On the unification of line processes, outlier rejection, and robust statistics with applications in early vision

Probing Renal Microstructure and Function with Advanced Diffusion MRI: Concepts, Applications, Challenges, and Future Directions

Diffusion measurements in the kidney are affected not only by renal microstructure but also by physiological processes (i.e., glomerular filtration, water reabsorption, and urine formation). Because of the superposition of passive tissue diffusion, blood perfusion, and tubular pre-urine flow, the limitations of the monoexponential apparent diffusion coefficient (ADC) model in assessing pathophysiological changes in renal tissue are becoming apparent and motivate the development of more advanced diffusion-weighted imaging (DWI) variants. These approaches take advantage of the fact that the length scale probed in DWI measurements can be adjusted by experimental parameters, including diffusion-weighting, diffusion gradient directions and diffusion time. This forms the basis by which advanced DWI models can be used to capture not only passive diffusion effects, but also microcirculation, compartmentalization, tissue anisotropy. In this review, we provide a comprehensive overview of the recent advancements in the field of renal DWI. Following a short introduction on renal structure and physiology, we present the key methodological approaches for the acquisition and analysis of renal DWI data, including intravoxel incoherent motion (IVIM), diffusion tensor imaging (DTI), non-Gaussian diffusion, and hybrid IVIM-DTI. We then briefly summarize the applications of these methods in chronic kidney disease and renal allograft dysfunction. Finally, we discuss the challenges and potential avenues for further development of renal DWI. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY: Stage 2.

Vision-Aided Localization and Mapping in Forested Environments Using Stereo Images

Forests are traditionally characterized by stand-level descriptors, such as basal area, mean diameter, and stem density. In recent years, there has been a growing interest in enhancing the resolution of forest inventory to examine the spatial structure and patterns of trees across landscapes. The spatial arrangement of individual trees is closely linked to various non-monetary forest aspects, including water quality, wildlife habitat, and aesthetics. Additionally, associating individual tree positions with dendrometric variables like diameter, taper, and species can provide data for highly optimized, site-specific silvicultural prescriptions designed to achieve diverse management objectives. Aerial photogrammetry has proven effective for mapping individual trees; however, its utility is limited due to the inability to directly estimate many dendrometric variables. In contrast, terrestrial mapping methods can directly observe essential individual tree characteristics, such as diameter, but their mapping accuracy is governed by the accuracy of the global satellite navigation system (GNSS) receiver and the density of the canopy obstructions between the receiver and the satellite constellation. In this paper, we introduce an integrated approach that combines a camera-based motion and tree detection system with GNSS positioning, yielding a stem map with twice the accuracy of using a consumer-grade GNSS receiver alone. We demonstrate that large-scale stem maps can be generated in real time, achieving a root mean squared position error of 2.16 m. We offer an in-depth explanation of a visual egomotion estimation algorithm designed to enhance the local consistency of GNSS-based positioning. Additionally, we present a least squares minimization technique for concurrently optimizing the pose track and the positions of individual tree stem[s].

Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated least squares (TLS), maximum consensus, Geman-McClure, Tukey's biweight, among others, can be reformulated as polynomial optimization problems (POPs). By focusing on the TLS cost, our second contribution is to exploit sparsity in the POP and propose a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre's hierarchy while preserving empirical exactness, i.e., the SDP recovers the optimizer of the nonconvex POP with an optimality certificate. Our third contribution is to solve the SDP relaxations at an unprecedented scale and accuracy by presenting [Formula: see text], a solver that blends global descent on the convex SDP with fast local search on the nonconvex POP. Our fourth contribution is an evaluation of the proposed framework on six geometric perception problems including single and multiple rotation averaging, point cloud and mesh registration, absolute pose estimation, and category-level object pose and shape estimation. Our experiments demonstrate that (i) our sparse SDP relaxation is empirically exact with up to 60%- 90% outliers across applications; (ii) while still being far from real-time, [Formula: see text] is up to 100 times faster than existing SDP solvers on medium-scale problems, and is the only solver that can solve large-scale SDPs with hundreds of thousands of constraints to high accuracy; (iii) [Formula: see text] safeguards existing fast heuristics for robust estimation (e.g., [Formula: see text] or Graduated Non-Convexity), i.e., it certifies global optimality if the heuristic estimates are optimal, or detects and allows escaping local optima when the heuristic estimates are suboptimal.

