Analysis of Robust Functions for Registration Algorithms

Registration accuracy is influenced by the presence of outliers and numerous robust solutions have been developed over the years to mitigate their effect. However, without a large scale comparison of solutions to filter outliers, it is becoming tedious to select an appropriate algorithm for a given application. This paper presents a comprehensive analyses of the effects of outlier filters on the ICP algorithm aimed at mobile robotic application. Fourteen of the most common outlier filters (such as M-estimators) have been tested in different types of environments, for a total of more than two million registrations. Furthermore, the influence of tuning parameters have been thoroughly explored. The experimental results show that most outlier filters have similar performance if they are correctly tuned. Nonetheless, filters such as Var. Trim., Cauchy, and Cauchy MAD are more stable against different environment types. Interestingly, the simple norm L1 produces comparable accuracy, while been parameterless

Multi-scale Non-Rigid Point Cloud Registration Using Robust Sliced-Wasserstein Distance via Laplace-Beltrami Eigenmap

In this work, we propose computational models and algorithms for point cloud registration with non-rigid transformation. First, point clouds sampled from manifolds originally embedded in some Euclidean space $\mathbb{R}^D$ are transformed to new point clouds embedded in $\mathbb{R}^n$ by Laplace-Beltrami(LB) eigenmap using the $n$ leading eigenvalues and corresponding eigenfunctions of LB operator defined intrinsically on the manifolds. The LB eigenmap are invariant under isometric transformation of the original manifolds. Then we design computational models and algorithms for registration of the transformed point clouds in distribution/probability form based on the optimal transport theory which provides both generality and flexibility to handle general point clouds setting. Our methods use robust sliced-Wasserstein distance, which is as the average of projected Wasserstein distance along different directions, and incorporate a rigid transformation to handle ambiguities introduced by the Laplace-Beltrami eigenmap. By going from smaller $n$, which provides a quick and robust registration (based on coarse scale features) as well as a good initial guess for finer scale registration, to a larger $n$, our method provides an efficient, robust and accurate approach for multi-scale non-rigid point cloud registration.Comment: 29 pages, 8 figure

Robust registration of medical images in the presence of spatially-varying noise

Spatially-varying intensity noise is a common source of distortion in medical images. Bias field noise is one example of such a distortion that is often present in the magnetic resonance (MR) images or other modalities such as retina images. In this paper, we first show that the bias field noise can be considerably reduced using Empirical Mode Decomposition (EMD) technique. EMD is a multi-resolution tool that decomposes a signal into several principle patterns and residual components. We show that the spatially-varying noise is highly expressed in the residual component of the EMD and could be filtered out. Then, we propose two hierarchical multi-resolution EMD-based algorithms for robust registration of images in the presence of spatially varying noise. One algorithm (LR-EMD) is based on registration of EMD feature-maps from both floating and reference images in various resolution levels. In the second algorithm (AFR-EMD), we first extract an average feature-map based on EMD from both floating and reference images. Then, we use a simple hierarchical multi-resolution algorithm to register the average feature-maps. For the brain MR images, both algorithms achieve lower error rate and higher convergence percentage compared to the intensity-based hierarchical registration. Specifically, using mutual information as the similarity measure, AFR-EMD achieves 42% lower error rate in intensity and 52% lower error rate in transformation compared to intensity-based hierarchical registration. For LR-EMD, the error rate is 32% lower for the intensity and 41% lower for the transformation. Furthermore, we demonstrate that our proposed algorithms improve the registration of retina images in the presence of spatially varying noise

Dependent landmark drift: robust point set registration with a Gaussian mixture model and a statistical shape model

The goal of point set registration is to find point-by-point correspondences between point sets, each of which characterizes the shape of an object. Because local preservation of object geometry is assumed, prevalent algorithms in the area can often elegantly solve the problems without using geometric information specific to the objects. This means that registration performance can be further improved by using prior knowledge of object geometry. In this paper, we propose a novel point set registration method using the Gaussian mixture model with prior shape information encoded as a statistical shape model. Our transformation model is defined as a combination of the similar transformation, motion coherence, and the statistical shape model. Therefore, the proposed method works effectively if the target point set includes outliers and missing regions, or if it is rotated. The computational cost can be reduced to linear, and therefore the method is scalable to large point sets. The effectiveness of the method will be verified through comparisons with existing algorithms using datasets concerning human body shapes, hands, and faces

