基于OpenCV的摄像头动态手势轨迹识别及其应用
基于OpenCV的摄像头动态手势轨迹识别及其应用,前沿的研究,最新论文2012B_0% random t XoX,XX4_1、42、B0Bhattacharyyaglsl. 8 gsl_ran_gaussianpp q1/3t=∑∵n8HSVcerterHSVIISV V44 HMM3IIMMA=SO4 B450AiI i j-+∑bk2HMM4+1=A_1*X1-X0+A_2*Xo1994-2013ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.netOpencvlIMMP., v3)A BP(IAIIMM(a)两点之间的方向夹角(b)轨迹的方间夹角分为8等份HMMBaum-WelchyO aB,i/∑a,iBtHMMAHMM∑s: t Hq,=======-s,qui a 6. o, B, 1 j/PolAa)向右的于势(b)向左的手势(c)向上的手势(d向下的手势动,O:B1j1+1J∑,ijtimermero∑点:1j/∑b kFirmerlimmer=3∑y,1/∑yIMM丌AB512Baum-welch4.3HMⅥHMMHMⅥHMM8(a)第5(b)第6帧第6幀第6帧o1994-2013ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net1322012(a第1(b)第72(a)第5帧(b)第60帧(c}第62帧(d)第G3帧(c)第75d)第呲5.4 HMMHMMHMMHMIHMM丌ABHMMa)第4帧.0()第50d)第54帧HMMHMM0.2928060.56l9010.2943160.5606530.1167910.1900640.0428680.1903360.041360.3217210.3235800.0173120.1166050.0155030.0708480.069680.1601290.0412690.1600400.039740.0749660.0738510.1859570.1468650.1466160.2136800.1587320.0954920.1586260.094620.2069880.207462HMM30.00l20.00100.0010.00I0.00l0.000.0050.00l.O001.000360.0010.00120.00I0.0010.00l0.001IIMMHMMIIMM320×240HMMo1994-2013ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.netOpencv133jck hand recogni tion2005,2611):29Openly获取直方图轨迹图像2010,30(71:59-61.在单击“轨迹「未选择-图像显示[5 QIN WEN, PENG QICONG. An improved particle filter algorithm图像时选择Chmm控制based on neural network for visual tracking[c / International Con个按钮选C控制贪食鱼ference on Communications, Circuits and SyLas v.项训练HMMIEEE.2007:765-768LD」停止退出2009[7 YU JINXIA, LIU WENJING, YANG Y. Impmved particle filter algorithms based on partial systematic resampling C|//IEEE InTernational Conference on Intelligent Computing and Intelligent SystemsLas vegas: IEEE, 2010: 483-4878 FAZLI S, POUR II M, BOUZARI ll. Particle filter based objecttracking with sift and color feature[C // Second International Conas Vegas: IEEE, 2009: 89-9(8:62-64.L10」LD」HMM,2004[ II YUAN LICHI. An improved HMM speech recognition model[c//International Conference on AudiO. las Vegas: IEEE, 2008: 1311LlOpenCVLD」1315.