{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T19:03:14Z","timestamp":1783105394778,"version":"3.54.6"},"reference-count":84,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T00:00:00Z","timestamp":1562889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1046-14"],"award-info":[{"award-number":["1046-14"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","award":["HR0011-16-C-0028"],"award-info":[{"award-number":["HR0011-16-C-0028"]}],"id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["635537"],"award-info":[{"award-number":["635537"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1730147."],"award-info":[{"award-number":["CCF-1730147."]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2019,8,31]]},"abstract":"<jats:p>We present a Monte Carlo rendering framework for the physically-accurate simulation of speckle patterns arising from volumetric scattering of coherent waves. These noise-like patterns are characterized by strong statistical properties, such as the so-called memory effect. These properties are at the core of imaging techniques for applications as diverse as tissue imaging, motion tracking, and non-line-of-sight imaging. Our rendering framework can replicate these properties computationally, in a way that is orders of magnitude more efficient than alternatives based on directly solving the wave equations. At the core of our framework is a path-space formulation for the covariance of speckle patterns arising from a scattering volume, which we derive from first principles. We use this formulation to develop two Monte Carlo rendering algorithms, for computing speckle covariance as well as directly speckle fields. While approaches based on wave equation solvers require knowing the microscopic position of wavelength-sized scatterers, our approach takes as input only bulk parameters describing the statistical distribution of these scatterers inside a volume. We validate the accuracy of our framework by comparing against speckle patterns simulated using wave equation solvers, use it to simulate memory effect observations that were previously only possible through lab measurements, and demonstrate its applicability for computational imaging tasks.<\/jats:p>","DOI":"10.1145\/3306346.3322950","type":"journal-article","created":{"date-parts":[[2019,7,12]],"date-time":"2019-07-12T19:04:08Z","timestamp":1562958248000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":37,"title":["A Monte Carlo framework for rendering speckle statistics in scattering media"],"prefix":"10.1145","volume":"38","author":[{"given":"Chen","family":"Bar","sequence":"first","affiliation":[{"name":"Technion, Haifa, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marina","family":"Alterman","sequence":"additional","affiliation":[{"name":"Technion, Haifa, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ioannis","family":"Gkioulekas","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anat","family":"Levin","sequence":"additional","affiliation":[{"name":"Technion, Haifa, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2019,7,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","volume-title":"Mesoscopic Physics of Electrons and Photons","author":"Akkermans Eric","DOI":"10.1017\/CBO9780511618833"},{"key":"e_1_2_2_2_1","doi-asserted-by":"crossref","unstructured":"M. Batarseh S. Sukhov Z. Shen H. Gemar R. Rezvani and A. Dogariu. 2018. Passive sensing around the corner using spatial coherence. Nature Communications.  M. Batarseh S. Sukhov Z. Shen H. Gemar R. Rezvani and A. Dogariu. 2018. Passive sensing around the corner using spatial coherence. Nature Communications.","DOI":"10.1038\/s41467-018-05985-w"},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Ibrahim Baydoun Diego Baresch Romain Pierrat and Arnaud Derode. 2016. Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation. Physical Review E.  Ibrahim Baydoun Diego Baresch Romain Pierrat and Arnaud Derode. 2016. Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation. Physical Review E.","DOI":"10.1103\/PhysRevE.94.053005"},{"key":"e_1_2_2_4_1","unstructured":"Stephan Bergmann Mahsa Mohammadikaji Stephan Irgenfried Heinz Worn J\u00fcrgen Beyerer and Carsten Dachsbacher. 2016. A Phenomenological Approach to Integrating Gaussian Beam Properties and Speckle into a Physically-Based Renderer. In Vision Modeling & Visualization.   