Error analysis of robust optical flow estimation by least median of squares methods for the varying illumination model

The apparent pixel motion in an image sequence, called optical flow, is a useful primitive for automatic scene analysis and various other applications of computer vision. In general, however, the optical flow estimation suffers from two significant problems: the problem of illumination that varies with time and the problem of motion discontinuities induced by objects moving with respect to either other objects or with respect to the background. Various integrated approaches for solving these two problems simultaneously have been proposed. Of these, those that are based on the LMedS (least median of squares) appear to be the most robust. The goal of this paper is to carry out an error analysis of two different LMedS-based approaches, one based on the standard LMedS regression and the other using a modification thereof as proposed by us recently. While it is to be expected that the estimation accuracy of any approach would decrease with increasing levels of noise, for LMedS-like methods, it is not always clear as to how much of that decrease in performance can be attributed to the fact that only a small number of randomly selected samples is used for forming temporary solutions. To answer this question, our study here includes a baseline implementation in which all of the image data is used for forming motion estimates. We then compare the estimation errors of the two LMedS-based methods with the baseline implementation. Our error analysis demonstrates that, for the case of Gaussian noise, our modified LMedS approach yields better estimates at moderate levels of noise, but is outperformed by the standard LMedS method as the level of noise increases. For the case of salt-and-pepper noise, the modified LMedS method consistently performs better than the standard LMedS method.     

Using symmetry in robust model fitting

The pattern recognition and computer vision communities often employ robust methods for model fitting. In particular, high breakdown-point methods such as least median of squares (LMedS) and least trimmed squares (LTS) have often been used in situations where the data are contaminated with outliers. However, though the breakdown point of these methods can be as high as 50% (they can be robust to up to 50% contamination), they can break down at unexpectedly lower percentages when the outliers are clustered. In this paper, we demonstrate the fragility of LMedS and LTS and analyze the reasons that cause the fragility of these methods in the situation when a large percentage of clustered outliers exist in the data. We adapt the concept of “symmetry distance” to formulate an improved regression method, called the least trimmed symmetry distance (LTSD). Experimental results are presented to show that the LTSD performs better than LMedS and LTS under a large percentage of clustered outliers and large standard variance of inliers.     

Robust adaptive-scale parametric model estimation for computer vision

Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the two-step scale estimator (TSSE) and the adaptive scale sample consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines random sample consensus (RANSAC) and TSSE, using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 percent outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than least median squares (LMedS), residual consensus (RESC), and adaptive least Kth order squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.     

基于LQS的基本矩阵计算方法

基本矩阵作为分析两视图对极几何的有力工具,在视觉领域中占用重要的地位.分析了传统鲁棒方法在基本矩阵的求解问题中存在的不足,引入了稳健回归分析中的LQS方法,并结合Bucket分割技术,提出一种鲁棒估计基本矩阵的新方法,克服了RANSAC方法和LMedS方法的缺陷.模拟数据和真实图像实验结果表明,本文方法具有更高的鲁棒性和精确度.     

Robust Optical Flow Computation Based on Least-Median-of-Squares Regression

An optical flow estimation technique is presented which is based on the least-median-of-squares (LMedS) robust regression algorithm enabling more accurate flow estimates to be computed in the vicinity of motion discontinuities. The flow is computed in a blockwise fashion using an affine model. Through the use of overlapping blocks coupled with a block shifting strategy, redundancy is introduced into the computation of the flow. This eliminates blocking effects common in most other techniques based on blockwise processing and also allows flow to be accurately computed in regions containing three distinct motions.A multiresolution version of the technique is also presented, again based on LMedS regression, which enables image sequences containing large motions to be effectively handled.An extensive set of quantitative comparisons with a wide range of previously published methods are carried out using synthetic, realistic (computer generated images of natural scenes with known flow) and natural images. Both angular and absolute flow errors are calculated for those sequences with known optical flow. Displaced frame difference error, used extensively in video compression, is used for those natural scenes with unknown flow. In all of the sequences tested, a comparison with those methods that result in a dense flow field (greater than 80% spatial coverage), show that the LMedS technique produces the least error irrespective of the error measure used.     