Robust Registration of Gaussian Mixtures for Colour Transfer

We present a flexible approach to colour transfer inspired by techniques recently proposed for shape registration. Colour distributions of the palette and target images are modelled with Gaussian Mixture Models (GMMs) that are robustly registered to infer a non linear parametric transfer function. We show experimentally that our approach compares well to current techniques both quantitatively and qualitatively. Moreover, our technique is computationally the fastest and can take efficient advantage of parallel processing architectures for recolouring images and videos. Our transfer function is parametric and hence can be stored in memory for later usage and also combined with other computed transfer functions to create interesting visual effects. Overall this paper provides a fast user friendly approach to recolouring of image and video materials

Discriminative Optimization: Theory and Applications to Computer Vision Problems

Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: (i) designing a cost function with a local optimum at an acceptable solution, and (ii) developing an efficient numerical method to search for one (or multiple) of these local optima. While designing such functions is feasible in the noiseless case, the stability and location of local optima are mostly unknown under noise, occlusion, or missing data. In practice, this can result in undesirable local optima or not having a local optimum in the expected place. On the other hand, numerical optimization algorithms in high-dimensional spaces are typically local and often rely on expensive first or second order information to guide the search. To overcome these limitations, this paper proposes Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. Specifically, DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D point cloud registration, camera pose estimation, and image denoising. We show that DO performed comparably or outperformed state-of-the-art algorithms in terms of accuracy, robustness to perturbations, and computational efficiency.Comment: 26 pages, 28 figure

Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial perception is jeopardized by the presence of incorrect data association, and in general, outliers. Although techniques to handle outliers do exist, they can fail in unpredictable manners (e.g., RANSAC, robust estimators), or can have exponential runtime (e.g., branch-and-bound). In this paper, we advance the state of the art in outlier rejection by making three contributions. First, we show that even a simple linear instance of outlier rejection is inapproximable: in the worst-case one cannot design a quasi-polynomial time algorithm that computes an approximate solution efficiently. Our second contribution is to provide the first per-instance sub-optimality bounds to assess the approximation quality of a given outlier rejection outcome. Our third contribution is to propose a simple general-purpose algorithm, named adaptive trimming, to remove outliers. Our algorithm leverages recently-proposed global solvers that are able to solve outlier-free problems, and iteratively removes measurements with large errors. We demonstrate the proposed algorithm on three spatial perception problems: 3D registration, two-view geometry, and SLAM. The results show that our algorithm outperforms several state-of-the-art methods across applications while being a general-purpose method

Image Registration of Very Large Images via Genetic Programming

Image registration (IR) is a fundamental task in image processing for matching two or more images of the same scene taken at different times, from different viewpoints and/or by different sensors. Due to the enormous diversity of IR applications, automatic IR remains a challenging problem to this day. A wide range of techniques has been developed for various data types and problems. However, they might not handle effectively very large images, which give rise usually to more complex transformations, e.g., deformations and various other distortions. In this paper we present a genetic programming (GP)-based approach for IR, which could offer a significant advantage in dealing with very large images, as it does not make any prior assumptions about the transformation model. Thus, by incorporating certain generic building blocks into the proposed GP framework, we hope to realize a large set of specialized transformations that should yield accurate registration of very large images

Robust Rigid Point Registration based on Convolution of Adaptive Gaussian Mixture Models

Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global probability alignment based on the convolution of adaptive Gaussian Mixture Models (GMM) from point clouds. Firstly, a novel adaptive GMM is defined using probability distributions from the corresponding points. Then rigid point cloud alignment is performed by maximizing the global probability from the convolution of dual adaptive GMMs in the whole 2D or 3D space, which can be efficiently optimized and has a large zone of accurate convergence. Thousands of trials have been conducted on 200 models from public 2D and 3D datasets to demonstrate superior robustness and accuracy in complex environments with unpredictable noise, outliers, occlusion, initial rotation, shape and missing points.Comment: 9 page

Image Registration Techniques: A Survey

Image Registration is the process of aligning two or more images of the same scene with reference to a particular image. The images are captured from various sensors at different times and at multiple view-points. Thus to get a better picture of any change of a scene or object over a considerable period of time image registration is important. Image registration finds application in medical sciences, remote sensing and in computer vision. This paper presents a detailed review of several approaches which are classified accordingly along with their contributions and drawbacks. The main steps of an image registration procedure are also discussed. Different performance measures are presented that determine the registration quality and accuracy. The scope for the future research are presented as well