Image downsampling expedited adaptive least-squares (IDEAL) fitting improves intravoxel incoherent motion (IVIM) analysis in the human kidney

PURPOSE

To improve the reliability of intravoxel incoherent motion (IVIM) model parameter estimation for the DWI in the kidney using a novel image downsampling expedited adaptive least-squares (IDEAL) approach.

METHODS

The robustness of IDEAL was investigated using simulated DW-MRI data corrupted with different levels of Rician noise. Subsequently, the performance of the proposed method was tested by fitting bi- and triexponential IVIM model to in vivo renal DWI data acquired on a clinical 3 Tesla MRI scanner and compared to conventional approaches (fixed D* and segmented fitting).

RESULTS

The numerical simulations demonstrated that the IDEAL algorithm provides robust estimates of the IVIM parameters in the presence of noise (SNR of 20) as indicated by relatively low absolute percentage bias (maximal sMdPB <20%) and normalized RMSE (maximal RMSE <28%). The analysis of the in vivo data showed that the IDEAL-based IVIM parameter maps were less noisy and more visually appealing than those obtained using the fixed D* and segmented methods. Further, coefficients of variation for nearly all IVIM parameters were significantly reduced in cortex and medulla for IDEAL-based biexponential (coefficients of variation: 4%-50%) and triexponential (coefficients of variation: 7.5%-75%) IVIM modelling compared to the segmented (coefficients of variation: 4%-120%) and fixed D* (coefficients of variation: 17%-174%) methods, reflecting greater accuracy of this method.

CONCLUSION

The proposed fitting algorithm yields more robust IVIM parameter estimates and is less susceptible to poor SNR than the conventional fitting approaches. Thus, the IDEAL approach has the potential to improve the reliability of renal DW-MRI analysis for clinical applications.

Towards fully automated robotic platform for remote auscultation

BACKGROUND

Since most developed countries are facing an increase in the number of patients per healthcare worker due to a declining birth rate and an ageing population, relatively simple and safe diagnosis tasks may need to be performed using robotics and automation technologies, without specialists and hospitals. This study presents an automated robotic platform for remote auscultation, which is a highly cost-effective screening tool for detecting abnormal clinical signs.

METHOD

The developed robotic platform is composed of a 6-degree-of-freedom cooperative robotic arm, LiDAR camera, and a spring-based mechanism holding an electric stethoscope. The platform enables autonomous stethoscope positioning based on external body information acquired using the LiDAR camera-based multi-way registration; the platform also ensures safe and flexible contact, maintaining the contact force within a certain range through the passive-actuated mechanism.

RESULTS

Our preliminary results confirm that the robotic platform enables estimation of the landing positions required for cardiac examinations based on the depth and landmark information of the body surface. It also handles the stethoscope while maintaining the contact force without relying on the push-in displacement by the robotic arm.

CONCLUSION

The developed robotic platform enables the estimation of the landing positions and handling the stethoscope while maintaining the contact force, which promises the potential of automatic remote auscultation.

CNN based facial aesthetics analysis through dynamic robust losses and ensemble regression

