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We propose a novel method for joint estimation of shape and pose of rigid objects from their sequentially observed RGB-D images. In sharp contrast to past approaches that rely on complex non-linear optimization, we propose to formulate it as a neural optimization that learns to efficiently estimate the shape and pose. We introduce Deep Directional Distance Function (DeepDDF), a neural network that directly outputs the depth image of an object given the camera viewpoint and viewing direction, for efficient error computation in 2D image space. We formulate the joint estimation itself as a Transformer which we refer to as TransPoser. We fully leverage the tokenization and multi-head attention to sequentially process the growing set of observations and to efficiently update the shape and pose with a learned momentum, respectively. Experimental results on synthetic and real data show that DeepDDF achieves high accuracy as a category-level object shape representation and TransPoser achieves state-of-the-art accuracy efficiently for joint shape and pose estimation.

Generalization is the ability of quantum machine learning models to make accurate predictions on new data by learning from training data. Here, we introduce the data quantum Fisher information metric (DQFIM) to determine when a model can generalize. For variational learning of unitaries, the DQFIM quantifies the amount of circuit parameters and training data needed to successfully train and generalize. We apply the DQFIM to explain when a constant number of training states and polynomial number of parameters are sufficient for generalization. Further, we can improve generalization by removing symmetries from training data. Finally, we show that out-of-distribution generalization, where training and testing data are drawn from different data distributions, can be better than using the same distribution. Our work opens up new approaches to improve generalization in quantum machine learning.

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary differential equations (NODEs). Solving systems with fine temporal and spatial grid scales is an ongoing computational challenge, and closure models are generally difficult to tune. Machine learning approaches have increased the accuracy and efficiency of computational fluid dynamics solvers. In this approach neural networks are used to learn the coarse- to fine-grid map, which can be viewed as subgrid-scale parameterization. We propose a strategy that uses the NODE and partial knowledge to learn the source dynamics at a continuous level. Our method inherits the advantages of NODEs and can be used to parameterize subgrid scales, approximate coupling operators, and improve the efficiency of low-order solvers. Numerical results with the two-scale Lorenz 96 ODE, the convection-diffusion PDE, and the viscous Burgers' PDE are used to illustrate this approach.

When factorized approximations are used for variational inference (VI), they tend to underestimate the uncertainty -- as measured in various ways -- of the distributions they are meant to approximate. We consider two popular ways to measure the uncertainty deficit of VI: (i) the degree to which it underestimates the componentwise variance, and (ii) the degree to which it underestimates the entropy. To better understand these effects, and the relationship between them, we examine an informative setting where they can be explicitly (and elegantly) analyzed: the approximation of a Gaussian,~$p$, with a dense covariance matrix, by a Gaussian,~$q$, with a diagonal covariance matrix. We prove that $q$ always underestimates both the componentwise variance and the entropy of $p$, \textit{though not necessarily to the same degree}. Moreover we demonstrate that the entropy of $q$ is determined by the trade-off of two competing forces: it is decreased by the shrinkage of its componentwise variances (our first measure of uncertainty) but it is increased by the factorized approximation which delinks the nodes in the graphical model of $p$. We study various manifestations of this trade-off, notably one where, as the dimension of the problem grows, the per-component entropy gap between $p$ and $q$ becomes vanishingly small even though $q$ underestimates every componentwise variance by a constant multiplicative factor. We also use the shrinkage-delinkage trade-off to bound the entropy gap in terms of the problem dimension and the condition number of the correlation matrix of $p$. Finally we present empirical results on both Gaussian and non-Gaussian targets, the former to validate our analysis and the latter to explore its limitations.

Locating 3D objects from a single RGB image via Perspective-n-Point (PnP) is a long-standing problem in computer vision. Driven by end-to-end deep learning, recent studies suggest interpreting PnP as a differentiable layer, allowing for partial learning of 2D-3D point correspondences by backpropagating the gradients of pose loss. Yet, learning the entire correspondences from scratch is highly challenging, particularly for ambiguous pose solutions, where the globally optimal pose is theoretically non-differentiable w.r.t. the points. In this paper, we propose the EPro-PnP, a probabilistic PnP layer for general end-to-end pose estimation, which outputs a distribution of pose with differentiable probability density on the SE(3) manifold. The 2D-3D coordinates and corresponding weights are treated as intermediate variables learned by minimizing the KL divergence between the predicted and target pose distribution. The underlying principle generalizes previous approaches, and resembles the attention mechanism. EPro-PnP can enhance existing correspondence networks, closing the gap between PnP-based method and the task-specific leaders on the LineMOD 6DoF pose estimation benchmark. Furthermore, EPro-PnP helps to explore new possibilities of network design, as we demonstrate a novel deformable correspondence network with the state-of-the-art pose accuracy on the nuScenes 3D object detection benchmark. Our code is available at //github.com/tjiiv-cprg/EPro-PnP-v2.

