We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. Additionally, as planar configurations form a submanifold in shape space, our representation allows for effective estimation of quasi-isometric surfaces flattenings. We evaluate the performance of our model w.r.t. shape-based classification of hippocampus and femur malformations due to Alzheimer's disease and osteoarthritis, respectively. In particular, we outperform state-of-the-art classifiers based on geometric deep learning as well as statistical shape modeling especially in presence of sparse training data. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing biological shape variability, we carry out an analysis of specificity and generalization ability.
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Safe autonomous driving technology heavily depends on accurate 3D object detection since it produces input to safety critical downstream tasks such as prediction and navigation. Recent advances in this field is made by developing the refinement stage for voxel-based region proposal networks to better strike the balance between accuracy and efficiency. A popular approach among state-of-the-art frameworks is to divide proposals, or Region of Interest (ROI), into grids and extract feature for each grid location before synthesizing them to ROI feature. While achieving impressive performances, such an approach involves a number of hand crafted components (e.g. grid sampling, set abstraction) which requires expert knowledge to be tuned correctly. This paper takes a more data-driven approach to ROI feature extraction using the attention mechanism. Specifically, points inside a ROI are positionally encoded to incorporate ROI 's geometry. The resulted position encoding and their features are transformed into ROI feature via vector attention. Unlike the original multi-head attention, vector attention assign different weights to different channels within a point feature, thus being able to capture a more sophisticated relation between pooled points and ROI. Experiments on KITTI \textit{validation} set show that our method achieves competitive performance of 84.84 AP for class Car at Moderate difficulty while having the least parameters compared to closely related methods and attaining a quasi-real time inference speed at 15 FPS on NVIDIA V100 GPU. The code will be released.
Benefiting from the contiguous representation ability, deep implicit functions can extract the iso-surface of a shape at arbitrary resolution. However, utilizing the neural network with a large number of parameters as the implicit function prevents the generation speed of high-resolution topology because it needs to forward a large number of query points into the network. In this work, we propose TaylorImNet inspired by the Taylor series for implicit 3D shape representation. TaylorImNet exploits a set of discrete expansion points and corresponding Taylor series to model a contiguous implicit shape field. After the expansion points and corresponding coefficients are obtained, our model only needs to calculate the Taylor series to evaluate each point and the number of expansion points is independent of the generating resolution. Based on this representation, our TaylorImNet can achieve a significantly faster generation speed than other baselines. We evaluate our approach on reconstruction tasks from various types of input, and the experimental results demonstrate that our approach can get slightly better performance than existing state-of-the-art baselines while improving the inference speed with a large margin.
We consider stochastic differential equations (SDEs) driven by small L\'evy noise with some unknown parameters, and propose a new type of least squares estimators based on discrete samples from the SDEs. To approximate the increments of a process from the SDEs, we shall use not the usual Euler method, but the Adams method, that is, a well-known numerical approximation of the solution to the ordinary differential equation appearing in the limit of the SDE. We show the consistency of the proposed estimators as well as the asymptotic distribution in a suitable observation scheme. We also show that our estimators can be better than the usual LSE based on the Euler method in the finite sample performance.
Simulation modeling of robots, objects, and environments is the backbone for all model-based control and learning. It is leveraged broadly across dynamic programming and model-predictive control, as well as data generation for imitation, transfer, and reinforcement learning. In addition to fidelity, key features of models in these control and learning contexts are speed, stability, and native differentiability. However, many popular simulation platforms for robotics today lack at least one of the features above. More recently, position-based dynamics (PBD) has become a very popular simulation tool for modeling complex scenes of rigid and non-rigid object interactions, due to its speed and stability, and is starting to gain significant interest in robotics for its potential use in model-based control and learning. Thus, in this paper, we present a mathematical formulation for coupling position-based dynamics (PBD) simulation and optimal robot design, model-based motion control and system identification. Our framework breaks down PBD definitions and derivations for various types of joint-based articulated rigid bodies. We present a back-propagation method with automatic differentiation, which can integrate both positional and angular geometric constraints. Our framework can critically provide the native gradient information and perform gradient-based optimization tasks. We also propose articulated joint model representations and simulation workflow for our differentiable framework. We demonstrate the capability of the framework in efficient optimal robot design, accurate trajectory torque estimation and supporting spring stiffness estimation, where we achieve minor errors. We also implement impedance control in real robots to demonstrate the potential of our differentiable framework in human-in-the-loop applications.
