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Alternating optimization for bundle adjustment with closed form solutions

Science China(Information Sciences) 2025年第06期 286-300页

作者： Chengzhe MENG Yiwen JIANG Weiwei XU State Key Lab of Computer-Aided Design & Computer Graphics Zhejiang University

This study proposes a novel alternating optimization algorithm for bundle adjustment, a critical process in structure from motion methods. We introduce the inverse depth of each three-dimensional(3D) point as an augmented independent variable and develop a low-order polynomial error metric. Theoretically, the error can be adjusted to align closely with the re-projection error since it essentially acts as a re-weighted re-projection error. We decouple the bundle adjustment problem by breaking it down into three separate tasks: estimating the camera's pose, determining the 3D structure, and optionally estimating the camera's intrinsic parameter. Each task can be handled independently, either by camera or by point, allowing for easy distribution of computation. Camera pose estimation is a case of the absolute orientation problem, which can be globally solved in closed form. A linearization scheme is proposed for 3D point estimation, which allows the computation of the update direction and line search in closed form. Our algorithm proves to be efficient, reliable,and accurate, as demonstrated by experimental results that confirm its superiority over recent alternatives.

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Alternating optimization for bundle adjustment with closed form solutions

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Science China Information Sciences 2025年第6期68卷 1-15页

作者： Meng, Chengzhe Jiang, Yiwen Xu, Weiwei State Key Lab of Computer-Aided Design & Computer Graphics Zhejiang University Hangzhou 310058 China

This study proposes a novel alternating optimization algorithm for bundle adjustment, a critical process in structure from motion methods. We introduce the inverse depth of each three-dimensional (3D) point as an augmented independent variable and develop a low-order polynomial error metric. Theoretically, the error can be adjusted to align closely with the re-projection error since it essentially acts as a re-weighted re-projection error. We decouple the bundle adjustment problem by breaking it down into three separate tasks: estimating the camera’s pose, determining the 3D structure, and optionally estimating the camera’s intrinsic parameter. Each task can be handled independently, either by camera or by point, allowing for easy distribution of computation. Camera pose estimation is a case of the absolute orientation problem, which can be globally solved in closed form. A linearization scheme is proposed for 3D point estimation, which allows the computation of the update direction and line search in closed form. Our algorithm proves to be efficient, reliable, and accurate, as demonstrated by experimental results that confirm its superiority over recent alternatives. © Science China Press 2025.

关键词： 3D reconstruction alternating optimization bundle adjustment vision localization

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View-Aware Image Object Compositing and Synthesis from Multiple Sources

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Journal of computer Science & Technology 2016年第3期31卷 463-478页

作者： Xiang Chen Wei-Wei Xu Sai-Kit Yeung Kun Zhou State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China Vision Graphics and Computational Design Group Singapore University of Technology and Design Singapore 487372 Singapore

Image compositing is widely used to combine visual elements from separate source images into a single image. Although recent image compositing techniques are capable of achieving smooth blending of the visual elements from different sources, most of them implicitly assume the source images are taken in the same viewpoint. In this paper, we present an approach to compositing novel image objects from multiple source images which have different viewpoints. Our key idea is to construct 3D proxies for meaningful components of the source image objects, and use these 3D component proxies to warp and seamlessly merge components together in the same viewpoint. To realize this idea, we introduce a coordinate- frame based single-view camera calibration algorithm to handle general types of image objects, a structure-aware cuboid optimization algorithm to get the cuboid proxies for image object components with correct structure relationship, and finally a 3D-proxy transformation guided image warping algorithm to stitch object components. We further describe a novel application based on this compositing approach to automatically synthesize a large number of image objects from a set of exemplars. Experimental results show that our compositing approach can be applied to a variety of image objects, such as chairs, cups, lamps, and robots, and the synthesis application can create novel image objects with significant shape and style variations from a small set of exemplars.

关键词： image cloning 3D proxy probabilistic modeling data-driven method

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GPU-based dynamic quad stream for forest rendering

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Science China(Information Sciences) 2010年第8期53卷 1539-1545页

作者： LIU Feng, HUA Wei & BAO HuJun state key lab of computer aided design and computer graphics, Zhejiang University, Hangzhou 310058, China 1. State Key Lab of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China

Rendering large-scale forest scenes in real-time is a challenging problem, since the geometric complexity is far beyond the capabilities of current graphics hardware. In this paper, we propose a novel approach that adopts a dynamic quad stream residing on GPU buffers for view-dependent forest rendering. The incremental quad stream updating process is well-suited to the massively parallel architecture of the GPU pipeline, and it requires no continuous data exchange between CPU and GPU. The implementation of the algorithm is quite straightforward. Despite its simplicity, the algorithm achieves good performance with low memory, storage, and CPU costs.

关键词： real-time rendering large-scale forest quad stream geometry shader

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Irradiance regression for efficient final gathering in global illumination

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Frontiers of computer Science 2015年第3期9卷 456-465页

作者： Xuezhen HUANG Xin SUN Zhong REN Xin TONG Baining GUO Kun ZHOU State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China Microsoft Research Asia Beijing 100029 China

Photon mapping is widely used for global illumi- nation rendering because of its high computational efficiency. But its efficiency is still limited, mainly by the intensive sam- piing required in final gathering, a process that is critical for removing low frequency artifacts of density estimation. In this paper, we propose a method to predict the final gather- ing estimation with direct density estimation, thereby achiev- ing high quality global illumination by photon mapping with high efficiency. We first sample the irradiance of a subset of shading points by both final gathering and direct radiance es- timation. Then we use the samples as a training set to predict the final gathered irradiance of other shading points through regression. Consequently, we are able to achieve about three times overall speedup compared with straightforward final gathering in global illumination computation with the same rendering quality.