Stephan Bergmann Mahsa Mohammadikaji Stephan Irgenfried Heinz Worn J\u00fcrgen Beyerer and Carsten Dachsbacher. 2016. A Phenomenological Approach to Integrating Gaussian Beam Properties and Speckle into a Physically-Based Renderer. In Vision Modeling & Visualization."},{"key":"e_1_2_2_5_1","volume-title":"Correlations in coherent multiple scattering. Physics Reports","author":"Berkovits Richard","year":"1994"},{"key":"e_1_2_2_6_1","volume-title":"Dynamic light scattering: with applications to chemistry, biology, and physics","author":"Berne Bruce J"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1038\/nature11578"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/3272127.3275103"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.14.000192"},{"key":"e_1_2_2_10_1","volume-title":"Huffman","author":"Bohren Craig F.","year":"1983"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2231816.2231820"},{"key":"e_1_2_2_12_1","unstructured":"Eugene d'Eon. 2018a. A Reciprocal Formulation of Non-Exponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation. arXiv preprint arXiv:1809.05881.  Eugene d'Eon. 2018a. A Reciprocal Formulation of Non-Exponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation. arXiv preprint arXiv:1809.05881."},{"key":"e_1_2_2_13_1","doi-asserted-by":"crossref","unstructured":"Eugene d'Eon. 2018b. A reciprocal formulation of non-exponential radiative transfer with uncorrelated sources detectors and boundaries. 1: Sketch and motivation. arXiv preprint arXiv:1803.03259.  Eugene d'Eon. 2018b. A reciprocal formulation of non-exponential radiative transfer with uncorrelated sources detectors and boundaries. 1: Sketch and motivation. arXiv preprint arXiv:1803.03259.","DOI":"10.1080\/23324309.2018.1481433"},{"key":"e_1_2_2_14_1","doi-asserted-by":"crossref","unstructured":"Ronald L. Dougherty Bruce J. Ackerson N.M. Reguigui F. Dorri-Nowkoorani and Ulf Nobbmann. 1994. Correlation transfer: Development and application. J. of Quantitative Spectroscopy and Radiative Transfer.  Ronald L. Dougherty Bruce J. Ackerson N.M. Reguigui F. Dorri-Nowkoorani and Ulf Nobbmann. 1994. Correlation transfer: Development and application. J. of Quantitative Spectroscopy and Radiative Transfer.","DOI":"10.1016\/0022-4073(94)90037-X"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.25.002088"},{"key":"e_1_2_2_16_1","volume-title":"Yodh","author":"Durduran Turgut","year":"2010"},{"key":"e_1_2_2_17_1","volume-title":"Advanced global illumination","author":"Dutr\u00e9 Philip"},{"key":"e_1_2_2_18_1","unstructured":"Robert Erf. 1978. Speckle Metrology. Elsevier.  Robert Erf. 1978. Speckle Metrology. Elsevier."},{"key":"e_1_2_2_19_1","doi-asserted-by":"crossref","unstructured":"Shechao Feng Charles Kane Patrick A Lee and A Douglas Stone. 1988. Correlations and fluctuations of coherent wave transmission through disordered media. Physical review letters 61 7 834.  Shechao Feng Charles Kane Patrick A Lee and A Douglas Stone. 1988. Correlations and fluctuations of coherent wave transmission through disordered media. Physical review letters 61 7 834.","DOI":"10.1103\/PhysRevLett.61.834"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1364\/AO.21.002758"},{"key":"e_1_2_2_21_1","doi-asserted-by":"crossref","unstructured":"Isaac Freund. 1990. Looking through walls and around corners. Physica: Statistical Mechanics and its App.  Isaac Freund. 1990. Looking through walls and around corners. Physica: Statistical Mechanics and its App.","DOI":"10.1016\/0378-4371(90)90357-X"},{"key":"e_1_2_2_22_1","volume-title":"Surface correlations in multiple-scattering media. Phys Rev A","author":"Freund Isaac","year":"1992"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.61.2328"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.72.000052"},{"key":"e_1_2_2_25_1","volume-title":"Niels J\u00f8rgen Christensen, and Henrik Wann Jensen","author":"Frisvad Jeppe Revall","year":"2007"},{"key":"e_1_2_2_26_1","doi-asserted-by":"crossref","unstructured":"Ioannis Gkioulekas Anat Levin and Todd Zickler. 2016. An Evaluation of Computational Imaging Techniques for Heterogeneous Inverse Scattering.  Ioannis Gkioulekas Anat Levin and Todd Zickler. 