Edge-Directed Error Diffusion Halftoning - Semantic Scholar
688
IEEE SIGNAL PROCESSING LETTERS, VOL. 13, NO. 11, NOVEMBER 2006
Edge-Directed Error Diffusion Halftoning Xin Li
Abstract—In this letter, we propose two simple extensions of the existing error diffusion (ED) halftoning technique: one stops the diffusion at edge pixels, and the other tunes the support of the diffusion kernel to match the local edge orientation. Experimental results are used to show that the proposed edge-directed ED schemes achieve noticeably better performance over existing ED with edge enhancement for a certain class of gray-scale images.
order (raster or serpentine [14]), the ED algorithm consists of the following three steps: (1)
otherwise
Index Terms—Adaptive halftoning, edge enhancement, edge location, error diffusion, shadowing artifact.
I. INTRODUCTION IGITAL halftoning [1] refers to the technique of converting a grayscale image into a halftoned version with minimal quality degradation. When compared with screening or search-based [2], error diffusion (ED) introduced by Floyd and Steinberg [3] has been widely used in practice due to its good tradeoff between visual quality and computational cost. Various studies have suggested different ways of improving ED halftoning by adjusting either the threshold [4]–[6] or filter coefficients [7]–[9]. One issue that is difficult to address is the evaluation of visual quality of halftoned images. Despite some existing models such as blue noise [1] or green noise [10], [11], subjective quality of halftoned images often heavily relies on visual perception model (e.g., viewing distance) [12], [13]. Despite our limited understanding of the human vision model, we argue that it is still possible to optimize the performance of ED for a certain class of image structures such as regular edges. Edges (in contrast to textures), which are abundant in computer-generated graphics and photographic images, play a critical role in our perception of halftoned images. Recognizing the importance of edges, we propose to explicitly extract a binary edge map to guide the ED process in this letter. More specifically, edge location information is exploited to either stop the diffusion or adjust the ED filter coefficients such that their support is aligned with the edge orientation. When compared with the existing ED with edge enhancement (e.g., [4]), the proposed edge-directed ED (we call them “ED2”) can better preserve the contrast and location of edges. We will use experimental results to demonstrate the performance of our ED2 algorithms.
D
II. ERROR DIFFUSION We start from a brief overview of ED and introduce some be the given continuous-tone necessary notations. Let image, and is the maximum intensity value. Given a scanning Manuscript received January 31, 2006; revised April 20, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Zhou Wang. The author is with the Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV 26506-6109 USA. Digital Object Identifier 10.1109/LSP.2006.879465
(2) (3)
where denote the state variable and quantization error, respectively. Among (1)–(3), the first one is the is diffused into key step in which quantization error a “causal” neighborhood (“causal” means that only errors in the previous-scanned pixels are diffused to the current loare empirication). Filtering coefficients of ED kernel cally tuned to minimize the quality degradation. For example, two well-known filters are Floyd–Steinberg [3, Fig. 1(a)] and Jarvis–Roberts [15]. The importance of spatially adapting the ED kernel has been recognized in the literature. In [7], a weighted mean-squareerror (MSE) criterion is used in the optimization of ED. An improved strategy based on local frequency weighting is later developed in [8]. The optimization of ED kernel and threshold modulation have also been considered in [6], [9], and [16]. Another approach of optimizing ED techniques is based on edgerelated heuristics. For example, ED with edge enhancement [4] has been proposed and demonstrated convincing improvements on visual quality of halftoned images. III. EDGE-DIRECTED ERROR DIFFUSION In this letter, we present two new ED techniques with edge enhancing capability but motivated differently from [4]. Instead of spatially adjusting the threshold, we propose to explicitly exploit the edge location information during ED. For the class of grayscale images with regular edges, edge location information can be readily extracted by standard edge detectors. Such location information, if exploited wisely, could lead to better preservation of edges in the halftoned images. We will present two different approaches of implementing such an idea next. One possible approach is to stop the diffusion at the edge location. A similar edge-stopping idea has been proposed to sharpen , the edges in grayscale images. Given a binary edge map we propose to modify the original ED algorithm as follows. Algorithm 1: Edge-Stopping Error Diffusion —Diffuse the error by (1) when (edge-stopping rule). —Perform the quantization (2). —Calculate the error term (3).
