270 likes | 309 Views
Error Diffusion (ED). Li Yang Campus Norrköping (ITN), University of Linköping. Fundamental concepts. Threshold error feedback Input -> threshold -> error -> input ->... It is adaptive algorithm;
E N D
Error Diffusion (ED) Li Yang Campus Norrköping (ITN), Universityof Linköping
Fundamental concepts • Threshold error feedback • Input -> threshold -> error -> input ->... • It is adaptive algorithm; • It takes neiborghood information into account to determine the output value. • Different from dither matrix.
A historical review • Sigma-delta modulation :Analog-to-digital conversion of 1-D audio signal (Inose and Yasuda, 1963); • Error diffusion: 2-D for halftoning (Floyd and Steinberg, 1975); • Massive of following studies: theoretical studies and practical applications about ED.
Two ways for error diffusion (descriptions) • Standard ED: error is diffused from p(i,j) to its neighbours directly after its halftoning -> modified input …; • Systematic error compensation: Halftone for the original input, collect the error from its neighbours and modify the output of the pixel according to ED filter. • They are mathematically equivalent.
Mathematical description of error diffusion (spatial domain)
Mathematical description of error diffusion (frequency domain)
Characteristics of the error filter, • is a high pass filter: it lets only high spatial frequency components of the texture noise in the error spectrum pass into the output spectrum,
Applications and problems • Worm artifacts
Topics of research • Optimum error filter design; • Stochastic error filter perturbation; • Modification of raster direction and space filling-path; • Threshold modulation; • Image adaptive error diffusion; • Model based error diffusion;
Optimum error filter design • Goal: to minimize the difference between the input- and output-images in a human vision perspective; • Mathematics:
Stochastic error filter perturbation • Add random noise to the weights of the error filter(Schreiber 1981, Woo 1984); • Some examples
Threshold modulation • Adopt to non-constant threshold values; • Add a set of random values to the threshold: t=0.50.5+t(m,n); • Varying the threshold spatially;
Image adaptive error diffusion • Based on the observation: the error spectrum distribution depends on the local tone values of the input image (Zeggel and Bryngdahl, 1994) • See examples