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Intra coding is an essential part of all video coding algorithms and applications. Additionally, intra coding algorithms are predestined for an efficient still image coding. To overcome limitations in existing intra coding algorithms (such as linear directional extrapolation, only one direction per block, small reference area), we propose non-linear Contour-based Multidirectional Intra Coding. This coding mode is based on four different non-linear contour models, on the connection of intersecting contours and on a boundary recall-based contour model selection algorithm. The different contour models address robustness against outliers for the detected contours and evasive curvature changes. Additionally, the information for the prediction is derived from already reconstructed pixels in neighboring blocks. The achieved coding efficiency is superior to those of related works from the literature. Compared with the closest related work, BD rate gains of 2.16% are achieved on average.