IEICE TRANS. ELECTRON., VOL.E90–C, NO.11 NOVEMBER 2007
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LETTER
Special Section on Electronic Displays
Image Adaptive Incremental Subfield Coding for Plasma Display Panels Myung Jin PARK†a) , Nonmember, Hyoun Soo PARK†b) , Student Member, and Young Hwan KIM†c) , Member
SUMMARY In this letter, we propose a new approach to incremental coding of the subfield codes for plasma display panels (PDPs). The proposed approach suppresses the halftone noise of the PDPs, while completely eliminating false contour noise, as do existing incremental subfield codes, by selecting an optimal incremental subfield code adaptively for a given input image. The proposed method maps the problem of selecting the optimal incremental subfield code onto a special-case shortest path problem. Results of experiment using 109 sample images illustrated that the proposed method improved the average peak signal-to-noise ratio by 4.4–6.2 dB in halftone noise compared with existing incremental subfield coding methods. key words: plasma display panel, subfield, false contour noise, halftone noise, incremental subfield coding method
1.
Introduction
Plasma display panels (PDPs) use the subfield method to realize gray levels, which selectively controls the number of plasma discharges for each pixel, depending on the gray level to be represented. The subfield method divides each field image into a set of subfield images and each subfield has its own number of plasma discharges to induce [1]. Then, the field image is represented as the sum of subfield images, and the subfield code is used to select the subfield images. The subfield method successfully realizes gray levels on PDPs. However, it induces an image artifact called false contour noise (FCN) [2], which does not exist on the original moving images. In the subfield method, each subfield has its own time points at which to begin inducing plasma discharges, and two adjacent gray levels may have quite different discharge time points. The difference in the discharge time points induces FCN. FCN degrades the image quality of PDPs seriously and is very annoying to human viewers. Several subfield coding methods have been proposed to suppress FCN. They include subfield vector relocation [3], subfield division [4], time compressing driving [4], gravity centre coding (GCC) [5], and incremental subfield coding methods [6]–[9]. GCC and incremental subfield coding methods select the subfield Manuscript received February 28, 2007. Manuscript revised May 10, 2007. † The authors are with the Division of Electrical and Computer Engineering, Pohang University of Science and Technology, Republic of Korea. a) E-mail:
[email protected] b) E-mail:
[email protected] c) E-mail:
[email protected] DOI: 10.1093/ietele/e90–c.11.2100
Fig. 1
Example of incremental subfield codes.
codes that reduce or remove FCN completely while sacrificing the number of gray levels that can be represented by the subfield method. The incremental subfield coding method uses a set of subfield codewords such that emitting subfields are grouped together, beginning from the start of the frame time. Since the incremental subfield coding method does not allow nonemitting subfields between emitting subfields, the number of gray levels it can represent is limited by the number of subfields used (Fig. 1). MPD-free coding [6], CLEAR [7], ALIS [8], and NFC [9] use the incremental subfield codes. The greatest advantage of the incremental subfield coding methods is the complete removal of FCN. However, like all other subfield coding methods that use a limited number of gray levels, they require the halftone technique to represent all 256 gray levels, and this induces a new type of artifact, called halftone noise (HN) [10]. Since HN can be quite noticeable, especially for still images or slowly moving images, it is desirable to suppress it as much as possible. We propose an adaptive incremental subfield coding (AISC) method that suppresses halftone noise. Like other incremental subfield coding methods, it has the advantage of the complete removal of FCN. In addition, while the existing approaches use the same subfield code for all images, our proposed method determines the optimal subfield code for a given image and, thus, uses a different subfield code for each image to minimize HN. This letter is organized as follows. Section 2 describes the proposed AISC method. Section 3 shows the experimental results for the proposed coding method. Finally, Sect. 4 concludes the letter. 2.
Adaptive Incremental Subfield Coding Method
The proposed AISC method first selects a set of gray levels, which minimizes the halftone noise for a given input image,
c 2007 The Institute of Electronics, Information and Communication Engineers Copyright
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exploiting the image characteristics. The number of the gray levels to choose depends on the number of subfields to use. It then determines the subfield weights so that the selected gray levels can be represented in the form of the incremental subfield code. The AISC method maps the problem of finding an optimal set of gray levels onto the problem of finding a specialcase shortest path on a single-source single-sink directed acyclic graph (DAG). 2.1 Estimation of Halftone Noise The metric to estimate the amount of halftone noise, appearing on the given image, is based on the mean square error. When gray level X is represented with two gray levels L and H using halftone techniques, the square of halftone noise occurring at gray level X, HN 2 (X, L, H), is given as [11] HN 2 (X, L, H) = (X − L)2 × PXL + (H − X)2 × PXH × N x (X−L) (H −X) = (X−L)2 × +(H −X)2 × × NX . (1) (H −L) (H −L) In Eq. (1), PXL represents the probability that gray level X will be halftoned by gray level L, PXH is the probability that gray level X will be halftoned by gray level H, and NX is the number of pixels whose gray level is X. The total amount of halftone noise induced by the pixels whose gray levels are between two gray levels X and Y, E HN (X, Y), is given as. E HN (X, Y) =
Y−1
HN 2 (m, X, Y) .
