Showing papers on "3D reconstruction published in 2011"

KinectFusion: real-time 3D reconstruction and interaction using a moving depth camera

Abstract: KinectFusion enables a user holding and moving a standard Kinect camera to rapidly create detailed 3D reconstructions of an indoor scene. Only the depth data from Kinect is used to track the 3D pose of the sensor and reconstruct, geometrically precise, 3D models of the physical scene in real-time. The capabilities of KinectFusion, as well as the novel GPU-based pipeline are described in full. Uses of the core system for low-cost handheld scanning, and geometry-aware augmented reality and physics-based interactions are shown. Novel extensions to the core GPU pipeline demonstrate object segmentation and user interaction directly in front of the sensor, without degrading camera tracking or reconstruction. These extensions are used to enable real-time multi-touch interactions anywhere, allowing any planar or non-planar reconstructed physical surface to be appropriated for touch.

StereoScan: Dense 3d reconstruction in real-time

Abstract: Accurate 3d perception from video sequences is a core subject in computer vision and robotics, since it forms the basis of subsequent scene analysis. In practice however, online requirements often severely limit the utilizable camera resolution and hence also reconstruction accuracy. Furthermore, real-time systems often rely on heavy parallelism which can prevent applications in mobile devices or driver assistance systems, especially in cases where FPGAs cannot be employed. This paper proposes a novel approach to build 3d maps from high-resolution stereo sequences in real-time. Inspired by recent progress in stereo matching, we propose a sparse feature matcher in conjunction with an efficient and robust visual odometry algorithm. Our reconstruction pipeline combines both techniques with efficient stereo matching and a multi-view linking scheme for generating consistent 3d point clouds. In our experiments we show that the proposed odometry method achieves state-of-the-art accuracy. Including feature matching, the visual odometry part of our algorithm runs at 25 frames per second, while - at the same time - we obtain new depth maps at 3-4 fps, sufficient for online 3d reconstructions.

3D Face Reconstruction from a Single Image Using a Single Reference Face Shape

Abstract: Human faces are remarkably similar in global properties, including size, aspect ratio, and location of main features, but can vary considerably in details across individuals, gender, race, or due to facial expression. We propose a novel method for 3D shape recovery of faces that exploits the similarity of faces. Our method obtains as input a single image and uses a mere single 3D reference model of a different person's face. Classical reconstruction methods from single images, i.e., shape-from-shading, require knowledge of the reflectance properties and lighting as well as depth values for boundary conditions. Recent methods circumvent these requirements by representing input faces as combinations (of hundreds) of stored 3D models. We propose instead to use the input image as a guide to "mold” a single reference model to reach a reconstruction of the sought 3D shape. Our method assumes Lambertian reflectance and uses harmonic representations of lighting. It has been tested on images taken under controlled viewing conditions as well as on uncontrolled images downloaded from the Internet, demonstrating its accuracy and robustness under a variety of imaging conditions and overcoming significant differences in shape between the input and reference individuals including differences in facial expressions, gender, and race.

Camera Models And Fundamental Concepts Used In Geometric Computer Vision

Abstract: This survey is mainly motivated by the increased availability and use of panoramic image acquisition devices, in computer vision and various of its applications. Different technologies and different computational models thereof exist and algorithms and theoretical studies for geometric computer vision ("structure-from-motion") are often re-developed without highlighting common underlying principles. One of the goals of this survey is to give an overview of image acquisition methods used in computer vision and especially, of the vast number of camera models that have been proposed and investigated over the years, where we try to point out similarities between different models. Results on epipolar and multi-view geometry for different camera models are reviewed as well as various calibration and self-calibration approaches, with an emphasis on non-perspective cameras. We finally describe what we consider are fundamental building blocks for geometric computer vision or structure-from-motion: epipolar geometry, pose and motion estimation, 3D scene modeling, and bundle adjustment. The main goal here is to highlight the main principles of these, which are independent of specific camera models.

