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We introduce a general framework for assigning distances between kanji basedon their dissimilarity. What we mean by this term may depend on the concreteapplication. The only assumption we make is that the dissimilarity between twokanji is adequately expressed as a weighted mean of penalties obtained frommatching nested structures of components in an optimal way. For the cost ofmatching, we suggest a number of modules that can be freely combined orreplaced with other modules, including the relative unbalanced ink transportbetween registered components, the distance between the transformationsrequired for registration, and the difference in prespecified labels.  We give a concrete example of a kanji distance function obtained in this wayas a proof of concept. Based on this function, we produce 2D kanji maps bymultidimensional scaling and a table of 100 randomly selected J\=oj\=o kanjiwith their 16 nearest neighbors.  Our kanji distance functions can be used to help Japanese learners fromnon-CJK backgrounds acquire kanji literacy. In addition, they may assisteditors of kanji dictionaries in presenting their materials and may serve intext processing and optical character recognition systems for assessing thelikelihood of errors.

Distance maps between Japanese kanji characters based on hierarchical optimal transport