視覺基礎(chǔ)矩陣估計方法的性能比較與分析(完整版)實用資料

視覺基礎(chǔ)矩陣估計方法的性能比較與分析（完整版）實用資料(可以直接使用，可編輯完整版實用資料，歡迎下載）

視覺基礎(chǔ)矩陣估計方法的性能比較與分析（完整版）實用資料(可以直接使用，可編輯完整版實用資料，歡迎下載）萬方數(shù)據(jù)萬方數(shù)據(jù)萬方數(shù)據(jù)萬方數(shù)據(jù)5.2數(shù)值仿真實驗(1實驗方法模擬透視成像攝像機,其內(nèi)參數(shù)為K=被觀測目標是200個3D點,隨機分布在邊長為360單位的立方體中,立方體中心距離攝像機光心600個單位。兩臺攝像機相對運動參數(shù)為:平移向量t=[40,o,o]7、旋轉(zhuǎn)軸方向為Eo,0,1]7、旋轉(zhuǎn)角度為10。。根據(jù)攝像機成像模型,將3D點投影到兩個成像平面上,然后疊加零均值高斯噪聲,其方差o(noisesigma從0到1變化,步長0.1,同時錯誤數(shù)據(jù)所占百分比r(outlierratio從o%到50%變化,步長10%。(2實驗結(jié)果將幾種典型方法計算結(jié)果的誤差分布曲面顯示在圖3中。圖3基礎(chǔ)矩陣計算的仿真實驗5.3真實圖像實驗(1實驗方法圖4真實圖像對和初始特征點匹配首先.采用改進的Harris角點檢測算法分別在左右兩幅圖像中檢測特征點,然后,使用零均值相關(guān)系數(shù)(ZNCC匹配方法獲得初始匹配;最后,將匹配結(jié)果作為輸入數(shù)據(jù)計算兩幅圖像的基礎(chǔ)矩陣。(2實驗結(jié)果這里給出3組圖像的實驗結(jié)果。其中,Mars為室外自然景物(512X512,圖4(a,Inria為室外人造建筑(512×256,圖4(b,Desk為室內(nèi)人造物(800X600,圖4(c。圖4中顯示了初始匹配特征點及其視差向量。圖中還顯示了通過LMedS+MEst方法得到的部分極線。為便于比較,將數(shù)值仿真實驗結(jié)果同真實圖像的實驗結(jié)果一并在表1中列出。表1基礎(chǔ)矩陣計算的實驗結(jié)果1-LinEig?2一LinLS,3-IterEig,4一herLS。5-GradEig。6-GradLS,7-NonParam.8-M—Est,9-RANSAC,10一LMedS,1卜M-Est+LMedSd=10o.00001000置:o.9931.0160.989r=u.J422=10‘.吉1.885f!?’36.55435.50232.07232.08144.45532.08131.3672.142o.990I.8861.839Man13.11313.20512.68612.88712.69112.88712.9000.8540.7590.872o.692Inria5.9795.9688.9317.4258.7717.4255.960Desk31.56829.88233.03830.41731.27739.4】629671l】9501178366613636分析與結(jié)論以仿真實驗以及真實圖像實驗結(jié)果為依據(jù),本文對不同的F矩陣計算方法有如下分析和結(jié)論。(1線性方法:如果特征點定位較精確并且沒有錯誤匹配,那么可以得到很好的結(jié)果。但是,這類方法對錯誤匹配的魯棒性非常差。(2非線性迭代方法:在一定程度上能夠處理定位噪聲的影響,但是實驗結(jié)果表明改善效果不明顯,同時,當存在錯誤匹配時,效率很低。(3參數(shù)空間優(yōu)化方法:比線性方法和迭代方法好,但是同樣不能處理錯誤匹配問題。(4魯棒方法:能夠同時處理數(shù)據(jù)噪聲和錯誤匹配。當存在錯誤匹配時,M.Kstimator方法的性能有所降低,特別是對于Desk圖像,由于初始匹配錯誤率較大導(dǎo)致聊s較大。這一現(xiàn)象證實了M—Estimator對定位噪聲是魯棒的,但是對錯誤數(shù)據(jù)的魯棒性較差。相比之下,RANSAC和LMedS體現(xiàn)出較好的品質(zhì)。(5如果使用LMedS方法預(yù)先剔除錯誤匹配,然后使用M—Estimator,可以得到最好的結(jié)果。(6同線性最dx_-乘優(yōu)化方法比較,基于特征分析技術(shù)的優(yōu)化方法效果更好。(下轉(zhuǎn)第289頁?247?●印√叫j筋弱●OO∞O∞OO陌一萬方數(shù)據(jù)Ｇｒａｐｈｉｃｓ，１９８４，１８（３）：卜１０２２３—２３１［５］ＰｒｕｓｉｎｋｉｅｗｉｃｚｏｆＰ，ＬｉｎｄｅｎｍｅｙｅｒＡ?ｅｔａ１．ＴｈｅＡｌｇｏｒｉｔｈｍｉｃＢｅａｕｔｙ［１１３ＨａｎｒａｈａｎＰ，ＬａｗｓｏｎＪ．Ａｌａｎｇｕａｇｅｆｏｒｓｈａｄｉｎｇａｎｄｌｉｇｈｔｉｎｇｃａｌ—Ｐｌａｎｔｓ［Ｍ］．Ｓｐｒｉｎｇｅｒ－Ｖｅｒｌａｇ．１９９０ｅｕｌａｔｉｏｎｓ［Ｊ］．Ｃｏｍｐｕｔｅｒ［１２］ＰｈａｒｒＧｒａｐｈｉｃｓ，１９９０，２４（４）：２８９—２９８［６］王輝．基于Ｌ系統(tǒng)的虛擬園林觀賞樹木生長建模研究［Ｄ］．長沙：中南林業(yè)科技大學(xué)，２００６：７－９Ｍ，ＨａｎｒａｈａｎＰ．Ｇｅｏｍｅｔｒｙｃａｃｈｉｎｇｆｏｒｒａｙ—ｔｒａｄｎｇｄｉｓ一Ｗｏｒｋｓｈｏｐｐｌａｃｅｍｅｎｔｍａｐｓ［Ｃ］∥Ｐｒｏｃ．ｏｆｔｈｅ７ｔｈＥｕｒｏｇｒａｐｈｉｃｓ［７３［８３ＨｅａｍＤ．ＢａｋｅｒＭＰ．計算機圖形學(xué)［Ｍ］．蔡士杰。吳春熔，孫正ｏｎＲｅｎｄｅｒｉｎｇ．Ｐｏｒｔｏ．Ｐｏｒｔｕｇａｌ．１９９６：３１—４０興，譯．