Qijian Zhang

Yifan Zhang, Qijian Zhang, Zhiyu Zhu et al.

The inherent ambiguity in ground-truth annotations of 3D bounding boxes, caused by occlusions, signal missing, or manual annotation errors, can confuse deep 3D object detectors during training, thus deteriorating detection accuracy. However, existing methods overlook such issues to some extent and treat the labels as deterministic. In this paper, we formulate the label uncertainty problem as the diversity of potentially plausible bounding boxes of objects. Then, we propose GLENet, a generative framework adapted from conditional variational autoencoders, to model the one-to-many relationship between a typical 3D object and its potential ground-truth bounding boxes with latent variables. The label uncertainty generated by GLENet is a plug-and-play module and can be conveniently integrated into existing deep 3D detectors to build probabilistic detectors and supervise the learning of the localization uncertainty. Besides, we propose an uncertainty-aware quality estimator architecture in probabilistic detectors to guide the training of the IoU-branch with predicted localization uncertainty. We incorporate the proposed methods into various popular base 3D detectors and demonstrate significant and consistent performance gains on both KITTI and Waymo benchmark datasets. Especially, the proposed GLENet-VR outperforms all published LiDAR-based approaches by a large margin and achieves the top rank among single-modal methods on the challenging KITTI test set. The source code and pre-trained models are publicly available at \url{https://github.com/Eaphan/GLENet}.

Yuming Zhao, Junhui Hou, Qijian Zhang et al.

Geometric analysis fundamentally distinguishes between \textit{extrinsic} and \textit{intrinsic} perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely \textbf{PRISM}, for \textbf{P}re-training, which learns isometric embeddings by \textbf{R}ecovering the \textbf{I}ntrinsic \textbf{S}urface geodesic \textbf{M}etric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.

Qijian Zhang, Junhui Hou, Yue Qian et al.

Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology as a completely regular 2D point geometry image (PGI) structure, in which coordinates of spatial points are captured in colors of image pixels. \mr{Intuitively, Flattening-Net implicitly approximates a locally smooth 3D-to-2D surface flattening process while effectively preserving neighborhood consistency.} \mr{As a generic representation modality, PGI inherently encodes the intrinsic property of the underlying manifold structure and facilitates surface-style point feature aggregation.} To demonstrate its potential, we construct a unified learning framework directly operating on PGIs to achieve \mr{diverse types of high-level and low-level} downstream applications driven by specific task networks, including classification, segmentation, reconstruction, and upsampling. Extensive experiments demonstrate that our methods perform favorably against the current state-of-the-art competitors. We will make the code and data publicly available at https://github.com/keeganhk/Flattening-Net.

Yifan Zhang, Qijian Zhang, Junhui Hou et al.

To achieve reliable and precise scene understanding, autonomous vehicles typically incorporate multiple sensing modalities to capitalize on their complementary attributes. However, existing cross-modal 3D detectors do not fully utilize the image domain information to address the bottleneck issues of the LiDAR-based detectors. This paper presents a new cross-modal 3D object detector, namely UPIDet, which aims to unleash the potential of the image branch from two aspects. First, UPIDet introduces a new 2D auxiliary task called normalized local coordinate map estimation. This approach enables the learning of local spatial-aware features from the image modality to supplement sparse point clouds. Second, we discover that the representational capability of the point cloud backbone can be enhanced through the gradients backpropagated from the training objectives of the image branch, utilizing a succinct and effective point-to-pixel module. Extensive experiments and ablation studies validate the effectiveness of our method. Notably, we achieved the top rank in the highly competitive cyclist class of the KITTI benchmark at the time of submission. The source code is available at https://github.com/Eaphan/UPIDet.

Yiming Zeng, Yue Qian, Qijian Zhang et al.

This paper investigates the problem of temporally interpolating dynamic 3D point clouds with large non-rigid deformation. We formulate the problem as estimation of point-wise trajectories (i.e., smooth curves) and further reason that temporal irregularity and under-sampling are two major challenges. To tackle the challenges, we propose IDEA-Net, an end-to-end deep learning framework, which disentangles the problem under the assistance of the explicitly learned temporal consistency. Specifically, we propose a temporal consistency learning module to align two consecutive point cloud frames point-wisely, based on which we can employ linear interpolation to obtain coarse trajectories/in-between frames. To compensate the high-order nonlinear components of trajectories, we apply aligned feature embeddings that encode local geometry properties to regress point-wise increments, which are combined with the coarse estimations. We demonstrate the effectiveness of our method on various point cloud sequences and observe large improvement over state-of-the-art methods both quantitatively and visually. Our framework can bring benefits to 3D motion data acquisition. The source code is publicly available at https://github.com/ZENGYIMING-EAMON/IDEA-Net.git.

