The presence of outliers can significantly degrade the performance of ellipse fitting methods. We develop an ellipse fitting method that is robust to outliers based on the maximum correntropy criterion with variable center (MCC-VC), where a Laplacian kernel is used. For single ellipse fitting, we formulate a non-convex optimization problem to estimate the kernel bandwidth and center and divide it into two subproblems, each estimating one parameter. We design sufficiently accurate convex approximation to each subproblem such that computationally efficient closed-form solutions are obtained. The two subproblems are solved in an alternate manner until convergence is reached. We also investigate coupled ellipses fitting. While there exist multiple ellipses fitting methods that can be used for coupled ellipses fitting, we develop a couple ellipses fitting method by exploiting the special structure. Having unknown association between data points and ellipses, we introduce an association vector for each data point and formulate a non-convex mixed-integer optimization problem to estimate the data associations, which is approximately solved by relaxing it into a second-order cone program. Using the estimated data associations, we extend the proposed method to achieve the final coupled ellipses fitting. The proposed method is shown to have significantly better performance over the existing methods in both simulated data and real images.
翻译:外部线的存在可以显著地降低椭圆调整方法的性能。 我们开发了一种对外线适用的灵略调整方法, 这种方法对外线的适用力强, 其依据是使用拉placian内核的可变中心( MCC- VC) 的最大 Correntropy 标准( MCC- VC), 使用拉placian 内核内核。 对于单一的椭圆调整, 我们开发了一个非colvex优化问题, 以估计内核带带带宽和中核, 并将其分为两个子问题, 每个参数都估算出一个参数。 我们设计出一个对每个子问题足够准确的相近度, 以便获得高效的闭合式解决方案。 两个子问题以不同的方式解决, 在达到趋同之前, 两种子号相交加的相交配相配。 虽然有多种的椭圆调整方法可以用于配合椭圆结构的安装, 我们开发了两组合的椭圆相匹配方法, 每个数据点之间都存在未知的联系, 我们为每个数据点设置一个非convevex 混合内最优化的问题, 来估计数据组合, 以更精确的方法可以大大地调整现有的方法 。