In recent years, estimating beauty of faces has attracted growing interest in the fields of computer vision and machine learning. This is due to the emergence of face beauty datasets (such as SCUT-FBP, SCUT-FBP5500 and KDEF-PT) and the prevalence of deep learning methods in many tasks. The goal of this work is to leverage the advances in Deep Learning architectures to provide stable and accurate face beauty estimation from static face images. To this end, our proposed approach has three main contributions. To deal with the complicated high-level features associated with the FBP problem by using more than one pre-trained Convolutional Neural Network (CNN) model, we propose an architecture with two backbones (2B-IncRex). In addition to 2B-IncRex, we introduce a parabolic dynamic law to control the behavior of the robust loss parameters during training. These robust losses are ParamSmoothL1, Huber, and Tukey. As a third contribution, we propose an ensemble regression based on five regressors, namely Resnext-50, Inception-v3 and three regressors based on our proposed 2B-IncRex architecture. These models are trained with the following dynamic loss functions: Dynamic ParamSmoothL1, Dynamic Tukey, Dynamic ParamSmoothL1, Dynamic Huber, and Dynamic Tukey, respectively. To evaluate the performance of our approach, we used two datasets: SCUT-FBP5500 and KDEF-PT. The dataset SCUT-FBP5500 contains two evaluation scenarios provided by the database developers: 60-40% split and five-fold cross-validation. Our approach outperforms state-of-the-art methods on several metrics in both evaluation scenarios of SCUT-FBP5500. Moreover, experiments on the KDEF-PT dataset demonstrate the efficiency of our approach for estimating facial beauty using transfer learning, despite the presence of facial expressions and limited data. These comparisons highlight the effectiveness of the proposed solutions for FBP. They also show that the proposed Dynamic robust losses lead to more flexible and accurate estimators.

A Practical O(N2) Outlier Removal Method for Correspondence-Based Point Cloud Registration

Point cloud registration (PCR) is an important and fundamental problem in 3D computer vision, whose goal is to seek an optimal rigid model to register a point cloud pair. Correspondence-based PCR techniques do not require initial guesses and gain more attentions. However, 3D keypoint techniques are much more difficult than their 2D counterparts, which results in extremely high outlier rates. Current robust techniques suffer from very high computational cost. In this paper, we propose a polynomial time ( O(N²), where N is the number of correspondences.) outlier removal method. Its basic idea is to reduce the input set into a smaller one with a lower outlier rate based on bound principle. To seek tight lower and upper bounds, we originally define two concepts, i.e., correspondence matrix (CM) and augmented correspondence matrix (ACM). We propose a cost function to minimize the determinant of CM or ACM, where the cost of CM rises to a tight lower bound and the cost of ACM leads to a tight upper bound. Then, we propose a scale-adaptive Cauchy estimator (SA-Cauchy) for further optimization. Extensive experiments on simulated and real PCR datasets demonstrate that the proposed method is robust at outlier rates above 99 percent and 1  ∼ 2 orders faster than its competitors. The source code will be made publicly available in https://ljy-rs.github.io/web/.

AEROS: AdaptivE RObust Least-Squares for Graph-Based SLAM

In robot localisation and mapping, outliers are unavoidable when loop-closure measurements are taken into account. A single false-positive loop-closure can have a very negative impact on SLAM problems causing an inferior trajectory to be produced or even for the optimisation to fail entirely. To address this issue, popular existing approaches define a hard switch for each loop-closure constraint. This paper presents AEROS, a novel approach to adaptively solve a robust least-squares minimisation problem by adding just a single extra latent parameter. It can be used in the back-end component of the SLAM system to enable generalised robust cost minimisation by simultaneously estimating the continuous latent parameter along with the set of sensor poses in a single joint optimisation. This leads to a very closely curve fitting on the distribution of the residuals, thereby reducing the effect of outliers. Additionally, we formulate the robust optimisation problem using standard Gaussian factors so that it can be solved by direct application of popular incremental estimation approaches such as iSAM. Experimental results on publicly available synthetic datasets and real LiDAR-SLAM datasets collected from the 2D and 3D LiDAR systems show the competitiveness of our approach with the state-of-the-art techniques and its superiority on real world scenarios.

An Efficient Solution to Non-Minimal Case Essential Matrix Estimation

Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of N ( ) inlier point correspondences, which is called N-point problem, existing methods are either inefficient or prone to local minima. In this paper, we propose a certifiably globally optimal and efficient solver for the N-point problem. First we formulate the problem as a quadratically constrained quadratic program (QCQP). Then a certifiably globally optimal solution to this problem is obtained by semidefinite relaxation. This allows us to obtain certifiably globally optimal solutions to the original non-convex QCQPs in polynomial time. The theoretical guarantees of the semidefinite relaxation are also provided, including tightness and local stability. To deal with outliers, we propose a robust N-point method using M-estimators. Though global optimality cannot be guaranteed for the overall robust framework, the proposed robust N-point method can achieve good performance when the outlier ratio is not high. Extensive experiments on synthetic and real-world datasets demonstrated that our N-point method is 2 ∼ 3 orders of magnitude faster than state-of-the-art methods. Moreover, our robust N-point method outperforms state-of-the-art methods in terms of robustness and accuracy.

