In random sample consensus (RANSAC), the problem of ellipsoid fitting can be
formulated as a problem of minimization of point-to-model distance, which is
realized by maximizing model score. Hence, the performance of ellipsoid fitting
is affected by distance metric. In this paper, we proposed a novel distance
metric called the axial distance, which is converted from the algebraic
distance by introducing a scaling factor to solve nongeometric problems of the
algebraic distance. There is complementarity between the axial distance and
Sampson distance because their combination is a stricter metric when
calculating the model score of sample consensus and the weight of the weighted
least squares (WLS) fitting. Subsequently, a novel sample-consensus-based
ellipsoid fitting method is proposed by using the combination between the axial
distance and Sampson distance (CAS). We compare the proposed method with
several representative fitting methods through experiments on synthetic and
real datasets. The results show that the proposed method has a higher
robustness against outliers, consistently high accuracy, and a speed close to
that of the method based on sample consensus.

本文提出了一种基于样本一致性的新型椭球拟合方法，使用轴向距离和 Sampson 距离的组合进行计算，在合成和实际数据集上的实验结果表明，所提出的方法具有更高的鲁棒性，一致的精度和接近于基于样本一致性方法的速度。

使用轴向距离和组合的稳健椭球拟合

Robust Ellipsoid Fitting Using Axial Distance and Combination

Pothole detection is one of the most important tasks for road maintenance.
Computer vision approaches are generally based on either 2D road image analysis
or 3D road surface modeling. However, these two categories are always used
independently. Furthermore, the pothole detection accuracy is still far from
satisfactory. Therefore, in this paper, we present a robust pothole detection
algorithm that is both accurate and computationally efficient. A dense
disparity map is first transformed to better distinguish between damaged and
undamaged road areas. To achieve greater disparity transformation efficiency,
golden section search and dynamic programming are utilized to estimate the
transformation parameters. Otsu's thresholding method is then used to extract
potential undamaged road areas from the transformed disparity map. The
disparities in the extracted areas are modeled by a quadratic surface using
least squares fitting. To improve disparity map modeling robustness, the
surface normal is also integrated into the surface modeling process.
Furthermore, random sample consensus is utilized to reduce the effects caused
by outliers. By comparing the difference between the actual and modeled
disparity maps, the potholes can be detected accurately. Finally, the point
clouds of the detected potholes are extracted from the reconstructed 3D road
surface. The experimental results show that the successful detection accuracy
of the proposed system is around 98.7% and the overall pixel-level accuracy is
approximately 99.6%.

本篇论文介绍了一种精确可靠且计算效率高的路面坑洞检测算法，该算法基于非常密集的视差图，利用双黄金分割搜索和动态规划来估计转换参数，然后通过二次曲面拟合表征提取潜在未受损路面区域，通过随机抽样共识算法减少异常点带来的干扰，最后利用重建的三维路面模型提取检测的路面坑洞点云。实验结果表明，该方法的成功检测率约为 98.7％，整体精度约为 99.6％。