電子工業(yè)出版社，２００２ＦａｒｍＧ．ＣｕｒｖｅｓａｎｄＳｕｒｆａｃｅｓｆｏｒＣｏｍｐｔｅｒＡｉｄｅｄＧｅｏｍｅｔｒｉｃＤｅ－ｓｉｇｎ：ＡＰｒａｃｔｉｃａｌＧｕｉｄｅ，４ｔｈＰｒｅｓｓ?１９９６［１３］ＳｅｈａｕｆｔｅｒＧ．Ｐｒｉｇｌｉｎｇｅｒ札Ｅｆｆｉｄｅｎｔｉｍａｇｅｄｉｓｐｌａｃｅｍｅｎｔｍａｐｐｉｎｇｂｙｗａｒｐｉｎｇ［Ｃ－］｝｝Ｐｒｏｃｏｆｔｈｅ１０ｔｈＥｕｒｏｇｒａｐｈｉｃｓＷｏｒｋｓｈｏｐＥｄｉｔｉｏｎ［Ｍ］．Ｂｏｓｔｏｎ：ＡｃａｄｅｍｉｃｏｎＲｅｎｄｅｒｉｎｇ．Ｇｒａｎａｄａ，Ｓｐａｉｎ，Ｅｕｒｏｇｒａｐｈｉｃｓ，１９９９：１７５—１８６［１４］付愷。李春霞，楊克儉，等．ＢｕｍｐＭａｐｐｉｎｇ原理及在ＯｐｅｎＧＬ下的實現(xiàn)口］．交通與計算機，２００４，２２（２）：５４—５７［１５］楊剛．全景圖拼接算法的設(shè)計與實現(xiàn)口］．重慶工學(xué)院學(xué)報；自然Ｇｒａｐｈｉｃｓ，１９８４，１８（３）：［９］李鋼，劉華明．基于ＮＵＲＢＳ的掃描曲面造型方法的研究［Ｊ］．機械研究與應(yīng)用，２０００，１３（３）：５－６［１０］ＣｏｏｋＲＬＳｈａｄｅｔｒｅｅｓＥＪ］．Ｃｏｍｐｕｔｅｒ科學(xué)版，２００７，２１（１９）：１０７—１１０（上接第２４７頁）結(jié)束語Ｆ矩陣是許多計算機視覺應(yīng)用中的重要參數(shù)，其計算的準確性決定了后續(xù)的處理步驟能否成功。本文將常見的Ｆ矩陣估計方法劃分為線性法、非線性法和魯棒法３大類，共計１１種，通過仿真數(shù)據(jù)和真實圖像實驗對各自的性能進行了評估。實際應(yīng)用中，由于視覺系統(tǒng)所采用的圖像特征定位及匹配方法各有差異，可根據(jù)具體情況合理選擇本文介紹的Ｆ矩陣計算方法，以實現(xiàn)高精度的３Ｄ信息獲取。Ｅ１１］ＦａｎｇｅｒａｓｆｅｒｅｎｃｅＤ，ＬｕｏｎｇＱＴ，ＭａｙｂａｎｋＳＪ．Ｃａｍｅｒａｓｅｌｆ－ｃａｌｉｂｒａｔｉｏｎ：ｔｈｅｏｒｙａｎｄｏｎｅｘｐｅｒｉｍｅｎｔ［Ｃ］？ｊＰｒｏｃｅｅｄｉｎｇｓｏｆｔｈｅＥｕｒｏｐｅａｎＣＯｎ－ＣｏｍｐｕｔｅｒＶｉｓｉｏｎ．ＳａｎｔａＭａｒｇｈｅｆｉｔａＬ．１９９２：３２１—３３４［１２３ＬｏｕｒａｋｉｓＭＩＡ。ＤｅｆｉｃｈｅＲＣａｍｅｒａｓｅｌｆ－ｃａｌｉｂｒａｔｉｏｎｕｓｉｎｇｔｈｅｓｉｎｇｕｌａｒｖａｌｕｅｄｅｃｏｍｐｏｓｉｔｉｏｎｏｆｔｈｅｆｕｎｄａｍｅｎｔａｌｔｏｍａｔｒｉｘ：Ｆｒｏｍｐｏｉｎｔｃｏｒｒｅｓｐｏｎｄｅｎｃｅｓ３Ｄ１９９９ｍｅａｓｕｒｅｍｅｎｔｓ［Ｒ］．３７４８．ＩＮＲＩＡＳｏｐｈｉａ－Ａｎｔｉｐｏｌｉｓ，Ａｕｇｕｓｔ［１３３ＬｏｕｒａｋｉｓＭＩＡ。ＤｅｆｉｃｈｅＲＣａｍｅｒａｓｅｌｆ—ｃａｌｉｂｒａｔｉｏｎｕｓｉｎｇｔｈｅＫｒｕｐｐａｅｑｕａｔｉｏｎｓａｎｄｔｈｅＳＶＤｏｆｔｈｅｆｕｎｄａｍｅｎｔａｌｍａｔｒｉｘ：Ｔｈｅｃａｓｅ參考文獻［１］馬頌德，張正友．計算機視覺一計算理論與算法基礎(chǔ)［Ｍ］．北京：科學(xué)出版社，１９９８［２３ＬｕｏｎｇＱ－Ｔ，ＦａｕｇｅｒａｓＯ１３．Ｔｈｅｆｕｎｄａｍｅｎｔａｌｍａｔｒｉｘ：Ｔｈｅｏｒｙ．ａｌ—ｇｏｒｉｔｈｍｓａｎｄｓｔａｂｉｌｉｔｙｐｕｔｅｒｏｆｖａｒｙｉｎｇｉｎｔｒｉｎｓｉｃｐａｒａｍｅｔｅｒｓ［Ｒ］．３９１１．ＩＮＲＩＡＳｏｐｈｉａ－Ａｎｔｉｐｏｌｉｓ，Ｍａｒｓ．２０００［１４］Ｈａｒｔｌｅｙ［１５］ＨａｒｔｌｅｙＲｌ。Ｚｉｓｓｅｒｍａｎ八Ｍｕｌｔｉｐｌｅｖｉｅｗｇｅｏｍｅｔｒｙｉｎｃｏｍｐｕｔｅｒｖｉｓｉｏｎ［Ｍ］．ＣａｍｂｒｉｄｇｅＵｎｉｖｅｒｓｉｔｙＰｒｅｓｓ，２０００ＲＬＩｎｄｅｆｅｎｓｅｏｆｔｈｅ８－ｐｏｉｎｔａｌｇｏｒｉｔｈｍ［Ｃ］∥Ｐｒｏｃｅｅ－ｏｎａｎａｌｙｓｉｓ［Ｊ］．ＩｎｔｅｒｎａｔｉｏｎａｌＪｏｕｒｎａｌｏｆＣｏｍ—ｄｉｎｇｓｏｆｔｈｅ５ｔｈＰｒｏｃ．ＩｎｔｅｍａｔｉｏｎａｌＣＯｎｆｅｒｅｎｃｅＣｏｍｐｕｔｅｒＶｉ－Ｖｉｓｉｏｎ，１９９６，Ｉ（１７）：４３—７６ｓｉｏｒｌ．Ｂｏｓｔｏｎ，／ＶＩＡ：ＩＥＥＥ１０７０ＣｏｍｐｕｔｅｒＳｏｃｉｅｔｙＰｒｅｓｓ，１９９５：１０６４—［３３Ｌｏｎｇｕｅｔ－ＨｉｇｇｉｎｓＨｃＡｃｏｍｐｕｔｅｒａｌｇｏｒｉｔｈｍｆｏｒｒｅｃｏｎｓｔｒｕｃｔｉｎｇａｓｃｅｎｅｆｒｏｍｔｗｏｐｒｏｉｅｅｔｉｏｎｓ［Ｊ］．Ｎａｔｕｒｅ，１９８１，２９３：１３３—１３５ｓｔｒｕｃｔｕｒｅ［１６］ＦａｕｇｅｒａｓｐｏｉｎｔＱ，ＭｏｕｒｒａｉｎＲＯｎｔｈｅｇｅｏｍｅｔｒｙａｎｄａｌｇｅｂｒａｏｆｔｈｅｎ［４］ＭｅｓｔｅｒＲｔｉｏｎＯｎｔｈｅｍａｔｈｅｍａｔｉｃａｌｏｆｄｉｒｅｃｔｉｏｎａｎｄｏｎｎｌｏ—ａｎｄｌｉｎｅｃｏｒｒｅｓｐｏｎｄｅｎｃｅｓｂｅｔｗｅｅｎｉｍａｇｅｓ［Ｃ］ｆ｝Ｐｒｏｃｅｅ－ｅｓｔｉｍａｔｉｏｎ［ｑｆ｝３ｒｄＩｎｔｅｒｎａｔｉｏｎａｌＳｙｍｐｏｓｉｕｍＰｈｙｓｉｃｓｉｎｄｉｎｇｓｏｆｔｈｅ５ｔｈＰｒｏｃＩｎｔｅｒｎａｔｉｏｎａｌＣｏｎｆｅｒｅｎｃｅｏｎＣｏｍｐｕｔｅｒＶｉ—ＳｉｇｎａｌａｎｄＩｍａｇｅＰｒｏｃｅｓｓｉｎｇ（ＰＳＩＰ）．Ｇｒｅｎｏｂｌｅ。Ｆｒａｎｃｅ，Ｊａｎｕａｒｙ２００３ｓｉｏｎ．Ｂｏｓｔｏｎ，ＭＡ：ＩＥＥＥＣｏｍｐｕｔｅｒＳｏｄｅｔｙＰｒｅｓｓ，１９９５：９５１－９５６［１７］Ｚｈａｎｇｚ，ＤｅｒｉｃｈｅＲ．ＦａｕｇｅｒａｓＯ，ｅｔａ１．Ａｒｏｂｕｓｔｔｅｃｈｎｉｑｕｅｆｏｒ［５３ＰｏｌｌｅｆｅｙｓｓｐｉｔｅＭ，ｅｔａ１．