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Formulation of an accurate discrete theory of median shifts

机译：精确的离散中位数理论的表述

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This paper presents an accurate discrete theory of median shifts. It shows that a quadratic law exists for low curvature values, and that this gives way only gradually to the linear law predicted by the earlier continuum model as the curvature increases. As a result, the variation is almost entirely quadratic for 3 x 3 neighbourhoods, but approaches linearity for 7 x 7 and larger neighbourhoods. In all cases the median shifts exhibit substantial angular variations, though the isotropy can be improved by truncating square neighbourhoods to make them more circular. Tests on circular objects show very good agreement between the new discrete theory and the observed results, with minor exceptions that are explainable by simple geometry. Thus the prime aim of this paper―to achieve a full understanding of the detailed mechanisms of the median filter including the way in which it produces shifts―is achieved.
机译：本文提出了一种精确的离散中位数理论。它表明对于低曲率值存在二次定律，并且随着曲率的增加，这仅逐渐让由早期连续模型预测的线性定律所取代。结果，对于3 x 3邻域，变化几乎是二次方的，但对于7 x 7及更大邻域，变化接近线性。在所有情况下，中位偏移都显示出很大的角度变化，尽管可以通过将正方形邻域截短以使其更加圆形来改善各向同性。对圆形物体的测试表明，新的离散理论与观察到的结果之间具有很好的一致性，只有少数例外可以通过简单的几何图形来解释。因此，本文的主要目标是-全面了解中值滤波器的详细机制，包括产生移位的方式。

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