halftone frame is generated by halftoning the first continuous-tone frame using image error diffusion algorithm. In this algorithm, the error diffusion quantization threshold is kept a constant . For the generation of subsequent halftone frames, the quantization threshold is not constant. Instead, the quantization threshold is modulated based on our flicker assessment framework. In the generation of each halftone frame for , , the quantization threshold for a pixel location is determined as follows:
As seen in (12), the amount of threshold perturbation is determined by , where is a constant that controls the effect of on . The threshold modulation is designed to reduce flicker in the halftone video.
With in (12), we produced the trevor halftone using FDFSED and compared with that generated using FIFSED. Figure 15 depicts the reduction in perceived average flicker in the trevor halftone produced using FDFSED. Visual evaluation of the two halftone sequences (generated using FIFSED and FDFSED methods) by the authors confirmed the reduction in perceived average flicker in the sequence generated using FDFSED method. Table 3 shows more results for comparison of flicker Index, , evaluation for five different sequences . For FDFSED algorithm, we used in (12). Table 3 shows the values of flicker Index, for the number of frames indicated in the table. The number of frames reported in Table 3 is for 30 fps playback. Thus, Table 3 gives , for 30 fps playback. As can be seen in the table, use of FDFSED resulted in significant reduction of flicker in every halftone sequence. The results are consistent with the authors' visual evaluation at 30 frames per second.
In this paper, we presented a generalized framework for the perceptual assessment of two temporal artifacts in medium frame rate binary video halftones produced from grayscale continuous-tone videos. The two temporal artifacts discussed in this paper were referred to as halftone flicker and halftone dirty-window-effect. For the perceptual evaluation of each artifact, a particular instantiation of the generalized framework, was presented and the associated results were discussed. We also presented two new video halftoning algorithms which were designed by modifying existing video halftoning algorithms. The modifications were based on the perceptual quality assessment framework and were thus geared towards reducing the temporal artifacts. Results of comparisons between the halftone videos generated using the original and the modified algorithms were presented and discussed.
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