Estimation of nonlinear errors-in-variables models for computer vision applications

Robust Regression

Discriminative methods (e.g., kernel regression, SVM) have been extensively used to solve problems such as object recognition, image alignment and pose estimation from images. These methods typically map image features ( X) to continuous (e.g., pose) or discrete (e.g., object category) values. A major drawback of existing discriminative methods is that samples are directly projected onto a subspace and hence fail to account for outliers common in realistic training sets due to occlusion, specular reflections or noise. It is important to notice that existing discriminative approaches assume the input variables X to be noise free. Thus, discriminative methods experience significant performance degradation when gross outliers are present. Despite its obvious importance, the problem of robust discriminative learning has been relatively unexplored in computer vision. This paper develops the theory of robust regression (RR) and presents an effective convex approach that uses recent advances on rank minimization. The framework applies to a variety of problems in computer vision including robust linear discriminant analysis, regression with missing data, and multi-label classification. Several synthetic and real examples with applications to head pose estimation from images, image and video classification and facial attribute classification with missing data are used to illustrate the benefits of RR.

Iterative most-likely point registration (IMLP): a robust algorithm for computing optimal shape alignment

We present a probabilistic registration algorithm that robustly solves the problem of rigid-body alignment between two shapes with high accuracy, by aptly modeling measurement noise in each shape, whether isotropic or anisotropic. For point-cloud shapes, the probabilistic framework additionally enables modeling locally-linear surface regions in the vicinity of each point to further improve registration accuracy. The proposed Iterative Most-Likely Point (IMLP) algorithm is formed as a variant of the popular Iterative Closest Point (ICP) algorithm, which iterates between point-correspondence and point-registration steps. IMLP’s probabilistic framework is used to incorporate a generalized noise model into both the correspondence and the registration phases of the algorithm, hence its name as a most-likely point method rather than a closest-point method. To efficiently compute the most-likely correspondences, we devise a novel search strategy based on a principal direction (PD)-tree search. We also propose a new approach to solve the generalized total-least-squares (GTLS) sub-problem of the registration phase, wherein the point correspondences are registered under a generalized noise model. Our GTLS approach has improved accuracy, efficiency, and stability compared to prior methods presented for this problem and offers a straightforward implementation using standard least squares. We evaluate the performance of IMLP relative to a large number of prior algorithms including ICP, a robust variant on ICP, Generalized ICP (GICP), and Coherent Point Drift (CPD), as well as drawing close comparison with the prior anisotropic registration methods of GTLS-ICP and A-ICP. The performance of IMLP is shown to be superior with respect to these algorithms over a wide range of noise conditions, outliers, and misalignments using both mesh and point-cloud representations of various shapes.

Generalized projection-based M-estimator

We propose a novel robust estimation algorithm—the generalized projection-based M-estimator (gpbM), which does not require the user to specify any scale parameters. The algorithm is general and can handle heteroscedastic data with multiple linear constraints for single and multicarrier problems. The gpbM has three distinct stages—scale estimation, robust model estimation, and inlier/outlier dichotomy. In contrast, in its predecessor pbM, each model hypotheses was associated with a different scale estimate. For data containing multiple inlier structures with generally different noise covariances, the estimator iteratively determines one structure at a time. The model estimation can be further optimized by using Grassmann manifold theory. We present several homoscedastic and heteroscedastic synthetic and real-world computer vision problems with single and multiple carriers.

Integration of model-based weighting into an ICP variant to account for measurement errors in intra-operative A-Mode ultrasound-based registration

This paper addresses error modeling in A-Mode ultrasound- (US-) based registration and integration of model-based weighting into the Random-ICP (R-ICP) algorithm. The R-ICP is a variant of the Iterative Closest Point (ICP) algorithm, and it was suggested for surface-based registration using A-Mode US in the context of skull surgery. In that application area the R-ICP could yield high accuracy even in case of a small number of data points and a very inaccurate user-interactive pre-registration. However, it cannot cope with unequal point uncertainty, which is an important drawback in the context of hip surgery: Uncertainty about the average speed of sound is an error source, whose impact on the registration accuracy increases with the thickness of the scanned soft tissue. It can, therefore, lead to considerable localization errors if a thick soft tissue layer is scanned, and it might vary a lot from data point to data point as the soft tissue thickness is inhomogeneous. The present work investigates how to account for this error source considering also other error sources such as the establishment of point correspondences. Simulation results show that registration accuracy can be substantially improved when model-based weighting is integrated into the R-ICP.