Ray tracing is an essential operation for realistic image synthesis. The acceleration of ray tracing has been studied for a long period of time because algorithms such as light transport simulations require a large amount of ray tracing. One of the major approaches to accelerate the intersections is to use bounding volumes for early pruning for primitives in the volume. The axis-aligned bounding box is a popular bounding volume for ray tracing because of its simplicity and efficiency. However, the conservative bounding volume may produce extra empty space in addition to its content. Especially, primitives that are thin and diagonal to the axis give false-positive hits on the box volume due to the extra space. Although more complex bounding volumes such as oriented bounding boxes may reduce more false-positive hits, they are computationally expensive. In this paper, we propose a novel culling approach to reduce false-positive hits for the bounding box by embedding a binary voxel data structure to the volume. As a ray is represented as a conservative voxel volume as well in our approach, the ray--voxel intersection is cheaply done by bitwise AND operations. Our method is applicable to hierarchical data structures such as bounding volume hierarchy (BVH). It reduces false-positive hits due to the ray--box test and reduces the number of intersections during the traversal of BVH in ray tracing. We evaluate the reduction of intersections with several scenes and show the possibility of performance improvement despite the culling overhead. We also introduce a compression approach with a lookup table for our voxel data. We show that our compressed voxel data achieves significant false-positive reductions with a small amount of memory.
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Generalized Time Warping Invariant Dictionary Learning for Time Series Classification and Clustering
Dictionary learning is an effective tool for pattern recognition and classification of time series data. Among various dictionary learning techniques, the dynamic time warping (DTW) is commonly used for dealing with temporal delays, scaling, transformation, and many other kinds of temporal misalignments issues. However, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparseness coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparing with various benchmark methods.
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear setting, but we allow for a certain type of dissipative nonlinearity in the drift as well. In a first step, a linear subspace is found that contains the solution space of the underlying rough differential equation (RDE). This subspace is associated to covariances of linear Ito-stochastic differential equations which is shown exploiting a Gronwall lemma for matrix differential equations. Orthogonal projections onto the identified subspace lead to a first exact reduced order system. Secondly, a linear map of the RDE solution (quantity of interest) is analyzed in terms of redundant information meaning that state variables are found that do not contribute to the quantity of interest. Once more, a link to Ito-stochastic differential equations is used. Removing such unnecessary information from the RDE provides a further dimension reduction without causing an error. Finally, we discretize a linear parabolic rough partial differential equation in space. The resulting large-order RDE is subsequently tackled with the exact reduction techniques studied in this paper. We illustrate the enormous complexity reduction potential in the corresponding numerical experiments.
With the commercial application of automated vehicles (AVs), the sharing of roads between AVs and human-driven vehicles (HVs) becomes a common occurrence in the future. While research has focused on improving the safety and reliability of autonomous driving, it's also crucial to consider collaboration between AVs and HVs. Human-like interaction is a required capability for AVs, especially at common unsignalized intersections, as human drivers of HVs expect to maintain their driving habits for inter-vehicle interactions. This paper uses the social value orientation (SVO) in the decision-making of vehicles to describe the social interaction among multiple vehicles. Specifically, we define the quantitative calculation of the conflict-involved SVO at unsignalized intersections to enhance decision-making based on the reinforcement learning method. We use naturalistic driving scenarios with highly interactive motions for performance evaluation of the proposed method. Experimental results show that SVO is more effective in characterizing inter-vehicle interactions than conventional motion state parameters like velocity, and the proposed method can accurately reproduce naturalistic driving trajectories compared to behavior cloning.
Deep neural networks (DNNs) offer the highest performance in a wide range of applications in computer vision. These results rely on over-parameterized backbones, which are expensive to run. This computational burden can be dramatically reduced by quantizing (in either data-free (DFQ), post-training (PTQ) or quantization-aware training (QAT) scenarios) floating point values to ternary values (2 bits, with each weight taking value in {-1,0,1}). In this context, we observe that rounding to nearest minimizes the expected error given a uniform distribution and thus does not account for the skewness and kurtosis of the weight distribution, which strongly affects ternary quantization performance. This raises the following question: shall one minimize the highest or average quantization error? To answer this, we design two operators: TQuant and MQuant that correspond to these respective minimization tasks. We show experimentally that our approach allows to significantly improve the performance of ternary quantization through a variety of scenarios in DFQ, PTQ and QAT and give strong insights to pave the way for future research in deep neural network quantization.