1070-9908/$20.00 © 2006 IEEE
LI: EDGE-DIRECTED ERROR DIFFUSION HALFTONING
689
Fig. 1. Example of modifying ED filter based on edge locations. a) h(k; l): Floyd–Steinberg filter. b) c(m; n): binary edge map. c) h (k; l): modified filter (numbers in the boxes indicate the normalization factor).
Since the diffusion process is stopped at the edge boundary, edge blurring associated with the conventional ED is alleviated. The only increase on computational complexity is the edge detection step. Alternatively, we can also modify the ED filtering coefficients in such a way that the diffusion direction matches the edge orientation. Specifically, we propose to reallocate the ED filter as follow.
Fig. 2. Comparison of grayscale and halftoned images for edge (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Algorithm 2: Edge-Adaptive Error Diffusion —Adaptively diffuse the error based on the following rule. If standard filter
(non-edge pixel), use in (1). (edge pixel)
If
—edge weighting: . filter normalization: . —Use modified filter
in (1).
Fig. 3. Comparison of grayscale and halftoned images for disk (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
—Perform the quantization (2). —Calculate the error term (3). Fig. 1 shows an example in which the east and south neighbors of the current pixel are edge pixels. Corresponding to the original Flyod–Steinberg filter , we find to be . Therefore, the weighting filter from , and after northe weighted filter becomes . It can be seen that the malization, we have errors are anisotropically diffused, in contrast to the isotropic diffusion in the standard method. We acknowledge that existing ED with edge enhancement [4] does appear to be more versatile than the proposed ED2 since it makes little assumption about the input image. However, for the class of graphic images and a significant portion of grayscale images, regular edges are important structures to preserve during ED, and their location information is readily available. Edge location information is difficult to be exploited by adjusting threshold [4] alone since it operates on the intensity values. By contrast, our scheme can better preserve the location as well as the contrast of regular edges in the halftoned images. Moreover, it is possible to combine ours with [4] for halftoning compound images (i.e., mixture of graphic and natural images).
IV. EXPERIMENTAL RESULTS In this section, we use experimental results to demonstrate the performance of the proposed ED2 techniques. Three classes of grayscale images with increasing edge complexity are used: 1) synthetic-edge and disk; 2) graphic-ESPLogo and finlab; and 3) natural-peppers and boats. In our MATLAB-based implementation, a binary edge map is generated by the Sobel operator, and we use raster scanning only. The running time of ED2 is approximately two to three times longer than that of standard ED. The implementation of ED with edge enhancement [4] is taken from the Halftoning Toolbox of the University of Texas at Austin [6]. The Flyod–Steinberg filter is used in all experiments, and the constant controlling edge enhancement strength in [4] is set to be 4. MATLAB codes along with test images and halftoning results can be downloaded at http://www.csee.wvu. edu/~xinl/code/halftone.zip. Figs. 2 and 3 contain the experimental results for the two synthetic images. For edge and disk images, we can observe that ED2 better preserves the edge contrast and location. It is interesting to see that for disk, [4] suffers from the “shadowing artifact” whose location depends on the scanning order. It can be
690
Fig. 4. Comparison of grayscale and halftoned images for EPSLogo (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
IEEE SIGNAL PROCESSING LETTERS, VOL. 13, NO. 11, NOVEMBER 2006
Fig. 7. Comparison of grayscale and halftoned images for boats (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Since it is difficult to completely avoid resampling operations in the publication process (e.g., graphics reproduction while generating PDF files), we suggest the readers to compare the halftoned images on a computer monitor at a normal viewing distance (about 1 foot). REFERENCES
Fig. 5. Comparison of grayscale and halftoned images for finlab (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Fig. 6. Comparison of grayscale and halftoned images for peppers (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
seen from Figs. 4 and 5 that ED2 also noticeably preserves textual/graphic information better for ESPLogo and finlab. For natural images containing regular edges, we have found that ED2 achieves comparable results to [4], as shown in Figs. 6 and 7.
