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Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization, better convergence speeds have been observed numerically. This makes it a rather useful heuristic to speed up the execution of optimization algorithms in machine learning. We present a primal dual analysis of the path-following algorithm and explore how to design its hyperparameters as well as determining how accurately each subproblem should be solved to guarantee a linear convergence rate on a target problem. Furthermore, considering optimization with a sparsity-inducing penalty, we analyze the change of the active sets with respect to the regularization parameter. The latter can then be adaptively calibrated to finely determine the number of features that will be selected along the solution path. This leads to simple heuristics for calibrating hyperparameters of active set approaches to reduce their complexity and improve their execution time.

Domain generalization involves learning a classifier from a heterogeneous collection of training sources such that it generalizes to data drawn from similar unknown target domains, with applications in large-scale learning and personalized inference. In many settings, privacy concerns prohibit obtaining domain labels for the training data samples, and instead only have an aggregated collection of training points. Existing approaches that utilize domain labels to create domain-invariant feature representations are inapplicable in this setting, requiring alternative approaches to learn generalizable classifiers. In this paper, we propose a domain-adaptive approach to this problem, which operates in two steps: (a) we cluster training data within a carefully chosen feature space to create pseudo-domains, and (b) using these pseudo-domains we learn a domain-adaptive classifier that makes predictions using information about both the input and the pseudo-domain it belongs to. Our approach achieves state-of-the-art performance on a variety of domain generalization benchmarks without using domain labels whatsoever. Furthermore, we provide novel theoretical guarantees on domain generalization using cluster information. Our approach is amenable to ensemble-based methods and provides substantial gains even on large-scale benchmark datasets. The code can be found at: //github.com/xavierohan/AdaClust_DomainBed

Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation accuracy. To tackle this question empirically, we have assembled a novel $\textbf{Geometric Pose Affordance}$ dataset, consisting of multi-view imagery of people interacting with a variety of rich 3D environments. We utilized a commercial motion capture system to collect gold-standard estimates of pose and construct accurate geometric 3D CAD models of the scene itself. To inject prior knowledge of scene constraints into existing frameworks for pose estimation from images, we introduce a novel, view-based representation of scene geometry, a $\textbf{multi-layer depth map}$, which employs multi-hit ray tracing to concisely encode multiple surface entry and exit points along each camera view ray direction. We propose two different mechanisms for integrating multi-layer depth information pose estimation: input as encoded ray features used in lifting 2D pose to full 3D, and secondly as a differentiable loss that encourages learned models to favor geometrically consistent pose estimates. We show experimentally that these techniques can improve the accuracy of 3D pose estimates, particularly in the presence of occlusion and complex scene geometry.

Visual odometry aims to track the incremental motion of an object using the information captured by visual sensors. In this work, we study the point cloud odometry problem, where only the point cloud scans obtained by the LiDAR (Light Detection And Ranging) are used to estimate object's motion trajectory. A lightweight point cloud odometry solution is proposed and named the green point cloud odometry (GPCO) method. GPCO is an unsupervised learning method that predicts object motion by matching features of consecutive point cloud scans. It consists of three steps. First, a geometry-aware point sampling scheme is used to select discriminant points from the large point cloud. Second, the view is partitioned into four regions surrounding the object, and the PointHop++ method is used to extract point features. Third, point correspondences are established to estimate object motion between two consecutive scans. Experiments on the KITTI dataset are conducted to demonstrate the effectiveness of the GPCO method. It is observed that GPCO outperforms benchmarking deep learning methods in accuracy while it has a significantly smaller model size and less training time.

When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural networks, the smoothness assumption of manifolds is violated at singular points which exhibit non-smooth neighborhoods in the parameter space. These singular models have been analyzed in the context of learning dynamics, where singularities can act as attractors on the learning trajectory and, therefore, negatively influence the convergence speed of models. We propose a general approach to circumvent the problem arising from singularities by using stratifolds, a concept from algebraic topology, to formally model singular parameter spaces. We use the property that specific stratifolds are equipped with a resolution method to construct a smooth manifold approximation of the singular space. We empirically show that using (natural) gradient descent on the smooth manifold approximation instead of the singular space allows us to avoid the attractor behavior and therefore improve the convergence speed in learning.