Tensor network (TN) representation is a powerful technique for data analysis and machine learning. It practically involves a challenging TN structure search (TN-SS) problem, which aims to search for the optimal structure to achieve a compact representation. Existing TN-SS methods mainly adopt a bi-level optimization method that leads to excessive computational costs due to repeated structure evaluations. To address this issue, we propose an efficient integrated (single-level) method named SVD-inspired TN decomposition (SVDinsTN), eliminating the need for repeated tedious structure evaluation. By inserting a diagonal factor for each edge of the fully-connected TN, we calculate TN cores and diagonal factors simultaneously, with factor sparsity revealing the most compact TN structure. Experimental results on real-world data demonstrate that SVDinsTN achieves approximately $10\sim{}10^3$ times acceleration in runtime compared to the existing TN-SS methods while maintaining a comparable level of representation ability.
Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated alternatively. However, the former is difficult to reflect comprehensive relationships among data points, and the latter is time-consuming and is even infeasible for large-scale problems. In this work, we propose a restarted clustering framework with self-guiding and block diagonal representation. An advantage of the strategy is that some useful clustering information obtained from previous cycles could be preserved as much as possible. To the best of our knowledge, this is the first work that applies restarting strategy to spectral clustering. The key difference is that we reclassify the samples in each cycle of our method, while they are classified only once in existing methods. To further release the overhead, we introduce a block diagonal representation with Nystr\"{o}m approximation for constructing the similarity matrix. Theoretical results are established to show the rationality of inexact computations in spectral clustering. Comprehensive experiments are performed on some benchmark databases, which show the superiority of our proposed algorithms over many state-of-the-art algorithms for large-scale problems. Specifically, our framework has a potential boost for clustering algorithms and works well even using an initial guess chosen randomly.
Recently, 3D object detection has attracted significant attention and achieved continuous improvement in real road scenarios. The environmental information is collected from a single sensor or multi-sensor fusion to detect interested objects. However, most of the current 3D object detection approaches focus on developing advanced network architectures to improve the detection precision of the object rather than considering the dynamic driving scenes, where data collected from sensors equipped in the vehicle contain various perturbation features. As a result, existing work cannot still tackle the perturbation issue. In order to solve this problem, we propose a group equivariant bird's eye view network (GeqBevNet) based on the group equivariant theory, which introduces the concept of group equivariant into the BEV fusion object detection network. The group equivariant network is embedded into the fused BEV feature map to facilitate the BEV-level rotational equivariant feature extraction, thus leading to lower average orientation error. In order to demonstrate the effectiveness of the GeqBevNet, the network is verified on the nuScenes validation dataset in which mAOE can be decreased to 0.325. Experimental results demonstrate that GeqBevNet can extract more rotational equivariant features in the 3D object detection of the actual road scene and improve the performance of object orientation prediction.
In this paper, we present an accurate and scalable approach to the face clustering task. We aim at grouping a set of faces by their potential identities. We formulate this task as a link prediction problem: a link exists between two faces if they are of the same identity. The key idea is that we find the local context in the feature space around an instance (face) contains rich information about the linkage relationship between this instance and its neighbors. By constructing sub-graphs around each instance as input data, which depict the local context, we utilize the graph convolution network (GCN) to perform reasoning and infer the likelihood of linkage between pairs in the sub-graphs. Experiments show that our method is more robust to the complex distribution of faces than conventional methods, yielding favorably comparable results to state-of-the-art methods on standard face clustering benchmarks, and is scalable to large datasets. Furthermore, we show that the proposed method does not need the number of clusters as prior, is aware of noises and outliers, and can be extended to a multi-view version for more accurate clustering accuracy.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
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.
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