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When we look at an object on a screen, even if we see a black and white binary image for each individual pixel, we experience that we can recognize the pixels as a pseudo halftone image when all pixels are viewed at once. In a previous paper, we showed aspects of vision that are performed hierarchically via the external world, retina, and brain according to a one-dimensional visual model and equivalence approximation method. The purpose of this paper is to clarify a strict, concrete analysis of evaluation methods for various types of modulated images according to a two-dimensional visual model and construct an objective evaluation method to be used for matching with subjective evaluations. This formal method is the basis of the previously published two-dimensional equivalence approximation method. We selected the pulse density four division image as the comparison standard and used a simple binary image, random dither image, least mean error image, and ordered dither image as modulated images to show specific values for the best numbers of approximation terms M0,N0 and obtain the measure of approximation with the reconstructed images to perform comparison inspections with subjective quality evaluations of these images. We evaluated the subjective quality by using the subjective mean ranking MOS of 15 assessors. From these results, we reconfirmed that the subjective quality of various modulated images can be objectively evaluated according to the measure of approximation. As a result, we clarified the strict, concrete analysis of evaluation methods for various types of modulated images according to the two-dimensional visual model of the formal method and constructed an objective evaluation method to be used for matching with subjective evaluations. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(10): 54–70, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20120 [ABSTRACT FROM AUTHOR]