[12 TAN WENJUN, WU CHENGDONG, ZHAO SHUYING. Recogni[2 CHlO JU, JIN S ll, PILAM X D. Object tracking circuit using partition of dynamic hand gesture based on SCllMM model[C]//Chi-cle filter with multiple features [C//SICE-ICASE: Internationalnese Control and Decision Conference. Log Vegas: IEEE. 2009Joint Conference. Las Vegas: IEEE, 2006: 1431-14362430-24341272011,28(2):242-244.C,2010,1(1):92-95SIFT[8 BEIS J S, LOWE D G. Shape indexing using approximate nearest-neighbour search in high-dimensional spaces [C]// Proceedings ofthe IEEE 1997 Computer Society Conference on Computer visionand Pattern Recognition. Washington, DC: IEEE Computer Socie-ly,997:1000-1006SIFT009,29(5):423-2262009,30(4):857-861[O][2] LOWE D G. Distinctive image features from scale-invariant key-points[ J]. International of Computer Vision, 2004, 60(2):91[11 SHUM H Y, SZELISKI R. Construction of panoramic image mosaicswith global and local alignment[ J International Journal of Comp3 MIKOLAJCZYK K, SClIMID C. A performance evaluation of localer visian,2000,36(2):101-130descriptors[ J|. IEEE Transactions on Pattern Analysis and Machine[12 ZOGIILAMI 1. FAUGERLAS O, DERICIIE R. Using geometric corIntelligence,2005,27(10):1615-1630ners to build a 2D mosaic from a set of images[C]// Proceedings of4 LINDEBERG T. Seale -space theory a basic foul for analyzingthe International Conference on Computer Vision and Pattern Recog-structures at different seales LJ. Journal of Applied StatisticitiL. Washington, DC: IEEE Computer Society, 1997: 1671994,21(2):224-270o1994-2013ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net
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北航矩阵论学习笔记
北京航空航天大学矩阵理论学习笔记,总结版,学霸总结,可以放心下载使用北京航空航天大学张京蕊工程系统工程系月录§0补充公式§1 Jordan(约当)标准形(简介)§2线性变换与矩阵.24§3欧式空间与QR分解.48§4常用矩阵分解●鲁D●●·,,,,,74§5范数与级数.81§6广义逆A..97§7直积拉直及应用105矩阵理论A笔记北京航空航天大学张京蕊工程系统工程系§0补充公式令A=(a)mxn∈C",风x)=4o+a1x0定义f(4)=a0+a1A+…+amAm,其中I=l若g(x)=bo+b1x+…+bkx,(x)g(x)=g(x)(x),则f(4)“g(A)=g(A)f(A)分块公式A10令A,A1,A2为方阵00 A(2)f(A),fx)为多项式令A=,A1,4为方阵AO(2)f(4)相似关系:A∽B,(PAP=B)则:(1)(P1AP)=P!AP,(k=0,1,2,(2)f(PAP)=PfA)P,f(x)为多项式许尔公式( schur):每个复方阼,A-(a)nxm都相似丁上三角形。共113页矩阵理论A笔记第1页北京航空航天大学张京蕊工程系统工程系即:P-1AP=其中41,,的次序可以任意指定Pf:用归纳法n=1时成立可以设为(n=1阶方阵成立对于n阶方阵A=(an)2×n设特征值为A,…,n取为对应的特征向量,记为a1≠0,A1=1ax1把a1扩展为可逆方阵Q=(a1,02,xn)22e又:g(a,a,…,.)=(Qa,Qba2,,Qan)其中Qe1,aQ0Q4=QA(a1a2,…an)2-I(Aa,,AAQ=(Qa,、+)…,(*)其中A1为(n-1所阶0人:0 A为由假设,对于A1必有(n-1)阶P,可推出PAPEg知n阶方阵A,适合A=0,则A+|=1共113页矩阵理论A笔记第2页北京航空航天大学张京蕊工程系统工程系Pf:A=0→任意特征值A=0→>=0即全体特征值为00,,00由需要P1AP=→PAP+7=1pAP+PP|=P(4+1)P=14+1→A+1=-1注(1)若AB(相似),则AB有相同特征值A,可引入记号:谱集(4)={2,2,…,λ}(全体特征值,含重复)A∽B→o()=o(B)(2)A∽B→1-A=1-B-(2-4元一2)…(-n),特征多项式PAP=B=A-A=p(1-A)P=A-B引理:若A0A2,则M-A|-|M1-4|-1-A1|2-A2→ar(4)=o(A)∪a(42k+1,Ak-2,…n1f(x2)设B,f(x)为多项式,则f(B)=o f(,)引理:若n阶方阵A的谱集(4)=1,42,…},则)的全体特社值为)2,…,),x)为多项式Pf:由许尔定理,A∽B→f(4)∽f(B)f(x)的全体特征值为(A1)(42),,()},fx)为多项式例如:4为A的特征值→x为4的特征值。