[1] R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987. [2] D. Lieberman and J. Allebach, “Dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process., vol. 9, no. 11, pp. 1950–1963, Nov. 2000. [3] R. Floyd and L. Steinberg, “An adaptive algorithm for spatial grayscale,” in Proc. Soc. Image Display, 1976. [4] R. Eschbach and K. Knox, “Error-diffusion algorithm with edge enhancement,” J. Opt. Soc. Am. A, vol. 8, pp. 1844–1850, 1991. [5] K. Knox and R. Eschbach, “Threshold modulation in error diffusion,” J. Electron. Imaging, vol. 2, pp. 185–192, 1993. [6] N. Damera-Venkata and B. L. Evans, “Adaptive threshold modulation for error diffusion halftoning,” IEEE Trans. Image Process., vol. 10, no. 2, pp. 104–116, Feb. 2001. [7] B. Kolpatzik and C. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging, vol. 1, pp. 277–292, 1992. [8] P. Wong, “Adaptive error diffusion and its application in multiresolution rendering,” IEEE Trans. Image Process., vol. 5, no. 7, pp. 1184–1196, Jul. 1996. [9] P. W. Wong and J. P. Allebach, “Optimum error-diffusion kernel design,” in Proc. SPIE Color Imaging: Device-Independent Color, Color Hard Copy, Graphic Arts II, 1997, pp. 236–242. [10] R. Levien, “Output dependent feedback in error diffusion halftoning,” IS&T Imag. Sci. Tech., pp. 115–118, 1993. [11] D. Lau, G. Arce, and N. Gallagher, “Green-noise digital halftoning,” Proc. IEEE, vol. 86, no. 12, pp. 2424–2444, Dec. 1998. [12] T. Pappas and D. Neuhoff, “Least-squares model-based halftoning,” IEEE Trans. Image Process., vol. 8, no. 8, pp. 1102–1116, Aug. 1999. [13] T. Kite, B. Evans, and A. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Process., vol. 9, no. 5, pp. 909–922, May 2000. [14] I. Witten and R. Neal, “Using Peano curves for bilevel display of continuous-tone images,” IEEE Comput. Graph. Appl., vol. CGA-??, pp. 47–51, 1982. [15] J. Jarvis and C. Roberts, “A new technique for displaying continuous tone images on a bilevel display,” IEEE Trans. Commun., vol. COM–24, pp. 891–898, 1976. [16] P. Li and J. Allebach, “Tone-dependent error diffusion,” IEEE Trans. Image Process., vol. 13, no. 2, pp. 201–215, Feb. 2004.
IEEE SIGNAL PROCESSING LETTERS, VOL. 13, NO. 11, NOVEMBER 2006
Edge-Directed Error Diffusion Halftoning Xin Li
Abstract—In this letter, we propose two simple extensions of the existing error diffusion (ED) halftoning technique: one stops the diffusion at edge pixels, and the other tunes the support of the diffusion kernel to match the local edge orientation. Experimental results are used to show that the proposed edge-directed ED schemes achieve noticeably better performance over existing ED with edge enhancement for a certain class of gray-scale images.
order (raster or serpentine [14]), the ED algorithm consists of the following three steps: (1)
otherwise
Index Terms—Adaptive halftoning, edge enhancement, edge location, error diffusion, shadowing artifact.
I. INTRODUCTION IGITAL halftoning [1] refers to the technique of converting a grayscale image into a halftoned version with minimal quality degradation. When compared with screening or search-based [2], error diffusion (ED) introduced by Floyd and Steinberg [3] has been widely used in practice due to its good tradeoff between visual quality and computational cost. Various studies have suggested different ways of improving ED halftoning by adjusting either the threshold [4]–[6] or filter coefficients [7]–[9]. One issue that is difficult to address is the evaluation of visual quality of halftoned images. Despite some existing models such as blue noise [1] or green noise [10], [11], subjective quality of halftoned images often heavily relies on visual perception model (e.g., viewing distance) [12], [13]. Despite our limited understanding of the human vision model, we argue that it is still possible to optimize the performance of ED for a certain class of image structures such as regular edges. Edges (in contrast to textures), which are abundant in computer-generated graphics and photographic images, play a critical role in our perception of halftoned images. Recognizing the importance of edges, we propose to explicitly extract a binary edge map to guide the ED process in this letter. More specifically, edge location information is exploited to either stop the diffusion or adjust the ED filter coefficients such that their support is aligned with the edge orientation. When compared with the existing ED with edge enhancement (e.g., [4]), the proposed edge-directed ED (we call them “ED2”) can better preserve the contrast and location of edges. We will use experimental results to demonstrate the performance of our ED2 algorithms.