Radiomics and deep learning have shown high popularity in automatic glioma grading. Radiomics can extract hand-crafted features that quantitatively describe the expert knowledge of glioma grades, and deep learning is powerful in extracting a large number of high-throughput features that facilitate the final classification. However, the performance of existing methods can still be improved as their complementary strengths have not been sufficiently investigated and integrated. Furthermore, lesion maps are usually needed for the final prediction at the testing phase, which is very troublesome. In this paper, we propose an expert knowledge-guided geometric representation learning (ENROL) framework . Geometric manifolds of hand-crafted features and learned features are constructed to mine the implicit relationship between deep learning and radiomics, and therefore to dig mutual consent and essential representation for the glioma grades. With a specially designed manifold discrepancy measurement, the grading model can exploit the input image data and expert knowledge more effectively in the training phase and get rid of the requirement of lesion segmentation maps at the testing phase. The proposed framework is flexible regarding deep learning architectures to be utilized. Three different architectures have been evaluated and five models have been compared, which show that our framework can always generate promising results.
We introduce HuMoR: a 3D Human Motion Model for Robust Estimation of temporal pose and shape. Though substantial progress has been made in estimating 3D human motion and shape from dynamic observations, recovering plausible pose sequences in the presence of noise and occlusions remains a challenge. For this purpose, we propose an expressive generative model in the form of a conditional variational autoencoder, which learns a distribution of the change in pose at each step of a motion sequence. Furthermore, we introduce a flexible optimization-based approach that leverages HuMoR as a motion prior to robustly estimate plausible pose and shape from ambiguous observations. Through extensive evaluations, we demonstrate that our model generalizes to diverse motions and body shapes after training on a large motion capture dataset, and enables motion reconstruction from multiple input modalities including 3D keypoints and RGB(-D) videos.
Self-supervised learning has been widely used to obtain transferrable representations from unlabeled images. Especially, recent contrastive learning methods have shown impressive performances on downstream image classification tasks. While these contrastive methods mainly focus on generating invariant global representations at the image-level under semantic-preserving transformations, they are prone to overlook spatial consistency of local representations and therefore have a limitation in pretraining for localization tasks such as object detection and instance segmentation. Moreover, aggressively cropped views used in existing contrastive methods can minimize representation distances between the semantically different regions of a single image. In this paper, we propose a spatially consistent representation learning algorithm (SCRL) for multi-object and location-specific tasks. In particular, we devise a novel self-supervised objective that tries to produce coherent spatial representations of a randomly cropped local region according to geometric translations and zooming operations. On various downstream localization tasks with benchmark datasets, the proposed SCRL shows significant performance improvements over the image-level supervised pretraining as well as the state-of-the-art self-supervised learning methods.
Knowledge graph (KG) completion aims to fill the missing facts in a KG, where a fact is represented as a triple in the form of $(subject, relation, object)$. Current KG completion models compel two-thirds of a triple provided (e.g., $subject$ and $relation$) to predict the remaining one. In this paper, we propose a new model, which uses a KG-specific multi-layer recurrent neural network (RNN) to model triples in a KG as sequences. It outperformed several state-of-the-art KG completion models on the conventional entity prediction task for many evaluation metrics, based on two benchmark datasets and a more difficult dataset. Furthermore, our model is enabled by the sequential characteristic and thus capable of predicting the whole triples only given one entity. Our experiments demonstrated that our model achieved promising performance on this new triple prediction task.
Neural waveform models such as the WaveNet are used in many recent text-to-speech systems, but the original WaveNet is quite slow in waveform generation because of its autoregressive (AR) structure. Although faster non-AR models were recently reported, they may be prohibitively complicated due to the use of a distilling training method and the blend of other disparate training criteria. This study proposes a non-AR neural source-filter waveform model that can be directly trained using spectrum-based training criteria and the stochastic gradient descent method. Given the input acoustic features, the proposed model first uses a source module to generate a sine-based excitation signal and then uses a filter module to transform the excitation signal into the output speech waveform. Our experiments demonstrated that the proposed model generated waveforms at least 100 times faster than the AR WaveNet and the quality of its synthetic speech is close to that of speech generated by the AR WaveNet. Ablation test results showed that both the sine-wave excitation signal and the spectrum-based training criteria were essential to the performance of the proposed model.
Because of continuous advances in mathematical programing, Mix Integer Optimization has become a competitive vis-a-vis popular regularization method for selecting features in regression problems. The approach exhibits unquestionable foundational appeal and versatility, but also poses important challenges. We tackle these challenges, reducing computational burden when tuning the sparsity bound (a parameter which is critical for effectiveness) and improving performance in the presence of feature collinearity and of signals that vary in nature and strength. Importantly, we render the approach efficient and effective in applications of realistic size and complexity - without resorting to relaxations or heuristics in the optimization, or abandoning rigorous cross-validation tuning. Computational viability and improved performance in subtler scenarios is achieved with a multi-pronged blueprint, leveraging characteristics of the Mixed Integer Programming framework and by means of whitening, a data pre-processing step.
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