Qijian Zhang, Junhui Hou, Yue Qian

As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era, remarkable progress in processing such two data modalities has been achieved through respectively customizing compatible 3D and 2D network architectures. However, unlike multi-view image-based 2D visual modeling paradigms, which have shown leading performance in several common 3D shape recognition benchmarks, point cloud-based 3D geometric modeling paradigms are still highly limited by insufficient learning capacity, due to the difficulty of extracting discriminative features from irregular geometric signals. In this paper, we explore the possibility of boosting deep 3D point cloud encoders by transferring visual knowledge extracted from deep 2D image encoders under a standard teacher-student distillation workflow. Generally, we propose PointMCD, a unified multi-view cross-modal distillation architecture, including a pretrained deep image encoder as the teacher and a deep point encoder as the student. To perform heterogeneous feature alignment between 2D visual and 3D geometric domains, we further investigate visibility-aware feature projection (VAFP), by which point-wise embeddings are reasonably aggregated into view-specific geometric descriptors. By pair-wisely aligning multi-view visual and geometric descriptors, we can obtain more powerful deep point encoders without exhausting and complicated network modification. Experiments on 3D shape classification, part segmentation, and unsupervised learning strongly validate the effectiveness of our method. The code and data will be publicly available at https://github.com/keeganhk/PointMCD.

Yingzhi Tang, Yue Qian, Qijian Zhang et al.

We propose WarpingGAN, an effective and efficient 3D point cloud generation network. Unlike existing methods that generate point clouds by directly learning the mapping functions between latent codes and 3D shapes, Warping-GAN learns a unified local-warping function to warp multiple identical pre-defined priors (i.e., sets of points uniformly distributed on regular 3D grids) into 3D shapes driven by local structure-aware semantics. In addition, we also ingeniously utilize the principle of the discriminator and tailor a stitching loss to eliminate the gaps between different partitions of a generated shape corresponding to different priors for boosting quality. Owing to the novel generating mechanism, WarpingGAN, a single lightweight network after one-time training, is capable of efficiently generating uniformly distributed 3D point clouds with various resolutions. Extensive experimental results demonstrate the superiority of our WarpingGAN over state-of-the-art methods in terms of quantitative metrics, visual quality, and efficiency. The source code is publicly available at https://github.com/yztang4/WarpingGAN.git.

Lintai Wu, Qijian Zhang, Junhui Hou et al.

Point clouds captured by scanning devices are often incomplete due to occlusion. To overcome this limitation, point cloud completion methods have been developed to predict the complete shape of an object based on its partial input. These methods can be broadly classified as supervised or unsupervised. However, both categories require a large number of 3D complete point clouds, which may be difficult to capture. In this paper, we propose Cross-PCC, an unsupervised point cloud completion method without requiring any 3D complete point clouds. We only utilize 2D images of the complete objects, which are easier to capture than 3D complete and clean point clouds. Specifically, to take advantage of the complementary information from 2D images, we use a single-view RGB image to extract 2D features and design a fusion module to fuse the 2D and 3D features extracted from the partial point cloud. To guide the shape of predicted point clouds, we project the predicted points of the object to the 2D plane and use the foreground pixels of its silhouette maps to constrain the position of the projected points. To reduce the outliers of the predicted point clouds, we propose a view calibrator to move the points projected to the background into the foreground by the single-view silhouette image. To the best of our knowledge, our approach is the first point cloud completion method that does not require any 3D supervision. The experimental results of our method are superior to those of the state-of-the-art unsupervised methods by a large margin. Moreover, our method even achieves comparable performance to some supervised methods. We will make the source code publicly available at https://github.com/ltwu6/cross-pcc.