D
II. ERROR DIFFUSION We start from a brief overview of ED and introduce some be the given continuous-tone necessary notations. Let image, and is the maximum intensity value. Given a scanning Manuscript received January 31, 2006; revised April 20, 2006. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Zhou Wang. The author is with the Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV 26506-6109 USA. Digital Object Identifier 10.1109/LSP.2006.879465
(2) (3)
where denote the state variable and quantization error, respectively. Among (1)–(3), the first one is the is diffused into key step in which quantization error a “causal” neighborhood (“causal” means that only errors in the previous-scanned pixels are diffused to the current loare empirication). Filtering coefficients of ED kernel cally tuned to minimize the quality degradation. For example, two well-known filters are Floyd–Steinberg [3, Fig. 1(a)] and Jarvis–Roberts [15]. The importance of spatially adapting the ED kernel has been recognized in the literature. In [7], a weighted mean-squareerror (MSE) criterion is used in the optimization of ED. An improved strategy based on local frequency weighting is later developed in [8]. The optimization of ED kernel and threshold modulation have also been considered in [6], [9], and [16]. Another approach of optimizing ED techniques is based on edgerelated heuristics. For example, ED with edge enhancement [4] has been proposed and demonstrated convincing improvements on visual quality of halftoned images. III. EDGE-DIRECTED ERROR DIFFUSION In this letter, we present two new ED techniques with edge enhancing capability but motivated differently from [4]. Instead of spatially adjusting the threshold, we propose to explicitly exploit the edge location information during ED. For the class of grayscale images with regular edges, edge location information can be readily extracted by standard edge detectors. Such location information, if exploited wisely, could lead to better preservation of edges in the halftoned images. We will present two different approaches of implementing such an idea next. One possible approach is to stop the diffusion at the edge location. A similar edge-stopping idea has been proposed to sharpen , the edges in grayscale images. Given a binary edge map we propose to modify the original ED algorithm as follows. Algorithm 1: Edge-Stopping Error Diffusion —Diffuse the error by (1) when (edge-stopping rule). —Perform the quantization (2). —Calculate the error term (3).
1070-9908/$20.00 © 2006 IEEE
LI: EDGE-DIRECTED ERROR DIFFUSION HALFTONING
689
Fig. 1. Example of modifying ED filter based on edge locations. a) h(k; l): Floyd–Steinberg filter. b) c(m; n): binary edge map. c) h (k; l): modified filter (numbers in the boxes indicate the normalization factor).
Since the diffusion process is stopped at the edge boundary, edge blurring associated with the conventional ED is alleviated. The only increase on computational complexity is the edge detection step. Alternatively, we can also modify the ED filtering coefficients in such a way that the diffusion direction matches the edge orientation. Specifically, we propose to reallocate the ED filter as follow.
Fig. 2. Comparison of grayscale and halftoned images for edge (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Algorithm 2: Edge-Adaptive Error Diffusion —Adaptively diffuse the error based on the following rule. If standard filter
(non-edge pixel), use in (1). (edge pixel)
If
—edge weighting: . filter normalization: . —Use modified filter
in (1).
Fig. 3. Comparison of grayscale and halftoned images for disk (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
—Perform the quantization (2). —Calculate the error term (3). Fig. 1 shows an example in which the east and south neighbors of the current pixel are edge pixels. Corresponding to the original Flyod–Steinberg filter , we find to be . Therefore, the weighting filter from , and after northe weighted filter becomes . It can be seen that the malization, we have errors are anisotropically diffused, in contrast to the isotropic diffusion in the standard method. We acknowledge that existing ED with edge enhancement [4] does appear to be more versatile than the proposed ED2 since it makes little assumption about the input image. However, for the class of graphic images and a significant portion of grayscale images, regular edges are important structures to preserve during ED, and their location information is readily available. Edge location information is difficult to be exploited by adjusting threshold [4] alone since it operates on the intensity values. By contrast, our scheme can better preserve the location as well as the contrast of regular edges in the halftoned images. Moreover, it is possible to combine ours with [4] for halftoning compound images (i.e., mixture of graphic and natural images).
