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Bit-length of digital images is decided by the Analog-to-Digital (AD) converter. The bit-length expansion technique is necessary for high-quality displays such as the liquid crystal display (LCD) and the plasma display. Bit-length expansion is also necessary for low-bit length images, which are degraded by the pseudo-contour. In this paper, we propose a bit-length expansion method from M-level to N-level [N=3(M-1)+1]. This operation means that two quantization levels are introduced between existing levels. The bit-length expansion method results in the estimation problem of an error image between an M-level's image and an N-level's image. The error image is the pattern image which consists of three values. We show the estimation method of the three values pattern image and that the proposed method can remove the pseudo-contour of digital images through several application results. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 92(10): 32–40, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10105 [ABSTRACT FROM AUTHOR]