Qijian Zhang, Junhui Hou

The past few years have witnessed the great success and prevalence of self-supervised representation learning within the language and 2D vision communities. However, such advancements have not been fully migrated to the field of 3D point cloud learning. Different from existing pre-training paradigms designed for deep point cloud feature extractors that fall into the scope of generative modeling or contrastive learning, this paper proposes a translative pre-training framework, namely PointVST, driven by a novel self-supervised pretext task of cross-modal translation from 3D point clouds to their corresponding diverse forms of 2D rendered images. More specifically, we begin with deducing view-conditioned point-wise embeddings through the insertion of the viewpoint indicator, and then adaptively aggregate a view-specific global codeword, which can be further fed into subsequent 2D convolutional translation heads for image generation. Extensive experimental evaluations on various downstream task scenarios demonstrate that our PointVST shows consistent and prominent performance superiority over current state-of-the-art approaches as well as satisfactory domain transfer capability. Our code will be publicly available at https://github.com/keeganhk/PointVST.

Qijian Zhang, Junhui Hou, Yohanes Yudhi Adikusuma et al.

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that require extensive querying of arbitrary point-to-point geodesics. Although neural implicit representations have emerged as a popular way of representing 3D shape geometries, there is still no research on representing geodesics with deep implicit functions. To bridge this gap, this paper presents the first attempt to represent geodesics on 3D mesh models using neural implicit functions. Specifically, we introduce neural geodesic fields (NeuroGFs), which are learned to represent the all-pairs geodesics of a given mesh. By using NeuroGFs, we can efficiently and accurately answer queries of arbitrary point-to-point geodesic distances and paths, overcoming the limitations of traditional algorithms. Evaluations on common 3D models show that NeuroGFs exhibit exceptional performance in solving the single-source all-destination (SSAD) and point-to-point geodesics, and achieve high accuracy consistently. Besides, NeuroGFs also offer the unique advantage of encoding both 3D geometry and geodesics in a unified representation. Moreover, we further extend generalizable learning frameworks of NeuroGFs by adding shape feature encoders, which also show satisfactory performances for unseen shapes and categories. Code is made available at https://github.com/keeganhk/NeuroGF/tree/master.

Yingzhi Tang, Qijian Zhang, Junhui Hou et al.

The latest trends in the research field of single-view human reconstruction devote to learning deep implicit functions constrained by explicit body shape priors. Despite the remarkable performance improvements compared with traditional processing pipelines, existing learning approaches still show different aspects of limitations in terms of flexibility, generalizability, robustness, and/or representation capability. To comprehensively address the above issues, in this paper, we investigate an explicit point-based human reconstruction framework called HaP, which adopts point clouds as the intermediate representation of the target geometric structure. Technically, our approach is featured by fully-explicit point cloud estimation, manipulation, generation, and refinement in the 3D geometric space, instead of an implicit learning process that can be ambiguous and less controllable. The overall workflow is carefully organized with dedicated designs of the corresponding specialized learning components as well as processing procedures. Extensive experiments demonstrate that our framework achieves quantitative performance improvements of 20% to 40% over current state-of-the-art methods, and better qualitative results. Our promising results may indicate a paradigm rollback to the fully-explicit and geometry-centric algorithm design, which enables to exploit various powerful point cloud modeling architectures and processing techniques. We will make our code and data publicly available at https://github.com/yztang4/HaP.

Yingzhi Tang, Qijian Zhang, Junhui Hou

Achieving consistent and high-fidelity geometry and appearance reconstruction of 3D digital humans from a single RGB image is inherently a challenging task. Existing studies typically resort to decoupled pipelines for geometry estimation and appearance synthesis, often hindering unified reconstruction and causing inconsistencies. This paper introduces \textbf{JGA-LBD}, a novel framework that unifies the modeling of geometry and appearance into a joint latent representation and formulates the generation process as bridge diffusion. Observing that directly integrating heterogeneous input conditions (e.g., depth maps, SMPL models) leads to substantial training difficulties, we unify all conditions into the 3D Gaussian representations, which can be further compressed into a unified latent space through a shared sparse variational autoencoder (VAE). Subsequently, the specialized form of bridge diffusion enables to start with a partial observation of the target latent code and solely focuses on inferring the missing components. Finally, a dedicated decoding module extracts the complete 3D human geometric structure and renders novel views from the inferred latent representation. Experiments demonstrate that JGA-LBD outperforms current state-of-the-art approaches in terms of both geometry fidelity and appearance quality, including challenging in-the-wild scenarios. Our code will be made publicly available at https://github.com/haiantyz/JGA-LBD.

