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Graph."],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"<jats:p>The depth resolution achieved by a continuous wave time-of-flight (C-ToF) imaging system is determined by the coding (modulation and demodulation) functions that it uses. Almost all current C-ToF systems use sinusoid or square coding functions, resulting in a limited depth resolution. In this article, we present a mathematical framework for exploring and characterizing the space of C-ToF coding functions in a geometrically intuitive space. Using this framework, we design families of novel coding functions that are based on Hamiltonian cycles on hypercube graphs. Given a fixed total source power and acquisition time, the new Hamiltonian coding scheme can achieve up to an order of magnitude higher resolution as compared to the current state-of-the-art methods, especially in low signal-to-noise ratio (SNR) settings. We also develop a comprehensive physically-motivated simulator for C-ToF cameras that can be used to evaluate various coding schemes prior to a real hardware implementation. Since most off-the-shelf C-ToF sensors use sinusoid or square functions, we develop a hardware prototype that can implement a wide range of coding functions. Using this prototype and our software simulator, we demonstrate the performance advantages of the proposed Hamiltonian coding functions in a wide range of imaging settings.<\/jats:p>","DOI":"10.1145\/3152155","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T15:27:23Z","timestamp":1519918043000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":37,"title":["What Are Optimal Coding Functions for Time-of-Flight Imaging?"],"prefix":"10.1145","volume":"37","author":[{"given":"Mohit","family":"Gupta","sequence":"first","affiliation":[{"name":"University of Wisconsin-Madison, Madison, WI"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andreas","family":"Velten","sequence":"additional","affiliation":[{"name":"University of Wisconsin-Madison, Madison, WI"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shree K.","family":"Nayar","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eric","family":"Breitbach","sequence":"additional","affiliation":[{"name":"University of Wisconsin-Madison, Madison, WI"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,2,28]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2016.2567379"},{"key":"e_1_2_2_2_1","volume-title":"Proc. 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