IV. EXPERIMENTAL RESULTS In this section, we use experimental results to demonstrate the performance of the proposed ED2 techniques. Three classes of grayscale images with increasing edge complexity are used: 1) synthetic-edge and disk; 2) graphic-ESPLogo and finlab; and 3) natural-peppers and boats. In our MATLAB-based implementation, a binary edge map is generated by the Sobel operator, and we use raster scanning only. The running time of ED2 is approximately two to three times longer than that of standard ED. The implementation of ED with edge enhancement [4] is taken from the Halftoning Toolbox of the University of Texas at Austin [6]. The Flyod–Steinberg filter is used in all experiments, and the constant controlling edge enhancement strength in [4] is set to be 4. MATLAB codes along with test images and halftoning results can be downloaded at http://www.csee.wvu. edu/~xinl/code/halftone.zip. Figs. 2 and 3 contain the experimental results for the two synthetic images. For edge and disk images, we can observe that ED2 better preserves the edge contrast and location. It is interesting to see that for disk, [4] suffers from the “shadowing artifact” whose location depends on the scanning order. It can be
690
Fig. 4. Comparison of grayscale and halftoned images for EPSLogo (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
IEEE SIGNAL PROCESSING LETTERS, VOL. 13, NO. 11, NOVEMBER 2006
Fig. 7. Comparison of grayscale and halftoned images for boats (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Since it is difficult to completely avoid resampling operations in the publication process (e.g., graphics reproduction while generating PDF files), we suggest the readers to compare the halftoned images on a computer monitor at a normal viewing distance (about 1 foot). REFERENCES
Fig. 5. Comparison of grayscale and halftoned images for finlab (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
Fig. 6. Comparison of grayscale and halftoned images for peppers (top-down, left-to-right): original, standard ED, ED with edge enhancement (raster scanning), ED with edge enhancement (serpentine scanning), Algorithm 1, and Algorithm 2.
seen from Figs. 4 and 5 that ED2 also noticeably preserves textual/graphic information better for ESPLogo and finlab. For natural images containing regular edges, we have found that ED2 achieves comparable results to [4], as shown in Figs. 6 and 7.
[1] R. Ulichney, Digital Halftoning. Cambridge, MA: MIT Press, 1987. [2] D. Lieberman and J. Allebach, “Dual interpretation for direct binary search and its implications for tone reproduction and texture quality,” IEEE Trans. Image Process., vol. 9, no. 11, pp. 1950–1963, Nov. 2000. [3] R. Floyd and L. Steinberg, “An adaptive algorithm for spatial grayscale,” in Proc. Soc. Image Display, 1976. [4] R. Eschbach and K. Knox, “Error-diffusion algorithm with edge enhancement,” J. Opt. Soc. Am. A, vol. 8, pp. 1844–1850, 1991. [5] K. Knox and R. Eschbach, “Threshold modulation in error diffusion,” J. Electron. Imaging, vol. 2, pp. 185–192, 1993. [6] N. Damera-Venkata and B. L. Evans, “Adaptive threshold modulation for error diffusion halftoning,” IEEE Trans. Image Process., vol. 10, no. 2, pp. 104–116, Feb. 2001. [7] B. Kolpatzik and C. Bouman, “Optimized error diffusion for image display,” J. Electron. Imaging, vol. 1, pp. 277–292, 1992. [8] P. Wong, “Adaptive error diffusion and its application in multiresolution rendering,” IEEE Trans. Image Process., vol. 5, no. 7, pp. 1184–1196, Jul. 1996. [9] P. W. Wong and J. P. Allebach, “Optimum error-diffusion kernel design,” in Proc. SPIE Color Imaging: Device-Independent Color, Color Hard Copy, Graphic Arts II, 1997, pp. 236–242. [10] R. Levien, “Output dependent feedback in error diffusion halftoning,” IS&T Imag. Sci. Tech., pp. 115–118, 1993. [11] D. Lau, G. Arce, and N. Gallagher, “Green-noise digital halftoning,” Proc. IEEE, vol. 86, no. 12, pp. 2424–2444, Dec. 1998. [12] T. Pappas and D. Neuhoff, “Least-squares model-based halftoning,” IEEE Trans. Image Process., vol. 8, no. 8, pp. 1102–1116, Aug. 1999. [13] T. Kite, B. Evans, and A. Bovik, “Modeling and quality assessment of halftoning by error diffusion,” IEEE Trans. Image Process., vol. 9, no. 5, pp. 909–922, May 2000. [14] I. Witten and R. Neal, “Using Peano curves for bilevel display of continuous-tone images,” IEEE Comput. Graph. Appl., vol. CGA-??, pp. 47–51, 1982. [15] J. Jarvis and C. Roberts, “A new technique for displaying continuous tone images on a bilevel display,” IEEE Trans. Commun., vol. COM–24, pp. 891–898, 1976. [16] P. Li and J. Allebach, “Tone-dependent error diffusion,” IEEE Trans. Image Process., vol. 13, no. 2, pp. 201–215, Feb. 2004.