AdaStereo: An Efficient Domain-Adaptive Stereo Matching Approach

Recently, records on stereo matching benchmarks are constantly broken by end-to-end disparity networks. However, the domain adaptation ability of these deep models is quite limited. Addressing such problem, we present a novel domain-adaptive approach called AdaStereo that aims to align multi-level representations for deep stereo matching networks. Compared to previous methods, our AdaStereo realizes a more standard, complete and effective domain adaptation pipeline. Firstly, we propose a non-adversarial progressive color transfer algorithm for input image-level alignment. Secondly, we design an efficient parameter-free cost normalization layer for internal feature-level alignment. Lastly, a highly related auxiliary task, self-supervised occlusion-aware reconstruction is presented to narrow the gaps in output space. We perform intensive ablation studies and break-down comparisons to validate the effectiveness of each proposed module. With no extra inference overhead and only a slight increase in training complexity, our AdaStereo models achieve state-of-the-art cross-domain performance on multiple benchmarks, including KITTI, Middlebury, ETH3D and DrivingStereo, even outperforming some state-of-the-art disparity networks finetuned with target-domain ground-truths. Moreover, based on two additional evaluation metrics, the superiority of our domain-adaptive stereo matching pipeline is further uncovered from more perspectives. Finally, we demonstrate that our method is robust to various domain adaptation settings, and can be easily integrated into quick adaptation application scenarios and real-world deployments.

A Robust Rigid Registration Framework of 3D Indoor Scene Point Clouds Based on RGB-D Information

Rigid registration of 3D indoor scenes is a fundamental yet vital task in various fields that include remote sensing (e.g., 3D reconstruction of indoor scenes), photogrammetry measurement, geometry modeling, etc. Nevertheless, state-of-the-art registration approaches still have defects when dealing with low-quality indoor scene point clouds derived from consumer-grade RGB-D sensors. The major challenge is accurately extracting correspondences between a pair of low-quality point clouds when they contain considerable noise, outliers, or weak texture features. To solve the problem, we present a point cloud registration framework in view of RGB-D information. First, we propose a point normal filter for effectively removing noise and simultaneously maintaining sharp geometric features and smooth transition regions. Second, we design a correspondence extraction scheme based on a novel descriptor encoding textural and geometry information, which can robustly establish dense correspondences between a pair of low-quality point clouds. Finally, we propose a point-to-plane registration technology via a nonconvex regularizer, which can further diminish the influence of those false correspondences and produce an exact rigid transformation between a pair of point clouds. Compared to existing state-of-the-art techniques, intensive experimental results demonstrate that our registration framework is excellent visually and numerically, especially for dealing with low-quality indoor scenes.

A Self-Adaptive Method for Mapping Coastal Bathymetry On-The-Fly from Wave Field Video

Mapping coastal bathymetry from remote sensing becomes increasingly more attractive for the coastal community. It is facilitated by a rising availability of drone and satellite data, advances in data science, and an open-source mindset. Coastal bathymetry, but also wave directions, celerity and near-surface currents can simultaneously be derived from aerial video of a wave field. However, the required video processing is usually extensive, requires skilled supervision, and is tailored to a fieldsite. This study proposes a video-processing algorithm that resolves these issues. It automatically adapts to the video data and continuously returns mapping updates and thereby aims to make wave-based remote sensing more inclusive to the coastal community. The code architecture for the first time includes the dynamic mode decomposition (DMD) to reduce the data complexity of wavefield video. The DMD is paired with loss-functions to handle spectral noise and a novel spectral storage system and Kalman filter to achieve fast converging measurements. The algorithm is showcased for fieldsites in the USA, the UK, the Netherlands, and Australia. The performance with respect to mapping bathymetry was validated using ground truth data. It was demonstrated that merely 32 s of video footage is needed for a first mapping update with average depth errors of 0.9–2.6 m. These further reduced to 0.5–1.4 m as the videos continued and more mapping updates were returned. Simultaneously, coherent maps for wave direction and celerity were achieved as well as maps of local near-surface currents. The algorithm is capable of mapping the coastal parameters on-the-fly and thereby offers analysis of video feeds, such as from drones or operational camera installations. Hence, the innovative application of analysis techniques like the DMD enables both accurate and unprecedentedly fast coastal reconnaissance. The source code and data of this article are openly available.