Qijian Zhang, Junhui Hou, Wenping Wang et al.

Surface parameterization plays an essential role in numerous computer graphics and geometry processing applications. Traditional parameterization approaches are designed for high-quality meshes laboriously created by specialized 3D modelers, thus unable to meet the processing demand for the current explosion of ordinary 3D data. Moreover, their working mechanisms are typically restricted to certain simple topologies, thus relying on cumbersome manual efforts (e.g., surface cutting, part segmentation) for pre-processing. In this paper, we introduce the Flatten Anything Model (FAM), an unsupervised neural architecture to achieve global free-boundary surface parameterization via learning point-wise mappings between 3D points on the target geometric surface and adaptively-deformed UV coordinates within the 2D parameter domain. To mimic the actual physical procedures, we ingeniously construct geometrically-interpretable sub-networks with specific functionalities of surface cutting, UV deforming, unwrapping, and wrapping, which are assembled into a bi-directional cycle mapping framework. Compared with previous methods, our FAM directly operates on discrete surface points without utilizing connectivity information, thus significantly reducing the strict requirements for mesh quality and even applicable to unstructured point cloud data. More importantly, our FAM is fully-automated without the need for pre-cutting and can deal with highly-complex topologies, since its learning process adaptively finds reasonable cutting seams and UV boundaries. Extensive experiments demonstrate the universality, superiority, and inspiring potential of our proposed neural surface parameterization paradigm. Our code is available at https://github.com/keeganhk/FlattenAnything.

Yiming Zeng, Junhui Hou, Qijian Zhang et al.

Dynamic 3D point cloud sequences serve as one of the most common and practical representation modalities of dynamic real-world environments. However, their unstructured nature in both spatial and temporal domains poses significant challenges to effective and efficient processing. Existing deep point cloud sequence modeling approaches imitate the mature 2D video learning mechanisms by developing complex spatio-temporal point neighbor grouping and feature aggregation schemes, often resulting in methods lacking effectiveness, efficiency, and expressive power. In this paper, we propose a novel generic representation called \textit{Structured Point Cloud Videos} (SPCVs). Intuitively, by leveraging the fact that 3D geometric shapes are essentially 2D manifolds, SPCV re-organizes a point cloud sequence as a 2D video with spatial smoothness and temporal consistency, where the pixel values correspond to the 3D coordinates of points. The structured nature of our SPCV representation allows for the seamless adaptation of well-established 2D image/video techniques, enabling efficient and effective processing and analysis of 3D point cloud sequences. To achieve such re-organization, we design a self-supervised learning pipeline that is geometrically regularized and driven by self-reconstructive and deformation field learning objectives. Additionally, we construct SPCV-based frameworks for both low-level and high-level 3D point cloud sequence processing and analysis tasks, including action recognition, temporal interpolation, and compression. Extensive experiments demonstrate the versatility and superiority of the proposed SPCV, which has the potential to offer new possibilities for deep learning on unstructured 3D point cloud sequences. Code will be released at https://github.com/ZENGYIMING-EAMON/SPCV.

Yuming Zhao, Qijian Zhang, Junhui Hou et al.

Surface parameterization is a fundamental geometry processing task, laying the foundations for the visual presentation of 3D assets and numerous downstream shape analysis scenarios. Conventional parameterization approaches demand high-quality mesh triangulation and are restricted to certain simple topologies unless additional surface cutting and decomposition are provided. In practice, the optimal configurations (e.g., type of parameterization domains, distribution of cutting seams, number of mapping charts) may vary drastically with different surface structures and task characteristics, thus requiring more flexible and controllable processing pipelines. To this end, this paper introduces FlexPara, an unsupervised neural optimization framework to achieve both global and multi-chart surface parameterizations by establishing point-wise mappings between 3D surface points and adaptively-deformed 2D UV coordinates. We ingeniously design and combine a series of geometrically-interpretable sub-networks, with specific functionalities of cutting, deforming, unwrapping, and wrapping, to construct a bi-directional cycle mapping framework for global parameterization without the need for manually specified cutting seams. Furthermore, we construct a multi-chart parameterization framework with adaptively-learned chart assignment. Extensive experiments demonstrate the universality, superiority, and inspiring potential of our neural surface parameterization paradigm. The code will be publicly available at https://github.com/AidenZhao/FlexPara