关键词： global illumination photon mapping final gath-ering radiance estimation regression

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Variance Analysis and Adaptive Sampling for Indirect Light Path Reuse

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Journal of computer Science & Technology 2016年第3期31卷 547-560页

作者： Hao Qin Xin Sun Jun Yan Qi-Ming Hou Zhong Ren Kun Zhou State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China Microsoft Research Asia Beijing 100080 China

In this paper, we study the estimation variance of a set of global illumination algorithms based on indirect light path reuse. These algorithms usually contain two passes -- in the first pass, a small number of indirect light samples are generated and evaluated, and they are then reused by a large number of reconstruction samples in the second pass. Our analysis shows that the covariance of the reconstruction samples dominates the estimation variance under high reconstruction rates and increasing the reconstruction rate cannot effectively reduce the covariance. We also find that the covariance represents to what degree the indirect light samples are reused during reconstruction. This analysis motivates us to design a heuristic approximating the covariance as well as an adaptive sampling scheme based on this heuristic to reduce the rendering variance. We validate our analysis and adaptive sampling scheme in the indirect light field reconstruction algorithm and the axis-aligned filtering algorithm for indirect lighting. Experiments are in accordance with our analysis and show that rendering artifacts can be greatly reduced at a similar computational cost.

关键词： Monte Carlo method global illumination variance indirect light path reuse

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A Survey of Visual Analytic Pipelines

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Journal of computer Science & Technology 2016年第4期31卷 787-804页

作者： Xu-Meng Wang Tian-Ye Zhang Yu-Xin Ma Jing Xia Wei Chen State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China Innovation Joint Research Center for Cyber-Physical-Society System Zhejiang University Hangzhou 310058 China

Visual analytics has been widely studied in the past decade. One key to make visual analytics practical for both research and industrial applications is the appropriate definition and implementation of the visual analytics pipeline which provides effective abstractions for designing and implementing visual analytics systems. In this paper we review the previous work on visual analytics pipelines and individual modules from multiple perspectives： data, visualization, model and knowledge. In each module we discuss various representations and descriptions of pipelines inside the module, and compare the commonalities and the differences among them.

关键词： visual analytics pipeline visualization model knowledge

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AN IBR METHOD:PANORAMIC MOSAICS OF SLIT IMAGES WITH DEPTH

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2001年第1期2卷 72-79页

作者：蒋纯石教英 State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou China

Providing a wider movement range of virtual camera is an unsolved problem for state-of-the-art image-based rendering system. In this paper, we present a new image based rendering technology called panoramic mosaics of slit images with depth that can provide large virtual camera motion region for some scenes. By limiting camera motion to a horizontal plane only, a slit image with united depth value is used as the rendering element. The panoramic mosaics of slit images with depth are easy to capture, and the data size is as small as that of panorama. We present here the capturing, construction as well as rendering process of panoramic slit images mosaic with depth. In addition, we present the join up process of multiple panoramic slit images mosaic with depth.

关键词： image based rendering (IBR) panorama slit images

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Mechanical Assembly Packing Problem Using Joint Constraints

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Journal of computer Science & Technology 2017年第6期32卷 1162-1171页

作者： Ming-Liang Xu Ning-Bo Gu Wei-Wei Xu Ming-Yuan Li Jun-Xiao Xue Bing Zhou School of Information Engineering Zhengzhou University Zhengzhou 450000 China State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310058 China School of Software Zhengzhou University Zhengzhou 450000 China

The three-dimensional packing problem is generally on how to pack a set of models into a given bounding box using the smallest packaging volume. It is known as an NP-hard problem. When discussing the packing problem in mechanical field, the space utilization of a mechanism is low due to the constraint of mechanical joints between different mechanical parts. Although such a situation can be improved by breaking the mechanism into components at every joint, it burdens the user when reassembling the mechanism and may also reduce the service life of mechanical parts. In this paper, we propose a novel mechanism packing algorithm that deliberately considers the DOFs （degrees of freedom） of mechanical joints. With this algorithm, we construct the solution space according to each joint. While building the search tree of the splitting scheme, we do not break the joint, but move the joint. Therefore, the algorithm proposed in this paper just requires the minimal number of splits to meet the goal of space utilization. Numerical examples show that the proposed method is convenient and efficient to pack three-dimensional models into a given bounding box with high space utilization.

关键词： NP-hard problem packing problem search tree

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Consistency maintenance for constraint in role-based access control model

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2002年第3期3卷 43-48页

作者：韩伟力陈刚董金祥尹建伟 State Key Laboratory of Computer Aided Design and Computer Graphics Zhejiang University Hangzhou 310027China

Constraint is an important aspect of role based access control and is sometimes argued to be the principal motivation for role based access control (RBAC). But so far few authors have discussed consistency maintenance for constraint in RBAC model. Based on researches of constraints among roles and types of inconsistency among constraints, this paper introduces corresponding formal rules, rule based reasoning and corresponding methods to detect, avoid and resolve these inconsistencies. Finally, the paper introduces briefly the application of consistency maintenance in ZD PDM, an enterprise oriented product data management (PDM) system.

关键词： Consistency maintenance Role based access control Product data management Constraint

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