A Framework of Learning Through Empirical Gain Maximization

We develop in this letter a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may be present in the response variable. The idea of EGM is to approximate the density function of the noise distribution instead of approximating the truth function directly as usual. Unlike the classical maximum likelihood estimation that encourages equal importance of all observations and could be problematic in the presence of abnormal observations, EGM schemes can be interpreted from a minimum distance estimation viewpoint and allow the ignorance of those observations. Furthermore, we show that several well-known robust nonconvex regression paradigms, such as Tukey regression and truncated least square regression, can be reformulated into this new framework. We then develop a learning theory for EGM by means of which a unified analysis can be conducted for these well-established but not fully understood regression approaches. This new framework leads to a novel interpretation of existing bounded nonconvex loss functions. Within this new framework, the two seemingly irrelevant terminologies, the well-known Tukey's biweight loss for robust regression and the triweight kernel for nonparametric smoothing, are closely related. More precisely, we show that Tukey's biweight loss can be derived from the triweight kernel. Other frequently employed bounded nonconvex loss functions in machine learning, such as the truncated square loss, the Geman-McClure loss, and the exponential squared loss, can also be reformulated from certain smoothing kernels in statistics. In addition, the new framework enables us to devise new bounded nonconvex loss functions for robust learning.

Multi-level height maps-based registration method for sparse LiDAR point clouds in an urban scene

The LiDAR sensor has been widely used for reconstruction in urban scenes. However, the current registration method makes it difficult to find stable 3D point correspondences from sparse and low overlapping LiDAR point clouds. In the urban situation, most of the LiDAR point clouds have a common flat ground. Therefore, we propose a novel, to the best of our knowledge, multi-level height (MH) maps-based coarse registration method. It requires that source and target point clouds have a common flat ground, which is easily satisfied for LiDAR point clouds in urban scenes. With MH maps, 3D registration is simplified as 2D registration, increasing the speed of registration. Robust correspondences are extracted in MH maps with different height intervals and statistic height information, improving the registration accuracy. The solid-state LiDAR Livox Mid-100 and mechanical LiDAR Velodyne HDL-64E are used in real-data and dataset experiments, respectively. Verification results demonstrate that our method is stable and outperforms state-of-the-art coarse registration methods for the sparse case. Runtime analysis shows that our method is faster than these methods, for it is non-iterative. Furthermore, our method can be extended for the unordered multi-view point clouds.

PALMNUT: An Enhanced Proximal Alternating Linearized Minimization Algorithm with Application to Separate Regularization of Magnitude and Phase

We introduce a new algorithm for complex image reconstruction with separate regularization of the image magnitude and phase. This optimization problem is interesting in many different image reconstruction contexts, although is nonconvex and can be difficult to solve. In this work, we first describe a novel implementation of the previous proximal alternating linearized minimization (PALM) algorithm to solve this optimization problem. We then make enhancements to PALM, leading to a new algorithm named PALMNUT that combines the PALM together with Nesterov's momentum and a novel approach that relies on uncoupled coordinatewise step sizes derived from coordinatewise Lipschitz-like bounds. Theoretically, we establish that a version of PALMNUT (without Nesterov's momentum) monotonically decreases the objective function, guaranteeing convergence of the cost function value. Empirical results obtained in the context of magnetic resonance imaging demonstrate that PALMNUT has computational advantages over common existing approaches like alternating minimization. Although our focus is on the application to separate magnitude and phase regularization, we expect that the same approach may also be useful in other nonconvex optimization problems with similar objective function structure.

