基于特征数的射影不变量计算方法
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摘要
射影不变量是物体几何形状在射影变换中保持不变的代数或微分量,在单视点图像识别三维物体中得到了广泛应用.本文以射影几何为工具,提出了共面五点和六点的三角特征数的一些构造方法.通过分析共面五点交比的表达式,找到了特征数与交比间的内在联系,并给出了一个特征数式射影不变量的框架性计算方法.
Projective invariants are algebraic or differential quantities of geometric shape of the object that keep invariant under projective transformation. They have been widely used in the field of single-view image recognition. By employing the knowledge of projective geometry,a method was developed in this paper for computing the triangular characteristic number(CN) on five or six planar points.Furthermore,the relationship between CN and cross ratio(CR) was found after analyzing the expression of CR,and a framework was also proposed to compute CN-like projective invariants.
Projective invariants are algebraic or differential quantities of geometric shape of the object that keep invariant under projective transformation. They have been widely used in the field of single-view image recognition. By employing the knowledge of projective geometry,a method was developed in this paper for computing the triangular characteristic number(CN) on five or six planar points.Furthermore,the relationship between CN and cross ratio(CR) was found after analyzing the expression of CR,and a framework was also proposed to compute CN-like projective invariants.
引文
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[2]Li L.,Tan C..Recognizing planar symbols with severe perspective transformation[J].IEEE Transactions on Patterm Analysis and Machine Intellegence,2010,32(4):755-762.
[3]罗钟铉,孟兆良,刘成明.计算几何-曲面表示论及应用[M].北京:科学出版社,2010.
[4]Fan X,Wang H,Luo Z,et al.Fiducial facial point extraction using a novel projective invariant[J].IEEE Transactions on Image Processing,2015,24(3):1164-1177.
[5]Li Y,Fan X,Liu R,et al.Characteristic number regression for facial feature extraction[C].IEEE International Conference on Multimedia and Expo(ICME),2015.
[6]罗钟铉,罗代耘,樊鑫,等.射影不变下新的形状匹配方法[J].计算机辅助设计与图形学学报,2014,26(4):559-565.
[7]Jia Q,Fan X,Liu Y,et al.Hierarchical projective invariant contexts for shape recognition[J].Pattern Recognition,2016,52:358-374.
[8]Luo Z,Zhou X,Gu X.From a projective invariant to some new properties of algebraic hypersurfaces[J].Science China Mathematics,2014,57(11):2273-2284.
[9]胡文玉,张荣,赵惠妍,等.一种基于平面六点的射影不变量构造方法[J].赣南师范大学学报,2016,(6):17-22.
[10]Branca A,Stella E,Distante A.Feature matching constrained by cross ratio invariance[J].Pattern Recognition,2000,33:465-481.