arXiv subjects
Publications and source records attributed to Yiming Zhao.
The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered disk. As an application, this ``uniqueness'' result is used to prove the existence of smooth small solutions to the Gaussian-Minkowski problem via a degree-theoretic approach.
With the rapid development of classical and quantum machine learning, a large number of machine learning frameworks have been proposed. However, existing machine learning frameworks usually only focus on classical or quantum, rather than both. Therefore, based on VQNet 1.0, we further propose VQNet 2.0, a new generation of unified classical and quantum machine learning framework that supports hybrid optimization. The core library of the framework is implemented in C++, and the user level is implemented in Python, and it supports deployment on quantum and classical hardware. In this article, we analyze the development trend of the new generation machine learning framework and introduce the design principles of VQNet 2.0 in detail: unity, practicality, efficiency, and compatibility, as well as full particulars of implementation. We illustrate the functions of VQNet 2.0 through several basic applications, including classical convolutional neural networks, quantum autoencoders, hybrid classical-quantum networks, etc. After that, through extensive experiments, we demonstrate that the operation speed of VQNet 2.0 is higher than the comparison method. Finally, through extensive experiments, we demonstrate that VQNet 2.0 can deploy on different hardware platforms, the overall calculation speed is faster than the comparison method. It also can be mixed and optimized with quantum circuits composed of multiple quantum computing libraries.
Point cloud semantic segmentation has attracted attentions due to its robustness to light condition. This makes it an ideal semantic solution for autonomous driving. However, considering the large computation burden and bandwidth demanding of neural networks, putting all the computing into vehicle Electronic Control Unit (ECU) is not efficient or practical. In this paper, we proposed a light weighted point cloud semantic segmentation network based on range view. Due to its simple pre-processing and standard convolution, it is efficient when running on deep learning accelerator like DPU. Furthermore, a near sensor computing system is built for autonomous vehicles. In this system, a FPGA-based deep learning accelerator core (DPU) is placed next to the LiDAR sensor, to perform point cloud pre-processing and segmentation neural network. By leaving only the post-processing step to ECU, this solution heavily alleviate the computation burden of ECU and consequently shortens the decision making and vehicles reaction latency. Our semantic segmentation network achieved 10 frame per second (fps) on Xilinx DPU with computation efficiency 42.5 GOP/W.
Given a set $P$ of $n$ points that are moving in the plane, we consider the problem of computing a spanning tree for these moving points that does not change its combinatorial structure during the point movement. The objective is to minimize the bottleneck weight of the spanning tree (i.e., the largest Euclidean length of all edges) during the whole movement. The problem was solved in $O(n^2)$ time previously [Akitaya, Biniaz, Bose, De Carufel, Maheshwari, Silveira, and Smid, WADS 2021]. In this paper, we present a new algorithm of $O(n^{4/3} \log^3 n)$ time.
Multi-scenario learning (MSL) enables a service provider to cater for users' fine-grained demands by separating services for different user sectors, e.g., by user's geographical region. Under each scenario there is a need to optimize multiple task-specific targets e.g., click through rate and conversion rate, known as multi-task learning (MTL). Recent solutions for MSL and MTL are mostly based on the multi-gate mixture-of-experts (MMoE) architecture. MMoE structure is typically static and its design requires domain-specific knowledge, making it less effective in handling both MSL and MTL. In this paper, we propose a novel Automatic Expert Selection framework for Multi-scenario and Multi-task search, named AESM^{2}. AESM^{2} integrates both MSL and MTL into a unified framework with an automatic structure learning. Specifically, AESM^{2} stacks multi-task layers over multi-scenario layers. This hierarchical design enables us to flexibly establish intrinsic connections between different scenarios, and at the same time also supports high-level feature extraction for different tasks. At each multi-scenario/multi-task layer, a novel expert selection algorithm is proposed to automatically identify scenario-/task-specific and shared experts for each input. Experiments over two real-world large-scale datasets demonstrate the effectiveness of AESM^{2} over a battery of strong baselines. Online A/B test also shows substantial performance gain on multiple metrics. Currently, AESM^{2} has been deployed online for serving major traffic.
Light Detection And Ranging (LiDAR) has been widely used in autonomous vehicles for perception and localization. However, the cost of a high-resolution LiDAR is still prohibitively expensive, while its low-resolution counterpart is much more affordable. Therefore, using low-resolution LiDAR for autonomous driving is an economically viable solution, but the point cloud sparsity makes it extremely challenging. In this paper, we propose a two-stage neural network framework that enables 3D object detection using a low-resolution LiDAR. Taking input from a low-resolution LiDAR point cloud and a monocular camera image, a depth completion network is employed to produce dense point cloud that is subsequently processed by a voxel-based network for 3D object detection. Evaluated with KITTI dataset for 3D object detection in Bird-Eye View (BEV), the experimental result shows that the proposed approach performs significantly better than directly applying the 16-line LiDAR point cloud for object detection. For both easy and moderate cases, our 3D vehicle detection results are close to those using 64-line high-resolution LiDARs.
Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at most r (the weight of the edge is 1 in the unweighted case and is the distance between p and q in the weighted case). Given a value λ>0 and two points s and t of P, we consider the following reverse shortest path problem: computing the smallest r such that the shortest path length between s and t in G_r(P) is at most λ. In this paper, we present an algorithm of O(\lfloor λ\rfloor \cdot n \log n) time and another algorithm of O(n^{5/4} \log^{7/4} n) time for the unweighted case, as well as an O(n^{5/4} \log^{5/2} n) time algorithm for the weighted case. We also consider the L_1 version of the problem where the distance of two points is measured by the L_1 metric; we solve the problem in O(n \log^3 n) time for both the unweighted and weighted cases.
Clustering objects from the LiDAR point cloud is an important research problem with many applications such as autonomous driving. To meet the real-time requirement, existing research proposed to apply the connected-component-labeling (CCL) technique on LiDAR spherical range image with a heuristic condition to check if two neighbor points are connected. However, LiDAR range image is different from a binary image which has a deterministic condition to tell if two pixels belong to the same component. The heuristic condition used on the LiDAR range image only works empirically, which suggests the LiDAR clustering algorithm should be robust to potential failures of the empirical heuristic condition. To overcome this challenge, this paper proposes a divide-and-merge LiDAR clustering algorithm. This algorithm firstly conducts clustering in each evenly divided local region, then merges the local clustered small components by voting on edge point pairs. Assuming there are $N$ LiDAR points of objects in total with $m$ divided local regions, the time complexity of the proposed algorithm is $O(N)+O(m^2)$. A smaller $m$ means the voting will involve more neighbor points, but the time complexity will become larger. So the $m$ controls the trade-off between the time complexity and the clustering accuracy. A proper $m$ helps the proposed algorithm work in real-time as well as maintain good performance. We evaluate the divide-and-merge clustering algorithm on the SemanticKITTI panoptic segmentation benchmark by cascading it with a state-of-the-art semantic segmentation model. The final performance evaluated through the leaderboard achieves the best among all published methods. The proposed algorithm is implemented with C++ and wrapped as a python function. It can be easily used with the modern deep learning framework in python.
Projecting the point cloud on the 2D spherical range image transforms the LiDAR semantic segmentation to a 2D segmentation task on the range image. However, the LiDAR range image is still naturally different from the regular 2D RGB image; for example, each position on the range image encodes the unique geometry information. In this paper, we propose a new projection-based LiDAR semantic segmentation pipeline that consists of a novel network structure and an efficient post-processing step. In our network structure, we design a FID (fully interpolation decoding) module that directly upsamples the multi-resolution feature maps using bilinear interpolation. Inspired by the 3D distance interpolation used in PointNet++, we argue this FID module is a 2D version distance interpolation on $(θ, ϕ)$ space. As a parameter-free decoding module, the FID largely reduces the model complexity by maintaining good performance. Besides the network structure, we empirically find that our model predictions have clear boundaries between different semantic classes. This makes us rethink whether the widely used K-nearest-neighbor post-processing is still necessary for our pipeline. Then, we realize the many-to-one mapping causes the blurring effect that some points are mapped into the same pixel and share the same label. Therefore, we propose to process those occluded points by assigning the nearest predicted label to them. This NLA (nearest label assignment) post-processing step shows a better performance than KNN with faster inference speed in the ablation study. On the SemanticKITTI dataset, our pipeline achieves the best performance among all projection-based methods with $64 \times 2048$ resolution and all point-wise solutions. With a ResNet-34 as the backbone, both the training and testing of our model can be finished on a single RTX 2080 Ti with 11G memory. The code is released.
LiDAR panoptic segmentation is a newly proposed technical task for autonomous driving. In contrast to popular end-to-end deep learning solutions, we propose a hybrid method with an existing semantic segmentation network to extract semantic information and a traditional LiDAR point cloud cluster algorithm to split each instance object. We argue geometry-based traditional clustering algorithms are worth being considered by showing a state-of-the-art performance among all published end-to-end deep learning solutions on the panoptic segmentation leaderboard of the SemanticKITTI dataset. To our best knowledge, we are the first to attempt the point cloud panoptic segmentation with clustering algorithms. Therefore, instead of working on new models, we give a comprehensive technical survey in this paper by implementing four typical cluster methods and report their performances on the benchmark. Those four cluster methods are the most representative ones with real-time running speed. They are implemented with C++ in this paper and then wrapped as a python function for seamless integration with the existing deep learning frameworks. We release our code for peer researchers who might be interested in this problem.