Nonlinear Regression via Deep Negative Correlation Learning

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear regression to a robust loss function which is jointly optimizable with the deep convolutional network, and ii) utilizing ensemble of deep networks. Although some improved performance is achieved, the former may be lacking due to the intrinsic limitation of choosing a single hypothesis and the latter may suffer from much larger computational complexity. To cope with those issues, we propose to regress via an efficient "divide and conquer" manner. The core of our approach is the generalization of negative correlation learning that has been shown, both theoretically and empirically, to work well for non-deep regression problems. Without extra parameters, the proposed method controls the bias-variance-covariance trade-off systematically and usually yields a deep regression ensemble where each base model is both "accurate" and "diversified." Moreover, we show that each sub-problem in the proposed method has less Rademacher Complexity and thus is easier to optimize. Extensive experiments on several diverse and challenging tasks including crowd counting, personality analysis, age estimation, and image super-resolution demonstrate the superiority over challenging baselines as well as the versatility of the proposed method. The source code and trained models are available on our project page: https://mmcheng.net/dncl/.

Robust Extrinsic Calibration of Multiple RGB-D Cameras with Body Tracking and Feature Matching

RGB-D cameras have been commercialized, and many applications using them have been proposed. In this paper, we propose a robust registration method of multiple RGB-D cameras. We use a human body tracking system provided by Azure Kinect SDK to estimate a coarse global registration between cameras. As this coarse global registration has some error, we refine it using feature matching. However, the matched feature pairs include mismatches, hindering good performance. Therefore, we propose a registration refinement procedure that removes these mismatches and uses the global registration. In an experiment, the ratio of inliers among the matched features is greater than 95% for all tested feature matchers. Thus, we experimentally confirm that mismatches can be eliminated via the proposed method even in difficult situations and that a more precise global registration of RGB-D cameras can be obtained.

A dictionary-based graph-cut algorithm for MRI reconstruction

PURPOSE

Compressive sensing (CS)-based image reconstruction methods have proposed random undersampling schemes that produce incoherent, noise-like aliasing artifacts, which are easier to remove. The denoising process is critically assisted by imposing sparsity-enforcing priors. Sparsity is known to be induced if the prior is in the form of the L_p (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L₁ norm, which may not exploit the full power of CS. An efficient, discrete optimization formulation is proposed, which works not only on arbitrary L_p -norm priors as some non-convex CS methods do, but also on highly non-convex truncated penalty functions, resulting in a specific type of edge-preserving prior. These advanced features make the minimization problem highly non-convex, and thus call for more sophisticated minimization routines.

THEORY AND METHODS

The work combines edge-preserving priors with random undersampling, and solves the resulting optimization using a set of discrete optimization methods called graph cuts. The resulting optimization problem is solved by applying graph cuts iteratively within a dictionary, defined here as an appropriately constructed set of vectors relevant to brain MRI data used here.

RESULTS

Experimental results with in vivo data are presented.

CONCLUSION

The proposed algorithm produces better results than regularized SENSE or standard CS for reconstruction of in vivo data.

Discriminative Optimization: Theory and Applications to Computer Vision

Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: designing a cost function with a local optimum at an acceptable solution, and developing an efficient numerical method to search for this optimum. 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, we propose Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to the desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D registration, camera pose estimation, and image denoising. We show that DO outperformed or matched state-of-the-art algorithms in terms of accuracy, robustness, and computational efficiency.