(2)
m=X+1
2.2 Graph Construction In the proposed approach, we construct a single-source single-sink DAG to find a set of optimal gray levels for minimum HN (Fig. 2). In the graph, each node represents a gray level; the source and the sink represent gray level 0 and the maximum gray level (n) of the given image, respectively. The length of the edge (X, Y) represents E HN (X, Y). The complexity of the DAG construction is given below, where n is the number of nodes and E is the number of edges [8].
Fig. 2 Example of single-source single-sink DAG used in proposed approach.
Complexity DAG n {(n − m) + 1} × (n − m) +1 =n+E = 2 m=1 ≤ n × [{(n − 1) + 1} × (n − 1) ÷ 2 + 1] = O n3 (3) Now, the problem of finding a set of optimal gray levels for minimum HN is mapped onto a problem to find the shortest path from the source to the sink. Note that, unlike the usual shortest-path problems, the proposed approach involves finding the shortest path of the DAG, which has a given number of nodes on it; the number of nodes on the shortest path is equal to k, where k is the number of gray levels used to display images. 2.3 Proposed Algorithm to Find the Special-Case Shortest Path Having k Nodes on the Path The proposed algorithm for the special-case shortest path problem, i.e., finding the shortest path with k nodes on it, is based on the DAG-shortest path algorithm [12]. Here, k is the number of gray levels used to display images. The usual DAG-shortest path algorithm finds one shortest path to each node from the source node, while progressing forward. On the other hand, the proposed algorithm finds one shortest path for each distance from the source node to each node, while progressing forward in the topological order of nodes from the source (gray level 0) to the sink (maximum gray level). Here, distance means the number of edges on the path. After reaching the sink node, we have one shortest path for each distance from the source to the sink, e.g., one shortest path with one edge, one shortest path with two edges, one shortest path with three edges, and so on, if they exist. Then, the shortest path with (k−1) edges is the one we are looking for; (k −1) subfields provide k gray levels. In the actual algorithm, if we find a shortest path whose distance from the source is greater than (k − 1) during the forward traversal, we prune the paths containing the shortest path from exploration. The detailed algorithm is shown in Fig. 3. In the figure,
Fig. 3
Proposed algorithm to find the shortest path with k nodes.
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i represents the node currently being explored, j is the next node to explore, and l is the distance, i.e., the number of edges on the path from the source to node i. In addition, length(i, l) is the length of the path from the source to node i, i.e., the sum of the lengths of all edges on the path, whose distance is l, and, finally, k is the number of gray levels used to represent 256 gray levels by the halftone technique. The storage requirement of the proposed algorithm is total storage = (k − 1) × n × (Ld + Li ) .
(4)
In Eq. (4), k is the number of gray levels that are used to display images, and n is the number of nodes. Ld and Li are the storage sizes to store double data and integer data, respectively. Since (Ld + Li ) is usually 12 bytes, if the number of gray levels that are used to display images is 11 (10 subfields), total storage requirement is 30,720 bytes. The complexity of the proposed algorithm is given by Complexity =
n
{k × (n − m)}
3.
Experimental Results
The performance of the proposed method, AISC, has been compared with the existing incremental subfield codes used in MPD-free coding, CLEAR, and NFC. MPD-free coding uses 10 subfields, and CLEAR and NFC use 12 subfields. Therefore, we used 10 and 12 subfields for AISC for comparison purposes. As the halftone technique, the error diffusion method [13] was used. As test images, we used 100 HDTV sample images and nine popular benchmark images: Lena, Peppers, Mandrill, Goldhill, Monarch, Airplane, Tiffany, Girls, and Barbara. To assess the image quality, we used the objective method [14] with peak signalto-noise ratio (PSNR). PSNR, given by Eq. (6), represents the level of differences between the reference image and the processed image. In Eq. (6), N is the number of pixels in the image, and xi and yi are the gray levels of the i-th pixels in the reference and the processed images, X and Y. L is the dynamic range of the pixel gray values.