Ｓｅｌｆ－ｃａｌｉｂｒａｔｉｏｎａｎｄｍｅｔｒｉｃｒｅｃｏｎｓｔｒｕｃｔｉｏｎｉｎｍａｔｃｈｉｎｇｔｗｏｕｎｃａｌｉｂｒａｔｅｄｉｍａｇｅｓｔｈｒｏｕｇｈｔｈｅｒｅｃｏｖｅｒｙｏｆｔｈｅｏｆｖａ叫ｌａｇａｎｄｕｎｋｎｏｖｃｎｉｎｔｅｒｎａｌｃａｍｅｒａｌｐａｒａｍｅｔｅｒｓ［Ｊ］．ｕｎｋｎｏｗｎｅｐｉｐｏｌａｒｇｅｏｍｅｔｒｙ［Ｊ］．ＡｒｔｉｆｉｃｉａｌＩｎｔｅｌｌｉｇｅｎｃｅＪｏｕｒｎａｌ，ＩｎｔｅｍａｔｉｏｎａｌＪｏｕｒｎａｌｏｆＣｏｍｐｕｔｅｒＶｉｓｉｏｎ，１９９９，３２（１）：７－２０１９９５，７８（１０）：８７－１１９［６３ＺｈａｎｇＺ，ＤｅｆｉｃｈｅＲ，ＦａｕｇｅｒａｓＯ，ｅｔａＬＡｒｏｂｕｓｔｔｅｃｈｎｉｑｕｅｆｏｒ［１８３Ｚｈａｎｇｚ．Ｄｅｔｅｒｍｉｎｉｎｇｔｈｅｅｐｉｐｏｌａｒｇｅｏｍｅｔｒｙａｎｄｉｔｓｕｎｃｅｒｔａｉｎｔｙ：Ａｍａｔ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gflakebeards1988(11/1216.LaksPE;ManningMJInorganicberatesaspreservativessystemsforwoodcomposites199417.KamdemDP;HopeJHJermannandA.Propertiesofplywoodandorientedstrandboardmanufacturedwithanorganicinsecticideincorporatedintheadhesive200018.KartalSN;GreenFⅢ.Decayandtermiteresistanceofmediumdensityfiberboard(MDFmadefromdifferentwoodspecies200319.MorrisPl;CooperPRecycledplastic/woodcompositelumberattackedbyfungi1998(0120.LaksPE;RichterDL;LarkinGMBiologicaldeteriorationofwoodbasecompositepanels2000(0421.LaksPE;RichterDL;LarkinGMFungalsusceptibilityofinteriorconnnerciaibuildingpanels[外Grapheneisthefirstexampleofatruly2Datomiccrystal1.Ithasuniqueelectronic,opticalandmechanicalproperties,andhasalsobeenwidelyinvestigatedforcatalysis,includ-ingelectrocatalysis2,3,photocatalysis4andconventionalheteroge-neouscatalysis5(Table1.Ithas,inparticular,beenshownthatperturbationstotheperfecthexagonalgraphenestructure,suchasdislocations,vacancies,edges(Fig.1a,impurities(Fig.1bandfunctionalgroups(Fig.1c,readilymodifythedensityofstatesingrapheneandpromoteitscatalyticproperties6–9.Recently,other2Datomiccrystals,andtheirpossibleapplicationsincatalysis,haveattractedconsiderableinterest10.Manyoftheselayeredmaterials(forexampleMoS2andWS2havelongbeenusedascatalystsintheir3Dforms.Buttheconsiderablechangesintheelectronicstructureof2Dmate-rialsincomparisonwiththeir3Dbulkstructures,aswellasthepossibilityofchemicalandstructuralmodifications,offernewopportunitiestousethe2Dmaterialsinmanydifferentchemicalreactions.Recentadvancesincreatingheterostructuresbasedon2Datomiccrystals11,12alsoprovidenewpossibilitiesincatalysis.Theabilitytocontroltheelectronicstateatthesurfaceofthecrystalsthroughdifferencesinworkfunction13–16(Fig.1d,thecreationofnanoreactorsinthespacebetweendifferent2Dcrystals17,18(Fig.1eandtheformationofsandwichstructuresbasedondif-ferent2Dcrystals(Fig.1fdeliverunprecedentedflexibilityincontrollingthechemicalreactivityofsuch3Dstacks.InthisReview,webrieflyoverviewrecentadvancesingraphenecatalysisbeforeconcentratingonthecatalyticpropertiesofother2Dmaterialsandthecatalyticpropertiesofheterogeneoussystems,suchasvanderWaalsheterostructuresandcombinationsof2Dmaterials(Table1.Weanalysethenewopportunitiesincatalysisprovidedby2Dcrystals,andthevariousroutes(Fig.1totunetheirelectronicstatesandcorrespondingactivesites.Wealsogobeyondthefundamentalpropertiesofthesestructuresanddiscussthepotentialofusingsuchmaterialsforfutureapplicationsincatalysis.Catalysiswithtwo-dimensionalmaterialsandtheirheterostructuresDehuiDeng1,K.S.Novoselov2*,QiangFu1,NanfengZheng3,ZhongqunTian3*andXinheBao1*Grapheneandother2Datomiccrystalsareofconsiderableinterestincatalysisbecauseoftheiruniquestructuralandelectronicproperties.Overthepastdecade,thematerialshavebeenusedinavarietyofreactions,includingtheoxygenreductionreac-tion,watersplittingandCO2activation,andhavebeenshowntoexhibitarangeofcatalyticmechanisms.Here,wereviewrecentadvancesintheuseofgrapheneandother2Dmaterialsincatalyticapplications,focusinginparticularonthecatalyticactivityofheterogeneoussystemssuchasvanderWaalsheterostructures(stacksofseveral2Dcrystals.Wediscusstheadvantagesofthesematerialsforcatalysisandthedifferentroutesavailabletotunetheirelectronicstatesandactivesites.Wealsoexplorethefutureopportunitiesofthesecatalyticmaterialsandthechallengestheyfaceintermsofbothfundamentalunderstandingandthedevelopmentofindustrialapplications.GrapheneanditsderivativesThefascinationwithgraphene-basedcatalystsoriginatesfromtheiruniquestructuralandelectronicproperties.Grapheneisa2Datomiccrystalconsistingofasinglelayerofsp2-hybridizedcarbon1.Itcanbeconsideredasabasicstructuralelementofvariouscarbonallotropes,including3Dbulkgraphite,1Dcarbonnanotubesand0Dfullerenes19.Suchuniquestructuralfeaturesendowgraphene-basedcatalystswiththefollowingadvantages.First,theyhaveaveryhighspecificsurfacearea(>2,600m2g–120,allowingahighdensityofsurfaceactivesites.Second,theyhaveexcellentmechanicalprop-erties21,andthereforehighstabilityanddurabilitycanbeexpectedwhengraphenematerialsareusedaseitherthecatalystorcatalystsupport.Third,theyhavehighthermalandelectricconductivity22:thehighthermalconductivityofgrapheneisbeneficialtothecon-ductionanddiffusionoftheheatgeneratedduringcatalyticreac-tions,especiallyforstronglyexothermicreactions;thehighelectricconductivityofgraphenemakesthematerialagoodcandidateforelectrocatalystsorelectrocatalystsupports.Fourth,theyofferaset-upinwhichtocombinetheoreticalresearch,modelresearchandrealisticapplicationsincatalysis:itispossibletocharacterizetheactivesitesongraphenebyhigh-resolutionimagingtoolssuchastransmissionelectronmicroscopy(TEMandscanningtunnellingmicroscopyevenduringthereactionprocess,whichischallengingfortraditionalcomplexcarbonmaterialssuchasactivatedcarbon.Theelectronicstructureofgraphene,however,presentsbothchallengesandopportunitiesforcatalyticapplications.Thechal-lengesoriginatefromthefactthatgrapheneisazero-overlapsemi-metalwithquasiparticlesobeyingalineardispersionrelation19,23,resultingintheverylowdensityofstatesattheFermilevelfortypicaldopinglevels(zeroattheDiracpoint.Therefore,pristinegrapheneisinertincatalysis.Buttheverysamefactprovidesnewopportunities,astheelectronicpropertiesofgraphenecanbeeasilytunedbyintroducingperturbations,offeringpossibilitiestoinducecatalyticactivityinthematerial.Therearevariousroutestotunetheelectronicstatesofgra-phene.(1Thesizeeffect:abandgapisopenedintheelectronic1StateKeyLaboratoryofCatalysis,iChEM,DalianInstituteofChemicalPhysics,ChineseAcademyofSciences,ZhongshanRoad457,Dalian116023,China.2SchoolofPhysicsandAstronomy,UniversityofManchester,OxfordRoad,M139PLManchester,UK.3StateKeyLaboratoryofPhysicalChemistryofSolidSurfaces,iChEM,DepartmentofChemistry,CollegeofChemistryandChemicalEngineering,XiamenUniversity,Xiamen361005,China.*e-mail:Konstantin.Novoselov@manchester.ac.uk;zqtian@;xhbao@dicp.acspectrumofgraphenenanoribbonsowingtothequantumconfine-menteffect,andthesizeofthegapwillincreasewhendecreasingthesizeofthenanoribbon24,25.(2Thelayereffect:theelectronicstructureofgraphenestronglydependsonthenumberoflayers26.(3Theedgeanddefecteffects:theelectronicdensityofstatescanbestronglyenhancedattheedgescomparedwiththeplaneofgra-phene,witharmchairandzigzagedgesalsohavingdifferentelec-tronicstructure24,27.Inaddition,defects,suchasvacanciesanddislocations,caninduceadditionalelectronicstatesandalsoaffecttheelectrontransferrateingraphene28–30.(4Thecurvatureeffect:graphene,beingonlyoneatomthick,isextremelyflexibleandcanbeeasilybent(intentionallyorunintentionally.Thebentorfoldedgraphenewilldisplaydistinctelectronicstatesfromthoseoftheflatnetworkofgraphene31,32.