Guaranteed Outlier Removal for Point Cloud Registration with Correspondences

An established approach for 3D point cloud registration is to estimate the registration function from 3D keypoint correspondences. Typically, a robust technique is required to conduct the estimation, since there are false correspondences or outliers. Current 3D keypoint techniques are much less accurate than their 2D counterparts, thus they tend to produce extremely high outlier rates. A large number of putative correspondences must thus be extracted to ensure that sufficient good correspondences are available. Both factors (high outlier rates, large data sizes) however cause existing robust techniques to require very high computational cost. In this paper, we present a novel preprocessing method called guaranteed outlier removal for point cloud registration. Our method reduces the input to a smaller set, in a way that any rejected correspondence is guaranteed to not exist in the globally optimal solution. The reduction is performed using purely geometric operations which are deterministic and fast. Our method significantly reduces the population of outliers, such that further optimization can be performed quickly. Further, since only true outliers are removed, the globally optimal solution is preserved. On various synthetic and real data experiments, we demonstrate the effectiveness of our preprocessing method. Demo code is available as supplementary material, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TPAMI.2017.2773482.

Robust continuous clustering

Clustering is a fundamental procedure in the analysis of scientific data. It is used ubiquitously across the sciences. Despite decades of research, existing clustering algorithms have limited effectiveness in high dimensions and often require tuning parameters for different domains and datasets. We present a clustering algorithm that achieves high accuracy across multiple domains and scales efficiently to high dimensions and large datasets. The presented algorithm optimizes a smooth continuous objective, which is based on robust statistics and allows heavily mixed clusters to be untangled. The continuous nature of the objective also allows clustering to be integrated as a module in end-to-end feature learning pipelines. We demonstrate this by extending the algorithm to perform joint clustering and dimensionality reduction by efficiently optimizing a continuous global objective. The presented approach is evaluated on large datasets of faces, hand-written digits, objects, newswire articles, sensor readings from the Space Shuttle, and protein expression levels. Our method achieves high accuracy across all datasets, outperforming the best prior algorithm by a factor of 3 in average rank.

Guided Wavelet Shrinkage for Edge-Aware Smoothing

Edge-aware smoothing has been extensively studied due to its wide range of applications in computer vision and graphics. Most published works have been focused on formulating the smoothing problem in the spatial domain. In this paper, we propose a new edge-aware smoothing framework called guided wavelet shrinkage (GWS), which is formulated in the wavelet domain as a maximum a posterior estimation problem. We impose a number of desirable properties on the statistical models and the associated parameters in order to derive an effective and computationally efficient algorithm. We compare the proposed GWS with classical image denoising in the wavelet domain. We have also compared different wavelet representations and found that the double-density dual-tree wavelet transform is the best choice. We show that the GWS can be configured as either self-guidance or external guidance. It can also be configured to operate in an iterative or non-iterative way. Experimental results and comparison with many state-of-the-algorithms demonstrate that the GWS-based algorithm can produce competitive results with O(N) computational complexity.

Estimating Articulated Human Motion with Covariance Scaled Sampling

We present a method for recovering three-dimensional (3D) human body motion from monocular video sequences based on a robust image matching metric, incorporation of joint limits and non-self-intersection constraints, and a new sample-and-refine search strategy guided by rescaled cost-function covariances. Monocular 3D body tracking is challenging: besides the difficulty of matching an imperfect, highly flexible, self-occluding model to cluttered image features, realistic body models have at least 30 joint parameters subject to highly nonlinear physical constraints, and at least a third of these degrees of freedom are nearly unobservable in any given monocular image. For image matching we use a carefully designed robust cost metric combining robust optical flow, edge energy, and motion boundaries. The nonlinearities and matching ambiguities make the parameter-space cost surface multimodal, ill-conditioned and highly nonlinear, so searching it is difficult. We discuss the limitations of CONDENSATION-like samplers, and describe a novel hybrid search algorithm that combines inflated-covariance-scaled sampling and robust continuous optimization subject to physical constraints and model priors. Our experiments on challenging monocular sequences show that robust cost modeling, joint and self-intersection constraints, and informed sampling are all essential for reliable monocular 3D motion estimation.

Local Spectral Component Decomposition for Multi-Channel Image Denoising

We propose a method for local spectral component decomposition based on the line feature of local distribution. Our aim is to reduce noise on multi-channel images by exploiting the linear correlation in the spectral domain of a local region. We first calculate a linear feature over the spectral components of an M -channel image, which we call the spectral line, and then, using the line, we decompose the image into three components: a single M -channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, and thus our algorithm needs to denoise only the two gray-scale images, regardless of the number of the channels. As a result, image deterioration due to the imbalance of the spectral component correlation can be avoided. The experiment shows that our method improves image quality with less deterioration while preserving vivid contrast. Our method is especially effective for hyperspectral images. The experimental results demonstrate that our proposed method can compete with the other state-of-the-art denoising methods.