Yingzhi Tang, Qijian Zhang, Junhui Hou

We present HuGDiffusion, a generalizable 3D Gaussian splatting (3DGS) learning pipeline to achieve novel view synthesis (NVS) of human characters from single-view input images. Existing approaches typically require monocular videos or calibrated multi-view images as inputs, whose applicability could be weakened in real-world scenarios with arbitrary and/or unknown camera poses. In this paper, we aim to generate the set of 3DGS attributes via a diffusion-based framework conditioned on human priors extracted from a single image. Specifically, we begin with carefully integrated human-centric feature extraction procedures to deduce informative conditioning signals. Based on our empirical observations that jointly learning the whole 3DGS attributes is challenging to optimize, we design a multi-stage generation strategy to obtain different types of 3DGS attributes. To facilitate the training process, we investigate constructing proxy ground-truth 3D Gaussian attributes as high-quality attribute-level supervision signals. Through extensive experiments, our HuGDiffusion shows significant performance improvements over the state-of-the-art methods. Our code will be made publicly available.

Qijian Zhang, Runmin Cong, Chongyi Li et al.

Despite the remarkable advances in visual saliency analysis for natural scene images (NSIs), salient object detection (SOD) for optical remote sensing images (RSIs) still remains an open and challenging problem. In this paper, we propose an end-to-end Dense Attention Fluid Network (DAFNet) for SOD in optical RSIs. A Global Context-aware Attention (GCA) module is proposed to adaptively capture long-range semantic context relationships, and is further embedded in a Dense Attention Fluid (DAF) structure that enables shallow attention cues flow into deep layers to guide the generation of high-level feature attention maps. Specifically, the GCA module is composed of two key components, where the global feature aggregation module achieves mutual reinforcement of salient feature embeddings from any two spatial locations, and the cascaded pyramid attention module tackles the scale variation issue by building up a cascaded pyramid framework to progressively refine the attention map in a coarse-to-fine manner. In addition, we construct a new and challenging optical RSI dataset for SOD that contains 2,000 images with pixel-wise saliency annotations, which is currently the largest publicly available benchmark. Extensive experiments demonstrate that our proposed DAFNet significantly outperforms the existing state-of-the-art SOD competitors. https://github.com/rmcong/DAFNet_TIP20

Qijian Zhang, Junhui Hou, Ying He

Surface parameterization is a fundamental geometry processing problem with rich downstream applications. Traditional approaches are designed to operate on well-behaved mesh models with high-quality triangulations that are laboriously produced by specialized 3D modelers, and thus unable to meet the processing demand for the current explosion of ordinary 3D data. In this paper, we seek to perform UV unwrapping on unstructured 3D point clouds. Technically, we propose ParaPoint, an unsupervised neural learning pipeline for achieving global free-boundary surface parameterization by building point-wise mappings between given 3D points and 2D UV coordinates with adaptively deformed boundaries. We ingeniously construct several geometrically meaningful sub-networks with specific functionalities, and assemble them into a bi-directional cycle mapping framework. We also design effective loss functions and auxiliary differential geometric constraints for the optimization of the neural mapping process. To the best of our knowledge, this work makes the first attempt to investigate neural point cloud parameterization that pursues both global mappings and free boundaries. Experiments demonstrate the effectiveness and inspiring potential of our proposed learning paradigm. The code will be publicly available.

Qijian Zhang, Xiaozheng Jian, Xuan Zhang et al.

