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Graph."],"published-print":{"date-parts":[[2014,12,29]]},"abstract":"<jats:p>We consider the problem of obtaining a recognizable shape as superposition moir\u00e9 of two line gratings. The method we propose generates moir\u00e9 lines located between the shape foreground and background centers and the shape boundaries. Upon relative displacement of the superposed base- and revealing-layer gratings, the moir\u00e9 lines move and give the impression of beating shapes. Original bilevel shapes are converted into elevation profiles that are embedded by small local shifts within the base-layer grating layout. The elevation profile's level lines are revealed as moir\u00e9 by superposing the base and revealing layers. Similar level line moir\u00e9s can be obtained by applying an identical geometric transformation to both the base and the revealing layers. In order to create grayscale or color images embedding several distinct moir\u00e9 shapes, we create as base layer a dither array made of several ditherband gratings, each one embedding its specific elevation profile. Further variants include the possibility of incorporating elevation profiles within both the base and the revealing layers, or having two elevation profiles sharing a same base layer by tiling the available space. The moir\u00e9-level line techniques can be advantageously used for decorative or for anti-counterfeiting applications. Their base- and revealing-layer gratings may be produced by printing techniques, by imaging on film, or by arrays of cylindrical microlenses.<\/jats:p>","DOI":"10.1145\/2644806","type":"journal-article","created":{"date-parts":[[2015,1,5]],"date-time":"2015-01-05T13:27:09Z","timestamp":1420464429000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Beating Shapes Relying on Moir\u00e9 Level Lines"],"prefix":"10.1145","volume":"34","author":[{"given":"Sylvain M.","family":"Chosson","sequence":"first","affiliation":[{"name":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roger D.","family":"Hersch","sequence":"additional","affiliation":[{"name":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne, Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2014,12,29]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Digital anti-counterfeiting software method and apparatus. 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