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Efficient and Robust Direct Image Registration Based on Joint Geometric and Photometric Lie Algebra

机译:基于联合几何和测光李代数的高效鲁棒直接图像配准

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This paper considers the joint geometric and photometric image registration problem. The inverse compositional (IC) algorithm and the efficient second-order minimization (ESM) algorithm are two typical efficient methods applied to the geometric registration problem. Their efficiency stems from the utilization of the group structure of geometric transformations. To allow for photometric variations, the dual IC algorithm (DIC) proposed by Bartoli performs joint geometric and photometric image registration by extending the IC algorithm. The group structures of both geometric and photometric transformations are exploited. Despite the robustness to large photometric variations, DIC is vulnerable to large geometric deformations. The ESM algorithm is extended by Silveiranet al.nto address photometric variations. In their approach, the photometric transformations are modeled in Euclidean space. Their approach is robust to relatively large geometric and photometric transformations; however, it is not efficient for large photometric variations. We propose a new efficient and robust image registration method by exploiting the non-Euclidean Lie group structure of joint geometric and photometric transformations for both grayscale and color images. The image registration is formulated as a nonlinear least squares problem. In our method, the geometric and photometric transformations are jointly parameterized by their corresponding Lie algebras. Based on this parameterization approach, the second-order approximation strategy of ESM is employed to optimize the joint geometric and photometric parameters. The error function in the nonlinear least squares problem is approximated by a second-order Taylor expansion with respect to joint geometric and photometric parameters without computing the Hessian matrix. For further efficiency, independent convergence criteria for geometric and photometric parameters are used in the iterative optimization process. The superiority of our proposed method over the previous methods, in terms of efficiency, accuracy, and robustness, is demonstrated through extensive experiments on synthetic and real data.
机译:本文考虑了联合几何和光度图像配准问题。逆成分(IC)算法和有效的二阶最小化(ESM)算法是应用于几何配准问题的两种典型的有效方法。它们的效率源于对几何变换的群结构的利用。为了允许光度变化,由Bartoli提出的双重IC算法(DIC)通过扩展IC算法执行联合几何和光度图像配准。利用了几何和光度转换的组结构。尽管对较大的光度变化具有鲁棒性,但DIC仍然容易受到较大的几何变形的影响。 ESM算法由Silveiran 扩展等。来解决光度变化。在他们的方法中,光度转换是在欧氏空间中建模的。他们的方法对于较大的几何和光度转换是可靠的。但是,它对于较大的光度变化不是很有效。通过对灰度和彩色图像进行联合几何和光度变换的非欧氏李群结构,我们提出了一种新的高效且鲁棒的图像配准方法。图像配准被公式化为非线性最小二乘问题。在我们的方法中,几何和光度转换由它们相应的李代数共同参数化。基于这种参数化方法,采用ESM的二阶近似策略来优化联合几何和光度学参数。非线性最小二乘问题中的误差函数通过相对于联合几何和光度学参数的二阶泰勒展开式近似,而无需计算Hessian矩阵。为了提高效率,在迭代优化过程中使用了针对几何和光度参数的独立收敛准则。通过对合成数据和真实数据进行的大量实验证明了我们提出的方法在效率,准确性和鲁棒性方面优于以前的方法。

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