基于微分几何的局部相似目标匹配算法研究
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摘要
局部相似目标匹配是目标匹配问题的一般形式,其研究的焦点,是在若干目标之中找出它们最相似的部分,其研究成果具有广泛的应用前景。论文针对局部相似目标匹配和基本微分几何量的结合进行了研究,利用微分几何方法来描述目标特征,设计了相应的匹配算法,取得了较好的效果。研究的领域包括二维局部相似目标的匹配、三维局部相似目标的匹配、等距变形体的匹配,并对局部相似目标匹配研究作了展望。
首先,针对二维目标,设计了一种高效的平面目标边界编码方法。为更好地识别目标形状,编码方法需要对目标的刚体变换具有不变性,同时最大限度保持目标的原有信息。鉴于刚体平面曲线作变换时其曲率的不变性,提出了基于轮廓曲率提取的目标边界编码方法,并对此方法实施了离散化处理。设计了基于改进的KMP(D.E.Knuth,V R.Pratt和J.H.Morris)算法的曲线匹配方法,并对目标轮廓的重建作出了描述。实验证明,利用微分几何的思想描述目标边界,提取方法简单,存储量小,其编码针对目标刚体变换具有不变性,为识别提供了较大的方便。
其次,考虑到二维微分几何编码在匹配时的精度问题,设计了基于相似骨架的二维局部相似目标匹配算法。根据微分几何原理,基于平面曲线作刚体变换时其曲率的不变性,利用曲率来表达目标轮廓的固有特征;筛选出待匹配目标轮廓上固有特征相似的点,形成点对集合;在点对集合中寻找相似线段对来定位可能的平面变换;通过得分函数,求出点对集合中相似线段对变换的最佳值,得出最佳匹配。仿真实验表明,该模型适合局部相似情况下的目标匹配,特别对于复杂形状目标,运算复杂度较低,具有较好的识别效果。另外,文章还将相似线段对的应用推广到了三维目标。对于三维曲线,利用像素点处的曲率和挠率来表达其固有特征;对于三维曲面,利用像素点的高斯曲率和平均曲率来表达其固有特征。然后筛选出待匹配目标上固有特征相似的点,形成点对集合;在点对集合中寻找相似三角形对来定位可能的平面变换;通过得分函数,求出点对集合中相似线段对的最佳值,得出最佳匹配。
此外,论文还针对等距变形体进行了研究。提出了一种针对等距变形目标识别的运算复杂度较低的新方法。首先利用FMTD(Fast Marching on Triangulated Domains)算法来计算曲面上点对之间的测地距离,构造特征矩阵;然后,通过归一化过程,构造出归一化特征矩阵,保证了同一目标特征矩阵的不变性;最后,利用矩不变量对归一化特征矩阵实施特征提取,构造了等距变形目标的变形矩。实验表明,与传统方法相比,在不降低识别效果的前提下,该算法具备较低的运算复杂度。
Partially similar object matching is a universal approach to object recognition. During the past decade, the problem of finding a partial match between three-dimensional surfaces attracted considerable attention. In this paper, the research of partially similar object matching is combined with fundamental differential geometry definitions, some matching algorithms are proposed and experimentations indicate encouraged results. The research fields include the two-dimensional partially similar object matching, three-dimensional partially similar object matching and three-dimensional deformed isometric surface matching. In addition, some prospects are proposed in the end of the paper.
An efficient coding approach is firstly proposed for two-dimensional partially similar object matching. Considering the invariance of curvature, a new coding approach based on the abstraction of contour curvature is presented, and then the discrete approximation storage and reconstruction solutions are demonstrated. The curve-matching algorithm based on improving KMP (D. E. Knuth, V. R. Pratt and J. H. Morris) algorithm is proposed. Experiments indicate a simpler matching algorithm, reduced storage and greater convenience for pattern recognition when the differential geometry approaches is utilized to describe the contour.
Secondly, considering the matching accuracy of the differential geometry coding, an improved approach based on similar skeleton is proposed for two-dimensional partially similar object matching. According to differential geometry, considering the invariance of curvature when rigid transformation is applied to plane curve, a new model utilizing curvature to illustrate the inherent characteristic of object contours is proposed; Point-pair set is constructed by means of filtrating points with similar inherent characteristic in object contours; possible transformation is located by similar straight line segments pair; finally, optimum transformation is computed and optimum matching is determined by score function. Simulation experiments indicate an encouraging matching efficiency and low run time complexity of the algorithm for partially similar object matching, especially for complex shape.
Thirdly, the idea of similar skeleton is extended to the case of three-dimensional partially similar object matching. Curvature and torsion are employed to represent the inherent characteristic of three-dimensional curves; Gauss curvature and mean curvature are used to represent the inherent characteristic of three-dimensional surfaces. After the construction of Point-pair set, possible transformation is located by similar asymmetry triangle pair; finally, optimum transformation and optimum matching are determined by score function.
In addition, a novel recognition approach for deformed isometric surfaces is presented in this paper. Firstly, some signatures of isometric surfaces are demonstrated based on geodesic distance, and then the Signature Matrix(SM) is constructed by computing the geodesic distance of every point pair using Fast Marching Method on Triangulate Domains (FMTD). Secondly, a normalization procedure is utilized to eliminate the difference of the Signature Matrices for the same object. A new series of moment invariants is proposed based on the Normalized Signature Matrix (NSM). In comparison with some recent methods, experiments indicate a lower computation complexity to the recognition for deformed isometric surfaces without reducing the recognition rate. Finally, extensions of this approach are introduced to the recognition for occluded and arbitrarily topologically deformed surfaces.
