Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and partial overlap) and high degrees of freedom. Existing methods typically adopt the $\ell_p$ type robust norm to measure the alignment error and regularize the smoothness of deformation, and use a proximal algorithm to solve the resulting non-smooth optimization problem. However, the slow convergence of such algorithms limits their wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust norm for alignment and regularization, which can effectively handle outliers and partial overlaps. The problem is solved using the majorization-minimization algorithm, which reduces each iteration to a convex quadratic problem with a closed-form solution. We further apply Anderson acceleration to speed up the convergence of the solver, enabling the solver to run efficiently on devices with limited compute capability. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlaps, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at //github.com/yaoyx689/AMM_NRR.
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Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an $n-1$ dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to three fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, and point set registration. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.
Trajectory optimization problems for legged robots are commonly formulated with fixed contact schedules. These multi-phase Hybrid Trajectory Optimization (HTO) methods result in locally optimal trajectories, but the result depends heavily upon the predefined contact mode sequence. Contact-Implicit Optimization (CIO) offers a potential solution to this issue by allowing the contact mode to be determined throughout the trajectory by the optimization solver. However, CIO suffers from long solve times and convergence issues. This work combines the benefits of these two methods into one algorithm: Staged Contact Optimization (SCO). SCO tightens constraints on contact in stages, eventually fixing them to allow robust and fast convergence to a feasible solution. Results on a planar biped and spatial quadruped demonstrate speed and optimality improvements over CIO and HTO. These properties make SCO well suited for offline trajectory generation or as an effective tool for exploring the dynamic capabilities of a robot.
Pathologists need to combine information from differently stained pathology slices for accurate diagnosis. Deformable image registration is a necessary technique for fusing multi-modal pathology slices. This paper proposes a hybrid deep feature-based deformable image registration framework for stained pathology samples. We first extract dense feature points via the detector-based and detector-free deep learning feature networks and perform points matching. Then, to further reduce false matches, an outlier detection method combining the isolation forest statistical model and the local affine correction model is proposed. Finally, the interpolation method generates the deformable vector field for pathology image registration based on the above matching points. We evaluate our method on the dataset of the Non-rigid Histology Image Registration (ANHIR) challenge, which is co-organized with the IEEE ISBI 2019 conference. Our technique outperforms the traditional approaches by 17% with the Average-Average registration target error (rTRE) reaching 0.0034. The proposed method achieved state-of-the-art performance and ranked 1st in evaluating the test dataset. The proposed hybrid deep feature-based registration method can potentially become a reliable method for pathology image registration.
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this work, we aim to further accelerate the rate of convergence by introducing a preconditioning technique. After constructing the preconditioner, we preprocess the progressive iterative approximation (PIA) and its variants, called the preconditioned GIMs. We show that the proposed preconditioned GIMs converge and the extra computation cost brought by the preconditioning technique is negligible. Several numerical experiments are given to demonstrate that our preconditioner can accelerate the convergence rate of PIA and its variants.
Due to the emergence of various wireless sensing technologies, numerous positioning algorithms have been introduced in the literature, categorized into \emph{geometry-driven positioning} (GP) and \emph{data-driven positioning} (DP). These approaches have respective limitations, e.g., a non-line-of-sight issue for GP and the lack of a labeled dataset for DP, which can be complemented by integrating both methods. To this end, this paper aims to introduce a novel principle called \emph{combinatorial data augmentation} (CDA), a catalyst for the two approaches' seamless integration. Specifically, GP-based datasets augmented from different combinations of positioning entities, called \emph{preliminary estimate locations} (PELs), can be used as DP's inputs. We confirm the CDA's effectiveness from field experiments based on WiFi \emph{round-trip times} (RTTs) and \emph{inertial measurement units} (IMUs) by designing several CDA-based positioning algorithms. First, we show that CDA offers various metrics quantifying each PEL's reliability, thereby filtering out unreliable PELs for WiFi RTT positioning. Second, CDA helps compute the measurement covariance matrix of a Kalman filter for fusing two position estimates derived by WiFi RTT and IMUs. Third, we use the above position estimate as the corresponding PEL's real-time label for fingerprint-based positioning as a representative DP algorithm. It provides accurate and reliable positioning results, says an average positioning error of $1.51$ (m) with a standard deviation of $0.88$~(m).