Conventional production workflow of high-precision mesh assets necessitates a cumbersome and laborious process of manual sculpting by specialized 3D artists/modelers. The recent years have witnessed remarkable advances in AI-empowered 3D content creation for generating plausible structures and intricate appearances from images or text prompts. However, synthesizing realistic surface details still poses great challenges, and enhancing the geometry fidelity of existing lower-quality 3D meshes (instead of image/text-to-3D generation) remains an open problem. In this paper, we introduce SuperCarver, a 3D geometry super-resolution pipeline for supplementing texture-consistent surface details onto a given coarse mesh. We start by rendering the original textured mesh into the image domain from multiple viewpoints. To achieve detail boosting, we construct a deterministic prior-guided normal diffusion model, which is fine-tuned on a carefully curated dataset of paired detail-lacking and detail-rich normal map renderings. To update mesh surfaces from potentially imperfect normal map predictions, we design a noise-resistant inverse rendering scheme through deformable distance field. Experiments demonstrate that our SuperCarver is capable of generating realistic and expressive surface details depicted by the actual texture appearance, making it a powerful tool to both upgrade historical low-quality 3D assets and reduce the workload of sculpting high-poly meshes.

Qijian Zhang, Junhui Hou, Yue Qian et al.

Although convolutional neural networks have achieved remarkable success in analyzing 2D images/videos, it is still non-trivial to apply the well-developed 2D techniques in regular domains to the irregular 3D point cloud data. To bridge this gap, we propose ParaNet, a novel end-to-end deep learning framework, for representing 3D point clouds in a completely regular and nearly lossless manner. To be specific, ParaNet converts an irregular 3D point cloud into a regular 2D color image, named point geometry image (PGI), where each pixel encodes the spatial coordinates of a point. In contrast to conventional regular representation modalities based on multi-view projection and voxelization, the proposed representation is differentiable and reversible. Technically, ParaNet is composed of a surface embedding module, which parameterizes 3D surface points onto a unit square, and a grid resampling module, which resamples the embedded 2D manifold over regular dense grids. Note that ParaNet is unsupervised, i.e., the training simply relies on reference-free geometry constraints. The PGIs can be seamlessly coupled with a task network established upon standard and mature techniques for 2D images/videos to realize a specific task for 3D point clouds. We evaluate ParaNet over shape classification and point cloud upsampling, in which our solutions perform favorably against the existing state-of-the-art methods. We believe such a paradigm will open up many possibilities to advance the progress of deep learning-based point cloud processing and understanding.

Qijian Zhang, Runmin Cong, Junhui Hou et al.

Co-Salient Object Detection (CoSOD) aims at discovering salient objects that repeatedly appear in a given query group containing two or more relevant images. One challenging issue is how to effectively capture co-saliency cues by modeling and exploiting inter-image relationships. In this paper, we present an end-to-end collaborative aggregation-and-distribution network (CoADNet) to capture both salient and repetitive visual patterns from multiple images. First, we integrate saliency priors into the backbone features to suppress the redundant background information through an online intra-saliency guidance structure. After that, we design a two-stage aggregate-and-distribute architecture to explore group-wise semantic interactions and produce the co-saliency features. In the first stage, we propose a group-attentional semantic aggregation module that models inter-image relationships to generate the group-wise semantic representations. In the second stage, we propose a gated group distribution module that adaptively distributes the learned group semantics to different individuals in a dynamic gating mechanism. Finally, we develop a group consistency preserving decoder tailored for the CoSOD task, which maintains group constraints during feature decoding to predict more consistent full-resolution co-saliency maps. The proposed CoADNet is evaluated on four prevailing CoSOD benchmark datasets, which demonstrates the remarkable performance improvement over ten state-of-the-art competitors.

Yue Qian, Junhui Hou, Qijian Zhang et al.

This paper explores the problem of task-oriented downsampling over 3D point clouds, which aims to downsample a point cloud while maintaining the performance of subsequent applications applied to the downsampled sparse points as much as possible. Designing from the perspective of matrix optimization, we propose MOPS-Net, a novel interpretable deep learning-based method, which is fundamentally different from the existing deep learning-based methods due to its interpretable feature. The optimization problem is challenging due to its discrete and combinatorial nature. We tackle the challenges by relaxing the binary constraint of the variables, and formulate a constrained and differentiable matrix optimization problem. We then design a deep neural network to mimic the matrix optimization by exploring both the local and global structures of the input data. MOPS-Net can be end-to-end trained with a task network and is permutation-invariant, making it robust to the input. We also extend MOPS-Net such that a single network after one-time training is capable of handling arbitrary downsampling ratios. Extensive experimental results show that MOPS-Net can achieve favorable performance against state-of-the-art deep learning-based methods over various tasks, including classification, reconstruction, and registration. Besides, we validate the robustness of MOPS-Net on noisy data.