Cascades of Regression Tree Fields for Image Restoration

Conditional random fields (CRFs) are popular discriminative models for computer vision and have been successfully applied in the domain of image restoration, especially to image denoising. For image deblurring, however, discriminative approaches have been mostly lacking. We posit two reasons for this: First, the blur kernel is often only known at test time, requiring any discriminative approach to cope with considerable variability. Second, given this variability it is quite difficult to construct suitable features for discriminative prediction. To address these challenges we first show a connection between common half-quadratic inference for generative image priors and Gaussian CRFs. Based on this analysis, we then propose a cascade model for image restoration that consists of a Gaussian CRF at each stage. Each stage of our cascade is semi-parametric, i.e., it depends on the instance-specific parameters of the restoration problem, such as the blur kernel. We train our model by loss minimization with synthetically generated training data. Our experiments show that when applied to non-blind image deblurring, the proposed approach is efficient and yields state-of-the-art restoration quality on images corrupted with synthetic and real blur. Moreover, we demonstrate its suitability for image denoising, where we achieve competitive results for grayscale and color images.

Spatially-constrained probability distribution model of incoherent motion (SPIM) for abdominal diffusion-weighted MRI

Quantitative diffusion-weighted MR imaging (DW-MRI) of the body enables characterization of the tissue microenvironment by measuring variations in the mobility of water molecules. The diffusion signal decay model parameters are increasingly used to evaluate various diseases of abdominal organs such as the liver and spleen. However, previous signal decay models (i.e., mono-exponential, bi-exponential intra-voxel incoherent motion (IVIM) and stretched exponential models) only provide insight into the average of the distribution of the signal decay rather than explicitly describe the entire range of diffusion scales. In this work, we propose a probability distribution model of incoherent motion that uses a mixture of Gamma distributions to fully characterize the multi-scale nature of diffusion within a voxel. Further, we improve the robustness of the distribution parameter estimates by integrating spatial homogeneity prior into the probability distribution model of incoherent motion (SPIM) and by using the fusion bootstrap solver (FBM) to estimate the model parameters. We evaluated the improvement in quantitative DW-MRI analysis achieved with the SPIM model in terms of accuracy, precision and reproducibility of parameter estimation in both simulated data and in 68 abdominal in-vivo DW-MRIs. Our results show that the SPIM model not only substantially reduced parameter estimation errors by up to 26%; it also significantly improved the robustness of the parameter estimates (paired Student's t-test, p < 0.0001) by reducing the coefficient of variation (CV) of estimated parameters compared to those produced by previous models. In addition, the SPIM model improves the parameter estimates reproducibility for both intra- (up to 47%) and inter-session (up to 30%) estimates compared to those generated by previous models. Thus, the SPIM model has the potential to improve accuracy, precision and robustness of quantitative abdominal DW-MRI analysis for clinical applications.

Anatomical Image Registration Using Volume Conservation to Assess Cardiac Deformation From 3D Ultrasound Recordings

Myocardial deformation imaging can provide valuable insights in myocardial mechanics and help in the diagnosis, prognosis and follow-up of cardiac diseases. However, extracting these indices in 3D is challenging due to the limitations in spatial and temporal resolution of the current volumetric ultrasound systems. For this purpose, we developed an anatomical free-form deformation image registration framework which is locally adapted to the anatomy of the heart. In this work we explored whether incorporating a myocardial volume conservation regularizer would improve strain estimates. We evaluated our technique on in silico echo sequences featuring realistic speckle textures and showed the volume conservation regularizer to be beneficial in reducing strain errors further when used in combination with a smoothness penalty. This combination led to more physiological boundary conditions. It also made distinguishing ischemic from normal segments easier in clinical images.