The author's recent research papers, "Cumulative deviation of a subpopulation from the full population" and "A graphical method of cumulative differences between two subpopulations" (both published in volume 8 of Springer's open-access "Journal of Big Data" during 2021), propose graphical methods and summary statistics, without extensively calibrating formal significance tests. The summary metrics and methods can measure the calibration of probabilistic predictions and can assess differences in responses between a subpopulation and the full population while controlling for a covariate or score via conditioning on it. These recently published papers construct significance tests based on the scalar summary statistics, but only sketch how to calibrate the attained significance levels (also known as "P-values") for the tests. The present article reviews and synthesizes work spanning many decades in order to detail how to calibrate the P-values. The present paper presents computationally efficient, easily implemented numerical methods for evaluating properly calibrated P-values, together with rigorous mathematical proofs guaranteeing their accuracy, and illustrates and validates the methods with open-source software and numerical examples.
We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of C-infinity bump functions of varying support sizes. We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at (//github.com/MathBioCU/WENDy).
Memory disaggregation is being considered as a strong alternative to traditional architecture to deal with the memory under-utilization in data centers. Disaggregated memory can adapt to dynamically changing memory requirements for the data center applications like data analytics, big data, etc., that require in-memory processing. However, such systems can face high remote memory access latency due to the interconnect speeds. In this paper, we explore a rack-scale disaggregated memory architecture and discuss the various design aspects. We design a trace-driven simulator that combines an event-based interconnect and a cycle-accurate memory simulator to evaluate the performance of disaggregated memory system at the rack scale. Our study shows that not only the interconnect but the contention in the remote memory queues also adds significantly to remote memory access latency. We introduces a memory allocation policy to reduce the latency compared to the conventional policies. We conduct experiments using various benchmarks with diverse memory access patterns. Our study shows encouraging results towards the rack-scale memory disaggregation and acceptable average memory access latency.
Loop Closure Detection (LCD) is an essential component of visual simultaneous localization and mapping (SLAM) systems. It enables the recognition of previously visited scenes to eliminate pose and map estimate drifts arising from long-term exploration. However, current appearance-based LCD methods face significant challenges, including high computational costs, viewpoint variance, and dynamic objects in scenes. This paper introduces an online based on Superpixel Grids (SGs) LCD approach, SGIDN-LCD, to find similarities between scenes via hand-crafted features extracted from SGs. Unlike traditional Bag-of-Words (BoW) models requiring pre-training, we propose an adaptive mechanism to group similar images called $\textbf{\textit{dynamic}}$ $\textbf{\textit{node}}$, which incremental adjusts the database in an online manner, allowing for efficient retrieval of previously viewed images. Experimental results demonstrate the SGIDN-LCD significantly improving LCD precision-recall and efficiency. Moreover, our proposed overall LCD method outperforms state-of-the-art approaches on multiple typical datasets.
The dynamics of neuron populations during diverse tasks often evolve on low-dimensional manifolds. However, it remains challenging to discern the contributions of geometry and dynamics for encoding relevant behavioural variables. Here, we introduce an unsupervised geometric deep learning framework for representing non-linear dynamical systems based on statistical distributions of local phase portrait features. Our method provides robust geometry-aware or geometry-agnostic representations for the unbiased comparison of dynamics based on measured trajectories. We demonstrate that our statistical representation can generalise across neural network instances to discriminate computational mechanisms, obtain interpretable embeddings of neural dynamics in a primate reaching task with geometric correspondence to hand kinematics, and develop a decoding algorithm with state-of-the-art accuracy. Our results highlight the importance of using the intrinsic manifold structure over temporal information to develop better decoding algorithms and assimilate data across experiments.
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