We present a new approach to instill 4D dynamic object priors into learned 3D representations by unsupervised pre-training. We observe that dynamic movement of an object through an environment provides important cues about its objectness, and thus propose to imbue learned 3D representations with such dynamic understanding, that can then be effectively transferred to improved performance in downstream 3D semantic scene understanding tasks. We propose a new data augmentation scheme leveraging synthetic 3D shapes moving in static 3D environments, and employ contrastive learning under 3D-4D constraints that encode 4D invariances into the learned 3D representations. Experiments demonstrate that our unsupervised representation learning results in improvement in downstream 3D semantic segmentation, object detection, and instance segmentation tasks, and moreover, notably improves performance in data-scarce scenarios.

Point cloud is point sets defined in 3D metric space. Point cloud has become one of the most significant data format for 3D representation. Its gaining increased popularity as a result of increased availability of acquisition devices, such as LiDAR, as well as increased application in areas such as robotics, autonomous driving, augmented and virtual reality. Deep learning is now the most powerful tool for data processing in computer vision, becoming the most preferred technique for tasks such as classification, segmentation, and detection. While deep learning techniques are mainly applied to data with a structured grid, point cloud, on the other hand, is unstructured. The unstructuredness of point clouds makes use of deep learning for its processing directly very challenging. Earlier approaches overcome this challenge by preprocessing the point cloud into a structured grid format at the cost of increased computational cost or lost of depth information. Recently, however, many state-of-the-arts deep learning techniques that directly operate on point cloud are being developed. This paper contains a survey of the recent state-of-the-art deep learning techniques that mainly focused on point cloud data. We first briefly discussed the major challenges faced when using deep learning directly on point cloud, we also briefly discussed earlier approaches which overcome the challenges by preprocessing the point cloud into a structured grid. We then give the review of the various state-of-the-art deep learning approaches that directly process point cloud in its unstructured form. We introduced the popular 3D point cloud benchmark datasets. And we also further discussed the application of deep learning in popular 3D vision tasks including classification, segmentation and detection.

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used to solve various 2D vision problems. However, deep learning on point clouds is still in its infancy due to the unique challenges faced by the processing of point clouds with deep neural networks. Recently, deep learning on point clouds has become even thriving, with numerous methods being proposed to address different problems in this area. To stimulate future research, this paper presents a comprehensive review of recent progress in deep learning methods for point clouds. It covers three major tasks, including 3D shape classification, 3D object detection and tracking, and 3D point cloud segmentation. It also presents comparative results on several publicly available datasets, together with insightful observations and inspiring future research directions.

The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a small-scale SLAM; the joining of submaps mainly involves solving linear least squares and performing nonlinear coordinate transformations. Through approximating the local submap information as the state estimate and its corresponding information matrix, judiciously selecting the submap coordinate frames, and approximating the joining of a large number of submaps by joining only two maps at a time, either sequentially or in a more efficient Divide and Conquer manner, the nonlinear optimization process involved in most of the existing submap joining approaches is avoided. Thus the proposed submap joining algorithm does not require initial guess or iterations since linear least squares problems have closed-form solutions. The proposed Linear SLAM technique is applicable to feature-based SLAM, pose graph SLAM and D-SLAM, in both two and three dimensions, and does not require any assumption on the character of the covariance matrices. Simulations and experiments are performed to evaluate the proposed Linear SLAM algorithm. Results using publicly available datasets in 2D and 3D show that Linear SLAM produces results that are very close to the best solutions that can be obtained using full nonlinear optimization algorithm started from an accurate initial guess. The C/C++ and MATLAB source codes of Linear SLAM are available on OpenSLAM.

We present PPF-FoldNet for unsupervised learning of 3D local descriptors on pure point cloud geometry. Based on the folding-based auto-encoding of well known point pair features, PPF-FoldNet offers many desirable properties: it necessitates neither supervision, nor a sensitive local reference frame, benefits from point-set sparsity, is end-to-end, fast, and can extract powerful rotation invariant descriptors. Thanks to a novel feature visualization, its evolution can be monitored to provide interpretable insights. Our extensive experiments demonstrate that despite having six degree-of-freedom invariance and lack of training labels, our network achieves state of the art results in standard benchmark datasets and outperforms its competitors when rotations and varying point densities are present. PPF-FoldNet achieves $9\%$ higher recall on standard benchmarks, $23\%$ higher recall when rotations are introduced into the same datasets and finally, a margin of $>35\%$ is attained when point density is significantly decreased.