m=1
= k × n2 ÷ 2 + k × n ÷ 2 = O n2 ,
(5)
where k is the number of gray levels that are used to display images, and n is the number of nodes. 2.4 Selection of Subfield Weight for Incremental Subfield Coding After finding a set of optimal gray levels, the proposed method converts them into an incremental subfield code. For code conversion, it is necessary to determine the weight values of subfields. The weight of each subfield is determined as the difference between two adjacent gray levels to represent. The gray levels of 0, 1, 10, 20, 25, 80, up to 255 in Fig. 1 were selected as the gray levels to be represented as an incremental subfield code. To represent gray level 1, we set the weight of the first subfield as 1. Then, for the next gray level 10, we set the weight of the next subfield to 9. In this way, the selected optimal gray levels can easily be converted into an incremental subfield code.
N 1 (xi − yi )2 N i=1
2
L L = 20×log10 √ PS NR = 10×log10 MS E MS E ∗MSE : Mean Square Error
∗MS E =
(6)
Image quality assessment methods are divided into subjective and objective methods [14]. The subjective assessment [15] has the advantage of reflecting the sensitivity of the human eye. Because the ultimate users of images are human beings, it is necessary to reflect the human eye sensitivity in evaluating the proposed method. However, subjective assessment does not provide quantitative results
2.5 Hardware Requirement to Implement Proposed Algorithm, AISC Assume that the proposed algorithm, AISC, is used to realize 256 gray levels in real time. The work for graph construction (Sect. 2.2) requires about 33,000 additions at maximum, and the work of finding a set of optimal gray levels (Sect. 2.3) for k=11 requires 360,000 additions and 360,000 comparison operations at maximum. This leads to 753,000 operations in total, that must to be completed in one frame time of 16.7 ms. Thus, the hardware must process data at the speed of 45 MFLOPS. Therefore, it is possible for modern microprocessors or DSPs to perform the proposed method in real time.
Fig. 4 PSNR values [dB] for 100 HDTV sample images displayed using the existing incremental subfield coding methods and the proposed AISC method.
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2103 Table 1 PSNR of images processed by proposed AISC method and existing methods (MPD-free coding, CLEAR, and NFC).
ceeds other methods in PSNR by 4.4–6.2 dB on average. Figure 5 shows the cropped Peppers images displayed using the MPD-free code and the proposed AISC method. AISC induces much less halftone noise. 4.
Fig. 5 Cropped images (Peppers) displayed using the MPD-free coding method and the proposed AISC method.
of image quality assessment, which are necessary to compare the performance of the proposed method with those of other methods. On the other hand, the objective assessment using PSNR provides quantitative assessment results, and these are highly useful for performance comparison. In addition, there exists a general expectation for the PSNR value of acceptable images; images with PSNR larger than 30 dB are generally acceptable [16]. Furthermore, PSNR is widely used to evaluate the performance of various image compression algorithms. Although some objective assessment methods reflect eye sensitivity, none of the modeling methods is accepted as a de facto standard yet. Thus, we used the objective assessment with PSNR in our experiments. Figure 4 shows the PSNR values for the 100 HDTV images processed by AISC and by existing incremental subfield codes. AISC clearly outperforms the three existing incremental subfield codes in terms of eliminating halftone noise. Table 1 lists the average PSNR values for the nine popular benchmark images and 100 HDTV sample images processed by each method. The proposed AISC method ex-
Conclusion
Incremental subfield coding methods have the advantage of removing FCN of PDPs completely. However, they induce halftone noise, because they require the use of halftone techniques to represent 256 gray levels with a limited number of gray levels. We proposed a new approach to incremental coding of the subfield codes for PDPs, called adaptive incremental subfield coding (AISC). The basic idea of AISC is to select an incremental subfield code adaptively for a given field image in order to minimize halftone noise. In AISC, the selection of the optimal incremental subfield code is mapped onto the special-case shortest path problem, which seeks the shortest path containing a specified number of nodes. Experiments indicated that AISC improved the PSNR values for the test images by 4.4–6.2 dB on average, compared with existing incremental subfield coding methods. The hardware speed requirement to implement AISC is 45 MFLOPS. Modern microprocessors or DSPs can perform the proposed method in real time. The proposed AISC method changes the subfield code for PDPs dynamically. Thus, it is worthwhile to investigate the effect of the dynamic change of the subfield code on image quality. Acknowledgments This work was supported by LG Electronics, IDEC, and the BK21 program. References [1] T. Shinoda, “Method and a circuit for gradationally driving a flat display device,” United States Patent no.US5724054, 1998.
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