(5Thedopantandfunctionalgroupeffect:theintroductionofdopantssuchasnitrogen8,33,34,boron35,36,phosphorus37,38,sulfur39,40andevenmetalatoms41–43intothegra-phenematrixcanefficientlytunetheelectronicstatesofthe2Dstructure.Inaddition,themodificationofgraphenewithdifferentfunctionalgroups,suchasthosecontainingoxygen44–46,hydro-gen47andhalogens48,49(F,Cl,Br,I,alsoaffectsitselectronicstates.Anincreaseinthedensityofstates(especiallyaroundtheFermienergyusuallyenhancesthecatalyticactivityofthematerial.Graphenethathasalargenumberofedgesordefects(Fig.1acanbedirectlyusedasacatalyst6,50.Densityfunctionaltheory(DFTcalculationsfromDaiandco-workersindicatedthatthezigzagedgesarechemicallyactive,tendingtoformC–Hbonds51.UsingDFTcalculations,Dengetal.foundthattheoxygenreductionreaction(ORRcanproceedatthezigzagedgesofgra-phenewhereasthearmchairedgesandin-planenetworkofgra-pheneareinactive6.Experimentally,theballmillingmethodwasappliedtocutgrapheneintosmallnanosheetsandincreasethezigzagedgedensity.TheORRactivitycanbesignificantlyincreasedbydecreasingthesizeofthegraphenenanosheets(Fig.2a,b,asthiswillincreasetheratioofedgeatomstobulkatomsinthegra-phenenetwork.Besidestheedgesofgraphene,heteroatomscansubstituteforCatomsofthegraphenematrix(Fig.1b,andthedopantscanactasanelectrondonororacceptordependingontheirelectronegativ-itycomparedwithC.Forexample,theNatompossesseshigherelectronegativitythantheCatom,leadingtoelectrontransferfromCtoNinN-dopedgraphene,whereasinB-dopedgrapheneaBatomhaslowerelectronegativitythanaCatom,resultinginelec-trontransferfromBtoC.Thisdifferencecangeneratetwodifferentactivesites.Inasubstitutivedopingcase,theactivesitesweregen-erallyconsideredtobetheCatomsadjacenttotheN-dopantsintheN-dopedgraphene9,34,whereastheBatomswereconsideredastheactivesitesinB-dopedgraphene38,52.Amongallheteroatom-dopedgraphenestructures,N-dopedgrapheneisthemostintensivelyinvestigatedsystemincatalysis8,9,34,53,54.Forexample,manygroupshaveshownthatN-dopedgraphenecanbeusedasametal-freecatalystfortheORRinH2–O2fuelcells8,34andLi–airbatteries55,56.DFTcalculationsbyYuetal.presenttworeasonsforchangesintheelectronicstructureinN-dopedgraphene9,57.OneisthehigherelectronegativityofNthanC,whichinducespositivechargesonC,andtheotheristheback-donationofthelone-pairelectronsfromNtoC.BotheffectssynergisticallyincreasethedensityofstatesattheFermileveloftheadjacentCatoms,asshowninFig.2d,whichincreasestheirORRactivity.ThereactionenergybarrieroftheORRoccurringattheadjacentCatomsofNatomsisrathermild,andthereforethereactioncanproceedwellwithanassocia-tivemechanismbyafour-electrontransferpathway9.ItshouldbenotedthatdifferentNspeciesandcarbonstructurescanchangetheselectivityofoxygenactivation.Forinstance,severalgroupshaveshownthatN-dopedgrapheneormesoporouscarboncanbeusedforH2O2productionviaatwo-electrontransferpathway58,59.Besidesthis,N-dopedgraphenecanalsobeusedasanefficientcat-alystforselectiveoxidation.Forexample,Gaoetal.andLongetal.reportedindependentlythatN-dopingcanpromotetheselectiveoxidationofethylbenzeneandaromaticalcohol53,60.ApartfromNandBdoping,otherheteroatomssuchasP,SandSehavealsoreceivedgreatinterestingraphene-basedcatalysis37–40,61.Forexam-ple,arecentstudyindicatesthatP-dopedorS-dopedgraphenecanserveasanefficientORRcatalystinalkalineelectrolytes37,39.Besidesnon-metalatoms,metalatomssuchasW,Pt,Co,InandFecanalsobeintroducedintothegraphenematrix41–43.SinglemetalatomsitesembeddedingraphenecanaffecttheelectronicstructureoftheadjacentCatoms,andmoreimportantlytheycanbedirectlyusedasactivesites.DFTcalculationsfromLuetal.62indicatedthatabdefce?e?e?Figure1|Schematicsofcatalysisoractivesitesforvariousgraphenestructuresandtheirheterostructures.a,Activesitesfromdefectsandedges.b,Activesitesfromdopedheteroatoms.c,Activesitesfromfunctionalgroupsandmetalclusters.d,Catalyticactivityduetoelectron(e–transferfrommetaltographenelayer.e,Catalysisinthespacebetweenametalsurfaceand2Dcrystal.f,Catalyticactivityfromsandwichstructurebasedon2Dmaterials,forexamplegrapheneorMoS2.REVIEWARTICLENATURENANOTECHNOLOGYDOI:10.1038/NNANO.2021.340inAu-dopedgraphenethesingleAusitescanefficientlycatalyseCOoxidation,andthehighestbarrierisonly0.31eV.Theproblemforthemetal-dopedgraphene,however,isthelowstabilityofthemetalsitesowingtotheweakbondingbetweenmetalandcarbonatoms.Forexample,thesingleWatomismobileunderelectronbeamirra-diation,implyinginstabilityinrealisticcatalyticconditions41.Onepossibleroutetostabilizethemetalatomsingrapheneistousehet-eroatomsastheanchor.Recently,Dengetal.reportedthatsingle-atomFecanbeconfinedinagraphenematrixbybondingwithNatomstoformastablesingleFeN4centre,whichcancatalyseben-zeneoxidationtophenolatroomtemperaturewithgoodstability63.Graphenestructuresfunctionalizedwithoxygen-containinggroupsincludinggrapheneoxide(GOandreducedgra-pheneoxide(RGO(Fig.1ccanbeproducedonalargescaleandhavebeenusedasacatalyst.Boehmetal.64firstusedRGOasacata-lysttosynthesizeHBrin1962.In2021,Bielawskiandco-workersreportedthatGOcancatalysetheoxidationofvariousalco-holsandalkenes,andthehydrationofvariousalkynesintotheirREVIEWARTICLENATURENANOTECHNOLOGYDOI:10.1038/NNANO.2021.340correspondingaldehydesandketoneswithgoodyields65,66(Fig.2e,f.Recently,Gaoetal.reportedthatRGOcanbeusedasaneffectivecatalystforthehydrogenationofnitrobenzeneevenatroomtem-perature67.Otheroxygen-containinggroups(forexample–SOx,–NOx,–POxongraphenehaverecentlyalsoreceivedwideatten-tionincatalysis45,68.Forexample,Xiaoandco-workersreportedthatsulfatedgraphenecanbeusedasanefficientsolidcatalystforacid-catalysedliquidreactions45.Theoxygen-containinggroupsoradjacentdefectswithabilitytomodifytheelectronicstructureofgrapheneareusuallyconsideredasthepossibleactivesites,depend-ingonthedifferentreactionsystems.Other2DmaterialsOneimportantoutcomeofgrapheneresearchisthatithasledtomanyother2Dmaterials(forexampleMoS2,C3N4beingresearchedandused10.Currently,morethantwodozen2Dmaterialshavebeeninvestigated11,12,69,70.Surprisingly,manyofthesearestableinambi-entconditions,andmoreoftenthannottheelectronicpropertiesof2Dcrystalsaredifferentfromthoseoftheir3Dcounterparts.Thesedifferencesinelectronicpropertiesmaycreatedifferentreactivityon2Dcrystalscomparedwiththeir3Drelatives.Aswellasshowingeffectssimilartothefiveroutestotuneelectronicstateslistedaboveforgraphene,theenlargedfamilyof2Dmaterialscansignificantlyincreasetherangeofcatalyticapplicationsincomparisonwithgra-phene(Table1.Forexample,thesurfaceacidityorbasicityofsome2Dmaterials(suchasC3N4cansignificantlyaffectcatalyticactivityandselectivity71.Inaddition,thesurfacesofsomepure2Dmetalcrystalscanbeactiveincatalysis,whichwillsignificantlyincreasetheactivesitescomparedwiththeir3Dcounterparts.Two-dimensionalgraphiticC3N4(g-C3N4isawidelyinvesti-gatedcatalyst72–75.Itconsistsofcyamellurictri-s-triazinebuildingblocksasshowninFig.3a(ref.72andhasa2Dstructuresimilartothatofgraphene.Unlikegraphene,g-C3N4hasabandgap,withsignificantelectronicdensityofstatesatthebandedge.Interestintheuseof2Dg-C3N4incatalysisoriginatesnotonlyfromitsuniqueelectronicstructure,butalsofromtherichLewisbasicfunctions,Br?nstedbasicfunctions,H-bondingmotifandhighspecificsur-facearea71.Therefore,g-C3N4showspromiseformanyapplicationsinconventionalheterogeneouscatalysis,photo-andelectrocataly-sis.Forinstance,Goettmannetal.foundthatg-C3N4canpromotetheconversionofCO2andbenzenetopheno