Robust pose estimation

Standard least-squares (LS) methods for pose estimation of objects are sensitive to outliers which can occur due to mismatches. Even a single mismatch can severely distort the estimated pose. This paper describes a least-median of squares (LMedS) approach to estimating pose using point matches. It is both robust (resistant to up to 50% outliers) and efficient (linear in the number of points). The basic algorithm is then extended to improve performance in the presence of two types of noise: 1) type I which perturbs all data values by small amounts (e.g., Gaussian) and 2) type II which can corrupt a few data values by large amounts     

Robust estimation of BRDF model parameters

The effect of the Bidirectional Reflectance Distribution Function (BRDF) is one of the most important factors in correcting the reflectance obtained from remotely sensed data. Estimation of BRDF model parameters can be deteriorated by various factors; contamination of the observations by undetected subresolution clouds or snow patches, inconsistent atmospheric correction in multiangular time series due to uncertainties in the atmospheric parameters, slight variations of the surface condition during a period of observation, for example due to soil moisture changes, diurnal effects on vegetation structure, and geolocation errors [Lucht and Roujean, 2000]. In the present paper, parameter estimation robustness is examined using Bidirectional Reflectance Factor (BRF) data measured for paddy fields in Japan. We compare both the M-estimator and the least median of squares (LMedS) methods for robust parameter estimation to the ordinary least squares method (LSM). In experiments, simulated data that were produced by adding noises to the data measured on the ground surface were used. Experimental results demonstrate that if a robust estimation is sought, the LMedS method can be adopted for the robust estimation of a BRDF model parameter.     

LSMAT Least Squares Medial Axis Transform

The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independent optimization of each sphere using Gauss–Newton, and its least‐squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real‐data.     

Computer vision-based framework for extracting tectonic lineaments from optical remote sensing data

ABSTRACT

The extraction of tectonic lineaments from digital satellite data is a fundamental application in remote sensing. The location of tectonic lineaments such as faults and dykes are of interest for a range of applications, particularly because of their association with hydrothermal mineralization. Although a wide range of applications have utilized computer vision techniques, a standard workflow for application of these techniques to tectonic lineament extraction is lacking. We present a framework for extracting tectonic lineaments using computer vision techniques. The proposed framework is a combination of edge detection and line extraction algorithms for extracting tectonic lineaments using optical remote sensing data. It features ancillary computer vision techniques for reducing data dimensionality, removing noise and enhancing the expression of lineaments. The efficiency of two convolutional filters are compared in terms of enhancing the lineaments. We test the proposed framework on Landsat 8 data of a mineral-rich portion of the Gascoyne Province in Western Australia. To validate the results, the extracted lineaments are compared to geologically mapped structures by the Geological Survey of Western Australia (GSWA). The results show that the best correlation between our extracted tectonic lineaments and the GSWA tectonic lineament map is achieved by applying a minimum noise fraction transformation and a Laplacian filter. Application of a directional filter shows a strong correlation with known sites of hydrothermal mineralization. Hence, our method using either filter can be used for mineral prospectivity mapping in other regions where faults are exposed and observable in optical remote sensing data.     

一种新的高精度的L-M基本矩阵估计算法

分析了基于随机抽样检测思想的现有鲁棒算法在基本矩阵估计中存在的不足,结合LMedS和M估计法各自的优点,提出一种新的高精度的L-M基本矩阵估计算法。利用LMedS思想方法获得内点集,此时内点集通常情况下不包含误匹配,但仍存在位置误差,用Torr-M估计法计算基本矩阵,因为当匹配点只存在位置误差时,用M估计法得到的基本矩阵非常精确。大量的模拟实验和真实图像实验数据表明,在高斯噪声和误匹配存在的情况下,该算法具有更高的鲁棒性和精确度。