首先,针对二维目标,设计了一种高效的平面目标边界编码方法。为更好地识别目标形状,编码方法需要对目标的刚体变换具有不变性,同时最大限度保持目标的原有信息。鉴于刚体平面曲线作变换时其曲率的不变性,提出了基于轮廓曲率提取的目标边界编码方法,并对此方法实施了离散化处理。设计了基于改进的KMP(D.E.Knuth,V R.Pratt和J.H.Morris)算法的曲线匹配方法,并对目标轮廓的重建作出了描述。实验证明,利用微分几何的思想描述目标边界,提取方法简单,存储量小,其编码针对目标刚体变换具有不变性,为识别提供了较大的方便。
其次,考虑到二维微分几何编码在匹配时的精度问题,设计了基于相似骨架的二维局部相似目标匹配算法。根据微分几何原理,基于平面曲线作刚体变换时其曲率的不变性,利用曲率来表达目标轮廓的固有特征;筛选出待匹配目标轮廓上固有特征相似的点,形成点对集合;在点对集合中寻找相似线段对来定位可能的平面变换;通过得分函数,求出点对集合中相似线段对变换的最佳值,得出最佳匹配。仿真实验表明,该模型适合局部相似情况下的目标匹配,特别对于复杂形状目标,运算复杂度较低,具有较好的识别效果。另外,文章还将相似线段对的应用推广到了三维目标。对于三维曲线,利用像素点处的曲率和挠率来表达其固有特征;对于三维曲面,利用像素点的高斯曲率和平均曲率来表达其固有特征。然后筛选出待匹配目标上固有特征相似的点,形成点对集合;在点对集合中寻找相似三角形对来定位可能的平面变换;通过得分函数,求出点对集合中相似线段对的最佳值,得出最佳匹配。
此外,论文还针对等距变形体进行了研究。提出了一种针对等距变形目标识别的运算复杂度较低的新方法。首先利用FMTD(Fast Marching on Triangulated Domains)算法来计算曲面上点对之间的测地距离,构造特征矩阵;然后,通过归一化过程,构造出归一化特征矩阵,保证了同一目标特征矩阵的不变性;最后,利用矩不变量对归一化特征矩阵实施特征提取,构造了等距变形目标的变形矩。实验表明,与传统方法相比,在不降低识别效果的前提下,该算法具备较低的运算复杂度。
Partially similar object matching is a universal approach to object recognition. During the past decade, the problem of finding a partial match between three-dimensional surfaces attracted considerable attention. In this paper, the research of partially similar object matching is combined with fundamental differential geometry definitions, some matching algorithms are proposed and experimentations indicate encouraged results. The research fields include the two-dimensional partially similar object matching, three-dimensional partially similar object matching and three-dimensional deformed isometric surface matching. In addition, some prospects are proposed in the end of the paper.
An efficient coding approach is firstly proposed for two-dimensional partially similar object matching. Considering the invariance of curvature, a new coding approach based on the abstraction of contour curvature is presented, and then the discrete approximation storage and reconstruction solutions are demonstrated. The curve-matching algorithm based on improving KMP (D. E. Knuth, V. R. Pratt and J. H. Morris) algorithm is proposed. Experiments indicate a simpler matching algorithm, reduced storage and greater convenience for pattern recognition when the differential geometry approaches is utilized to describe the contour.
Secondly, considering the matching accuracy of the differential geometry coding, an improved approach based on similar skeleton is proposed for two-dimensional partially similar object matching. According to differential geometry, considering the invariance of curvature when rigid transformation is applied to plane curve, a new model utilizing curvature to illustrate the inherent characteristic of object contours is proposed; Point-pair set is constructed by means of filtrating points with similar inherent characteristic in object contours; possible transformation is located by similar straight line segments pair; finally, optimum transformation is computed and optimum matching is determined by score function. Simulation experiments indicate an encouraging matching efficiency and low run time complexity of the algorithm for partially similar object matching, especially for complex shape.
Thirdly, the idea of similar skeleton is extended to the case of three-dimensional partially similar object matching. Curvature and torsion are employed to represent the inherent characteristic of three-dimensional curves; Gauss curvature and mean curvature are used to represent the inherent characteristic of three-dimensional surfaces. After the construction of Point-pair set, possible transformation is located by similar asymmetry triangle pair; finally, optimum transformation and optimum matching are determined by score function.
In addition, a novel recognition approach for deformed isometric surfaces is presented in this paper. Firstly, some signatures of isometric surfaces are demonstrated based on geodesic distance, and then the Signature Matrix(SM) is constructed by computing the geodesic distance of every point pair using Fast Marching Method on Triangulate Domains (FMTD). Secondly, a normalization procedure is utilized to eliminate the difference of the Signature Matrices for the same object. A new series of moment invariants is proposed based on the Normalized Signature Matrix (NSM). In comparison with some recent methods, experiments indicate a lower computation complexity to the recognition for deformed isometric surfaces without reducing the recognition rate. Finally, extensions of this approach are introduced to the recognition for occluded and arbitrarily topologically deformed surfaces.
引文
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