2016. An Evaluation of Computational Imaging Techniques for Heterogeneous Inverse Scattering.","DOI":"10.1007\/978-3-319-46487-9_42"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508377"},{"key":"e_1_2_2_28_1","volume-title":"Dynamic light scattering. American Journal of Physics","author":"Goldburg W. I.","year":"1999"},{"key":"e_1_2_2_29_1","volume-title":"Speckle Phenomena in Optics: Theory and Applications"},{"key":"e_1_2_2_30_1","doi-asserted-by":"crossref","unstructured":"Vadim Holodovski Yoav Y. Schechner Anat Levin Aviad Levis and Amit Aides. 2016. In-situ multi-view multi-scattering stochastic tomography. In ICCP.  Vadim Holodovski Yoav Y. Schechner Anat Levin Aviad Levis and Amit Aides. 2016. In-situ multi-view multi-scattering stochastic tomography. In ICCP.","DOI":"10.1109\/ICCPHOT.2016.7492869"},{"key":"e_1_2_2_31_1","volume-title":"Coherent backscattering enhancement in highly anisotropically scattering media: Numerical solution. Journal of Quantitative Spectroscopy and Radiative Transfer","author":"Ilyushin Y.A.","year":"2012"},{"key":"e_1_2_2_32_1","doi-asserted-by":"crossref","volume-title":"Wave propagation and scattering in random media","author":"Ishimaru Akira","DOI":"10.1109\/9780470547045"},{"key":"e_1_2_2_33_1","doi-asserted-by":"crossref","unstructured":"P. Jacquot and J. M. Fournier. 2000. Interferometry in Speckle Light. Springer.  P. Jacquot and J. M. Fournier. 2000. Interferometry in Speckle Light. Springer.","DOI":"10.1007\/978-3-642-57323-1"},{"key":"e_1_2_2_34_1","volume-title":"Rastogi","author":"Jacquot Pierre","year":"1979"},{"key":"e_1_2_2_35_1","unstructured":"Wenzel Jakob. 2010. Mitsuba renderer. http:\/\/www.mitsuba-renderer.org.  Wenzel Jakob. 2010. Mitsuba renderer. http:\/\/www.mitsuba-renderer.org."},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778790"},{"key":"e_1_2_2_37_1","doi-asserted-by":"crossref","unstructured":"M. L. Jakobsen H. T. Yura and S. G. Hanson. 2012. Spatial filtering velocimetry of objective speckles for measuring out-of-plane motion. Appl. Opt. (2012).  M. L. Jakobsen H. T. Yura and S. G. Hanson. 2012. Spatial filtering velocimetry of objective speckles for measuring out-of-plane motion. Appl. Opt. (2012).","DOI":"10.1117\/12.922911"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201282"},{"key":"e_1_2_2_39_1","volume-title":"Computer Graphics Forum","author":"Jarabo Adrian"},{"key":"e_1_2_2_40_1","doi-asserted-by":"crossref","unstructured":"O. Katz P. Heidmann M. Fink and S. Gigan. 2014. Non-invasive single-shot imaging through scattering layers and around corners via speckle correlation. Nat. Photonics (2014).  O. Katz P. Heidmann M. Fink and S. Gigan. 2014. Non-invasive single-shot imaging through scattering layers and around corners via speckle correlation. Nat. Photonics (2014).","DOI":"10.1038\/nphoton.2014.189"},{"key":"e_1_2_2_41_1","doi-asserted-by":"crossref","unstructured":"O. Katz E. Small and Y. Silberberg. 2012. Looking around corners and through thin turbid layers in real time with scattered incoherent light. Nature (2012).  O. Katz E. Small and Y. Silberberg. 2012. Looking around corners and through thin turbid layers in real time with scattered incoherent light. Nature (2012).","DOI":"10.1038\/nphoton.2012.150"},{"key":"e_1_2_2_42_1","volume-title":"Advances in Speckle Metrology and Related Techniques","author":"Kaufmann Guillermo H."},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073665"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.386"},{"key":"e_1_2_2_45_1","article-title":"Correlation in laser speckle","author":"Li J. H.","year":"1994","journal-title":"Phys. Rev. E 49"},{"key":"e_1_2_2_46_1","volume-title":"Monte Carlo modeling of optical coherence tomography imaging through turbid media. Applied optics 43, 8","author":"Lu Qiang","year":"2004"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766949"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1117\/1.JBO.18.11.117010"},{"key":"e_1_2_2_49_1","unstructured":"M.I. Mishchenko L.D. Travis and A.A. Lacis. 2006. Multiple scattering of light by particles: radiative transfer and coherent backscattering. Cambridge Univ Pr.  M.I. Mishchenko L.D. Travis and A.A. Lacis. 2006. Multiple scattering of light by particles: radiative transfer and coherent backscattering. Cambridge Univ Pr."