Motivated by applications in personalized medicine and individualized policy making, there is a growing interest in techniques for quantifying treatment effect heterogeneity in terms of the conditional average treatment effect (CATE). Some of the most prominent methods for CATE estimation developed in recent years are T-Learner, DR-Learner and R-Learner. The latter two were designed to improve on the former by being Neyman-orthogonal. However, the relations between them remain unclear, and likewise does the literature remain vague on whether these learners converge to a useful quantity or (functional) estimand when the underlying optimization procedure is restricted to a class of functions that does not include the CATE. In this article, we provide insight into these questions by discussing DR-learner and R-learner as special cases of a general class of Neyman-orthogonal learners for the CATE, for which we moreover derive oracle bounds. Our results shed light on how one may construct Neyman-orthogonal learners with desirable properties, on when DR-learner may be preferred over R-learner (and vice versa), and on novel learners that may sometimes be preferable to either of these. Theoretical findings are confirmed using results from simulation studies on synthetic data, as well as an application in critical care medicine.

Efficient and accurate estimation of multivariate empirical probability distributions is fundamental to the calculation of information-theoretic measures such as mutual information and transfer entropy. Common techniques include variations on histogram estimation which, whilst computationally efficient, are often unable to precisely capture the probability density of samples with high correlation, kurtosis or fine substructure, especially when sample sizes are small. Adaptive partitions, which adjust heuristically to the sample, can reduce the bias imparted from the geometry of the histogram itself, but these have commonly focused on the location, scale and granularity of the partition, the effects of which are limited for highly correlated distributions. In this paper, I reformulate the differential entropy estimator for the special case of an equiprobable histogram, using a k-d tree to partition the sample space into bins of equal probability mass. By doing so, I expose an implicit rotational orientation parameter, which is conjectured to be suboptimally specified in the typical marginal alignment. I propose that the optimal orientation minimises the variance of the bin volumes, and demonstrate that improved entropy estimates can be obtained by rotationally aligning the partition to the sample distribution accordingly. Such optimal partitions are observed to be more accurate than existing techniques in estimating entropies of correlated bivariate Gaussian distributions with known theoretical values, across varying sample sizes (99% CI).

Most recent 6D object pose estimation methods first use object detection to obtain 2D bounding boxes before actually regressing the pose. However, the general object detection methods they use are ill-suited to handle cluttered scenes, thus producing poor initialization to the subsequent pose network. To address this, we propose a rigidity-aware detection method exploiting the fact that, in 6D pose estimation, the target objects are rigid. This lets us introduce an approach to sampling positive object regions from the entire visible object area during training, instead of naively drawing samples from the bounding box center where the object might be occluded. As such, every visible object part can contribute to the final bounding box prediction, yielding better detection robustness. Key to the success of our approach is a visibility map, which we propose to build using a minimum barrier distance between every pixel in the bounding box and the box boundary. Our results on seven challenging 6D pose estimation datasets evidence that our method outperforms general detection frameworks by a large margin. Furthermore, combined with a pose regression network, we obtain state-of-the-art pose estimation results on the challenging BOP benchmark.

This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.

Object detection is an important and challenging problem in computer vision. Although the past decade has witnessed major advances in object detection in natural scenes, such successes have been slow to aerial imagery, not only because of the huge variation in the scale, orientation and shape of the object instances on the earth's surface, but also due to the scarcity of well-annotated datasets of objects in aerial scenes. To advance object detection research in Earth Vision, also known as Earth Observation and Remote Sensing, we introduce a large-scale Dataset for Object deTection in Aerial images (DOTA). To this end, we collect $2806$ aerial images from different sensors and platforms. Each image is of the size about 4000-by-4000 pixels and contains objects exhibiting a wide variety of scales, orientations, and shapes. These DOTA images are then annotated by experts in aerial image interpretation using $15$ common object categories. The fully annotated DOTA images contains $188,282$ instances, each of which is labeled by an arbitrary (8 d.o.f.) quadrilateral To build a baseline for object detection in Earth Vision, we evaluate state-of-the-art object detection algorithms on DOTA. Experiments demonstrate that DOTA well represents real Earth Vision applications and are quite challenging.