(x)=x)共113页矩阵理论A笔记第3页北京航空航天大学张京蕊工程系统工程系引理:令B,f(x)=x-B|=(x-41)(x-12)….(x-n)则fB)=(B-1D(B-21)…(B-A1D=0Pf:当n=2时,B=0x2f(x)=(x-1)(x-2)000→f(B)-(B-41)(B-21)(2-元)0(00∴得证★ Cayley公式:设n阶方阵A的特征多项式为f(x)=|x-A|=a+a1x+…,+x则f4)=anl+a14+…,+4=0Pf:由许尔PAP=B=→P(4)P=fp3P)=f(B)=0(引理)定义若多项式x)使(4)=0,则称(x)为A的个零化式结论方阵A的特征多项式)=1x1-4为A的一个零化式g特征多项式fx)=x2可知:f(A)=A2+1=+I=00-1Hx)=|xI-A|=(x-)(x+i,(i=√-1,t2=-1)f(A)=(A-i)(4+i1=0也可取P=则PPAP=,对角形共113页矩阵理论A笔记第4页北京航空航天大学张京蕊工程系统工程系g:知A则A"=0Onxn由 Cayley特征多项式:f(x)=x"→f(4)=4"=0Ex 1. A=求P使得PP为对角阵,并验证 Cayley定理2.A=cd/,求fx)=x1-4验证f4)-0补充知识( schur公式、 Cayley公式)应用由A"=-(a0I+a1A+1A·AanA+a142+…+a.,A把①代入②→Am1=(-)+(+)4+…+(+)41可知:任何和(m≥n)都可写成,4,,A的线性组合任何多项式g(A),可写成lA,…,4的组合。Fg:若A|≠0,fx)=xI-A|=a0+a1x+…+x",ao=|-A|≠则A可用A的多项式表示∵a1A+a242+…+an21A-+A"--a072A(a1+a24+…+an-142+A)Aa1+…+an1A"2+A-1零化式定义:若g(x)=b+b1x+…+bnx,使得g(4)=bn+b14+…+bn4m=0,称g(x)为方阵A的零化式注:方阵A的零化式有无穷多个∴取特征多项式x)则4)=0任取式M(x),f(A(4)=0→f(x)(x)也是零化式极小式定义:在方阵A的零化式集合中,去次数最小的且首项系数为1的零化式m(x),称它为A的极小式共113页矩阵理论A笔记第5页北京航空航天大学张京蕊工程系统工程系注:极小式唯一性质:①极小式m(x)必为特征多项式fx)=|xI-A的因式。②特征多项式fx)=|x1-A的每个单因子(x-4)也是极小式的因子)f(x)=|x1-4=(x-x)(x-2)则极小式m(x)=(x-x)(x-2)y…(x-,),且1≤l1≤m1,1≤l2≤m2,…,1≤l≤n,41,A2…,n互不相同210EgA=020,B=020,求极小式mA(),m()解:(1)|xI-A|=(x-2)(x-1)极小式为:(x-2)(x-1)或(x-2)(x-1)计算:(4-2/)4-1)=000010k≠000000∴极小式为m4(x)=(x-2)2(x-1)(2)|-B|-=(x-2)2(x-1)00000计算:(B-2)B-1)=000010=000-1八000∴极小式为m(x)=(x-2)(x-1)Eg求下列极小式m(x)4604-60(1)A=-3-50,(2)B=2-303-6100210(3)C,(4)D=000010002000解:(1)特征多项式|x7-A|-(x-1)(x+2)极小式为:(x-1)(x+2)或(x-1)(x+2)共113页矩阵理论A笔记第6页北京航空航天大学张京蕊工程系统工程系验证:(4-D(A+2D=0∴极小式为m(x)-(x-1)(x+2)(3)解法如下引理:A1,A2的极小式为m1(x),m2(x)A10的极小式m(x)等丁m1(x),m2(x)的最小公倍式0A2(此引力可推广到A1,42,43)0100极小式为(x-1)2,0010极小式为(x-1)0取最小公倍式(x-1)2为C的极小式。460(5)F-/40,A1=020|,A00 A0123-6101O引理;设D=,则D的极小式m(x)O验证:先证D的性质(右推公式)设A-(an)xn=(a1,2,…,n)则有AD=(0,01,a2,,.m1)AD2=(0,0,∞1,,x12)AD=(0,….0.,a1,,axn)单位向量技巧:∵AI=A(en,e2…,en)=(el,leAen)=A=(a1, a2,. a,)∴Ae1=01,Ae2=(2,.,A→AD=A(0,e1,e2,…,en-1)=(0,a1,a2…,an-)同理AD2=(AD)D=(0,.01,.12)可知:D-1-(D)Dy2-(0.,0,,e1)≠0D"=(D)D1=0,而特征多项式(x)=|x1-D|=x,极小式为某个x共113页矩阵理论A笔记第7页
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