},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383847.2383878"},{"key":"e_1_2_2_51_1","volume-title":"Controlling waves in space and time for imaging and focusing in complex media. Nat. Photonics","author":"Mosk Allard P.","year":"2013"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982429"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141986"},{"key":"e_1_2_2_54_1","volume-title":"Real-time wavefront shaping through scattering media by all-optical feedback. Nat. Photonics","author":"Nixon Micha","year":"2013"},{"key":"e_1_2_2_55_1","volume-title":"Monte Carlo Methods for Volumetric Light Transport Simulation. Computer Graphics Forum","author":"Novak Jan","year":"2018"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1364\/OPTICA.4.000886"},{"key":"e_1_2_2_57_1","volume-title":"Low-coherence optical tomography in turbid tissue: theoretical analysis. Applied optics 34, 28","author":"Pan Yingtian","year":"1995"},{"key":"e_1_2_2_58_1","unstructured":"Matt Pharr Wenzel Jakob and Greg Humphreys. 2016. Physically based rendering: From theory to implementation. Morgan Kaufmann.   Matt Pharr Wenzel Jakob and Greg Humphreys. 2016. Physically based rendering: From theory to implementation. Morgan Kaufmann."},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.22.002329"},{"key":"e_1_2_2_60_1","volume-title":"Diffusing wave spectroscopy. Physical review letters 60, 12","author":"Pine DJ","year":"1988"},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1364\/OE.16.005728"},{"key":"e_1_2_2_62_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.14.001231"},{"key":"e_1_2_2_63_1","volume-title":"Characterization of the angular memory effect of scattered light in biological tissues. Opt","year":"2015"},{"key":"e_1_2_2_64_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.34.002189"},{"key":"e_1_2_2_65_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073607"},{"key":"e_1_2_2_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311546"},{"key":"e_1_2_2_67_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073309"},{"key":"e_1_2_2_68_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-017-0779-4"},{"key":"e_1_2_2_69_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2015.03.013"},{"key":"e_1_2_2_70_1","doi-asserted-by":"crossref","unstructured":"B. E. Treeby and B. T. Cox. 2010. k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields . J. Biomed. Opt. (2010).  B. E. Treeby and B. T. Cox. 2010. k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields . J. Biomed. Opt. (2010).","DOI":"10.1117\/1.3360308"},{"key":"e_1_2_2_71_1","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/016\/0163605"},{"key":"e_1_2_2_73_1","volume-title":"Photorealistic Rendering Techniques","author":"Veach Eric"},{"key":"e_1_2_2_74_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218498"},{"key":"e_1_2_2_75_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258775"},{"key":"e_1_2_2_76_1","doi-asserted-by":"publisher","DOI":"10.1364\/OL.35.001245"},{"key":"e_1_2_2_77_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531398"},{"key":"e_1_2_2_78_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130840"},{"key":"e_1_2_2_79_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90067-3"},{"key":"e_1_2_2_80_1","doi-asserted-by":"publisher","DOI":"10.1364\/OPEX.12.006530"},{"key":"e_1_2_2_81_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201351"},{"key":"e_1_2_2_82_1","first-page":"3","article-title":"Imaging blood cells through scattering biological tissue using speckle scanning microscopy","volume":"22","author":"Yang Xin","year":"2014","journal-title":"Opt. Express"},{"key":"e_1_2_2_83_1","volume-title":"Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. EEE Trans. on Antennas and Propagation","author":"Yee K.","year":"1966"},{"key":"e_1_2_2_84_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508420"},{"key":"e_1_2_2_85_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601104"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3322950","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3306346.3322950","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3306346.3322950","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:25:44Z","timestamp":1750206344000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3306346.3322950"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,12]]},"references-count":84,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8,31]]}},"alternative-id":["10.1145\/3306346.3322950"],"URL":"https:\/\/doi.org\/10.1145\/3306346.3322950","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,12]]},"assertion":[{"value":"2019-07-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}