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In this work, we apply a progressive, view\u2010dependent Monte Carlo\u2010based approach for the visualization of such Lagrangian fields in time\u2010dependent flows. Our approach avoids grid discretization and ray marching errors completely, is consistent, and has a low memory consumption. The system provides noisy previews that converge over time to an accurate high\u2010quality visualization. Compared to traditional approaches, the proposed system avoids explicitly predefined fieldline seeding structures, and uses a Monte Carlo sampling strategy named Woodcock tracking to distribute samples along the view ray. An acceleration of this sampling strategy requires local upper bounds for the FTLE values, which we progressively acquire during the rendering. Our approach is tailored for high\u2010quality visualizations of complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface structures as indicators for Lagrangian coherent structures (LCS). We demonstrate the effectiveness of our approach by using a set of analytic test cases and real\u2010world numerical simulations.<\/jats:p>","DOI":"10.1111\/cgf.12914","type":"journal-article","created":{"date-parts":[[2016,7,4]],"date-time":"2016-07-04T13:54:40Z","timestamp":1467640480000},"page":"381-390","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["MCFTLE: Monte Carlo Rendering of Finite\u2010Time Lyapunov Exponent Fields"],"prefix":"10.1111","volume":"35","author":[{"given":"Tobias","family":"G\u00fcnther","sequence":"first","affiliation":[{"name":"Visual Computing Group University of Magdeburg"}]},{"given":"Alexander","family":"Kuhn","sequence":"additional","affiliation":[{"name":"Zuse Institute Berlin"}]},{"given":"Holger","family":"Theisel","sequence":"additional","affiliation":[{"name":"Visual Computing Group University of Magdeburg"}]}],"member":"311","published-online":{"date-parts":[[2016,7,4]]},"reference":[{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2467963"},{"key":"e_1_2_10_3_2","first-page":"93970K","article-title":"A multi\u2010resolution interpolation scheme for pathline based Lagrangian flow representations","volume":"9397","author":"Agranovsky A.","year":"2015","journal-title":"Proc. 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