Structure-aware error-diffusion approach using entropy-constrained threshold modulation

Error diffusion is known as a commonly used digital halftoning technique. We present a novel and efficient error-diffusion algorithm which is capable of preserving appreciable structures and tones with blue-noise property. According to the theoretical analysis of threshold modulation, the extraction of the high-frequency image contents is helpful to preserve human vision-sensitive textures. The pixel intensity’s influence on the structural distortion is observed based on a key statistic phenomenon. This effect leads to the non-uniform conservation of diversiform detail contents. To alleviate this influence, an entropy is introduced to measure the intensity’s impact and adaptively constrain the threshold-modulation strength. Compared with the existing edge-enhancement halftoning, our entropy-based method does not suffer from the failure to detect weak edges or improper emphasis of details. On the other hand, this structural improvement enables the modification of error-diffusion coefficients to eliminate visually harmful tonal artifacts, which results in the seamless integration with the best tone-aware techniques (Ostromoukhov in Proceedings of ACM SIGGRAPH, SIGGRAPH ’01, pp 567–572, 2001 , Zhou and Fang in ACM Trans Graph (TOG) 22(3):437–444, 2003 ). Comparisons with the state-of-the-art structure-preserving error diffusions (Chang et al. in ACM Trans Graph (TOG) 28(5): 162:1–162:8, 2009 , Li and Mould in Forum 29(2):273–280, 2010 ) indicate that our methods can achieve better structural similarity with better tone consistency. Our performance is one order of magnitude faster than (Chang et al. in ACM Trans Graph (TOG) 28(5): 162:1–162:8, 2009 , Li and Mould in Forum 29(2): 273–280, 2010 ) while ensuring higher visual quality on typical images. Due to low computational overhead and high halftone quality, the proposed methods in this paper can be widely applicable in many practical applications.