Estimating homography to align image pairs captured by different sensors or image pairs with large appearance changes is an important and general challenge for many computer vision applications. In contrast to others, we propose a generic solution to pixel-wise align multimodal image pairs by extending the traditional Lucas-Kanade algorithm with networks. The key contribution in our method is how we construct feature maps, named as deep Lucas-Kanade feature map (DLKFM). The learned DLKFM can spontaneously recognize invariant features under various appearance-changing conditions. It also has two nice properties for the Lucas-Kanade algorithm: (1) The template feature map keeps brightness consistency with the input feature map, thus the color difference is very small while they are well-aligned. (2) The Lucas-Kanade objective function built on DLKFM has a smooth landscape around ground truth homography parameters, so the iterative solution of the Lucas-Kanade can easily converge to the ground truth. With those properties, directly updating the Lucas-Kanade algorithm on our feature maps will precisely align image pairs with large appearance changes. We share the datasets, code, and demo video online.
LiDAR depth completion is a task that predicts depth values for every pixel on the corresponding camera frame, although only sparse LiDAR points are available. Most of the existing state-of-the-art solutions are based on deep neural networks, which need a large amount of data and heavy computations for training the models. In this letter, a novel non-learning depth completion method is proposed by exploiting the local surface geometry that is enhanced by an outlier removal algorithm. The proposed surface geometry model is inspired by the observation that most pixels with unknown depth have a nearby LiDAR point. Therefore, it is assumed those pixels share the same surface with the nearest LiDAR point, and their respective depth can be estimated as the nearest LiDAR depth value plus a residual error. The residual error is calculated by using a derived equation with several physical parameters as input, including the known camera intrinsic parameters, estimated normal vector, and offset distance on the image plane. The proposed method is further enhanced by an outlier removal algorithm that is designed to remove incorrectly mapped LiDAR points from occluded regions. On KITTI dataset, the proposed solution achieves the best error performance among all existing non-learning methods and is comparable to the best self-supervised learning method and some supervised learning methods. Moreover, since outlier points from occluded regions is a commonly existing problem, the proposed outlier removal algorithm is a general preprocessing step that is applicable to many robotic systems with both camera and LiDAR sensors.
We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \log^3 n) time and O(n) space [Oh and Ahn, ISAAC 2016], or in O(n^2) time and O(n^2) space [Bilò, ISAAC 2018].
The Minkowski problem in Gaussian probability space is studied in this paper. In addition to providing an existence result on a Gaussian-volume-normalized version of this problem, the main goal of the current work is to provide uniqueness and existence results on the Gaussian Minkowski problem (with no normalization required).
Autonomous vehicles rely heavily on sensors such as camera and LiDAR, which provide real-time information about their surroundings for the tasks of perception, planning and control. Typically a LiDAR can only provide sparse point cloud owing to a limited number of scanning lines. By employing depth completion, a dense depth map can be generated by assigning each camera pixel a corresponding depth value. However, the existing depth completion convolutional neural networks are very complex that requires high-end GPUs for processing, and thus they are not applicable to real-time autonomous driving. In this paper, a light-weight network is proposed for the task of LiDAR point cloud depth completion. With an astonishing 96.2% reduction in the number of parameters, it still achieves comparable performance (9.3% better in MAE but 3.9% worse in RMSE) to the state-of-the-art network. For real-time embedded platforms, depthwise separable technique is applied to both convolution and deconvolution operations and the number of parameters decreases further by a factor of 7.3, with only a small percentage increase in RMSE and MAE performance. Moreover, a system-on-chip architecture for depth completion is developed on a PYNQ-based FPGA platform that achieves real-time processing for HDL-64E LiDAR at the speed 11.1 frame per second.
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of $P$. Previously, the "continuous" version of the problem where a center may be a point in the interior of an edge of the graph was studied and a linear-time algorithm was known. Our "discrete" version of the problem has not been studied before. We present a linear-time algorithm for the problem.
Convolutional neural networks (CNNs) have been widely deployed in the fields of computer vision and pattern recognition because of their high accuracy. However, large convolution operations are computing-intensive that often requires a powerful computing platform such as Graphics Processing Unit (GPU). This makes it difficult to apply CNNs to portable devices. The state-of-the-art CNNs, such as MobileNetV2 and Xception, adopt depthwise separable convolution to replace the standard convolution for embedded platforms. That significantly reduces operations and parameters with only limited loss in accuracy. This highly structured model is very suitable for Field-Programmable Gate Array (FPGA) implementation. In this paper, a scalable high performance depthwise separable convolution optimized CNN accelerator is proposed. The accelerator can be fit into an FPGA of different sizes, provided the balancing between hardware resources and processing speed. As an example, MobileNetV2 is implemented on Arria 10 SoC FPGA, and the results show this accelerator can classify each picture from ImageNet in 3.75ms, which is about 266.6 frames per second. This achieves 20x speedup if compared to CPU.
The $L_p$ Aleksandrov integral curvature and its corresponding characterization problem---the $L_p$ Aleksandrov problem---were recently introduced by Huang, Lutwak, Yang, and Zhang. The current work presents a solution to the $L_p$ Aleksandrov problem for origin-symmetric polytopes when $-1<p<0$.