Experimentation of structured light and stereo vision for underwater 3D reconstruction

Abstract: Current research on underwater 3D imaging methods is mainly addressing long range applications like seafloor mapping or surveys of archeological sites and shipwrecks. Recently, there is an increasing need for more accessible and precise close-range 3D acquisition technologies in some application fields like, for example, monitoring the growth of coral reefs or reconstructing underwater archaeological pieces that in most cases cannot be recovered from the seabed. This paper presents the first results of a research project that aims to investigate the possibility of using active optical techniques for the whole-field 3D reconstructions in an underwater environment. In this work we have tested an optical technique, frequently used for in air acquisition, based on the projection of structured lighting patterns acquired by a stereo vision system. We describe the experimental setup used for the underwater tests, which were conducted in a water tank with different turbidity conditions. The tests have evidenced that the quality of 3D reconstruction is acceptable even with high turbidity values, despite the heavy presence of scattering and absorption effects.

Residual Reconstruction for Block-Based Compressed Sensing of Video

Abstract: A simple block-based compressed-sensing reconstruction for still images is adapted to video. Incorporating reconstruction from a residual arising from motion estimation and compensation, the proposed technique alternatively reconstructs frames of the video sequence and their corresponding motion fields in an iterative fashion. Experimental results reveal that the proposed technique achieves significantly higher quality than a straightforward reconstruction that applies a still-image reconstruction independently frame by frame, a 3D reconstruction that exploits temporal correlation between frames merely in the form of a motion-agnostic 3D transform, and a similar, yet non-iterative, motion-compensated residual reconstruction.

Monocular Template-based Reconstruction of Inextensible Surfaces

Abstract: We present a monocular 3D reconstruction algorithm for inextensible deformable surfaces. It uses point correspondences between a single image of the deformed surface taken by a camera with known intrinsic parameters and a template. The main assumption we make is that the surface shape as seen in the template is known. Since the surface is inextensible, its deformations are isometric to the template. We exploit the distance preservation constraints to recover the 3D surface shape as seen in the image. Though the distance preservation constraints have already been investigated in the literature, we propose a new way to handle them. Spatial smoothness priors are easily incorporated, as well as temporal smoothness priors in the case of reconstruction from a video. The reconstruction can be used for 3D augmented reality purposes thanks to a fast implementation. We report results on synthetic and real data. Some of them are compared to stereo-based 3D reconstructions to demonstrate the efficiency of our method.

Direct Iterative Closest Point for real-time visual odometry

Abstract: In RGB-D sensor based visual odometry the goal is to estimate a sequence of camera movements using image and/or range measurements Direct methods solve the problem by minimizing intensity error In this work a depth map obtained from a RGB-D sensor is considered as a new measurement which is combined with a direct photometric cost function The minimization of the bi-objective cost function produces 3D camera motion parameters which registers two 3D surfaces within a same coordinate system The given formulation does not require any predetermined temporal correspondencies nor feature extraction when having a sufficient frame rate It is shown how incorporating the depth measurement robustifies the cost function in case of insufficient texture information and non-Lambertian surfaces Finally the method is demonstrated in the Planetary Robotics Vision Ground Processing (PRoVisG) competition where visual odometry and 3D reconstruction results are solved for a stereo image sequence captured using a Mars rover

Energy based multiple model fitting for non-rigid structure from motion

Abstract: In this paper we reformulate the 3D reconstruction of deformable surfaces from monocular video sequences as a labeling problem. We solve simultaneously for the assignment of feature points to multiple local deformation models and the fitting of models to points to minimize a geometric cost, subject to a spatial constraint that neighboring points should also belong to the same model. Piecewise reconstruction methods rely on features shared between models to enforce global consistency on the 3D surface. To account for this overlap between regions, we consider a super-set of the classic labeling problem in which a set of labels, instead of a single one, is assigned to each variable. We propose a mathematical formulation of this new model and show how it can be efficiently optimized with a variant of α-expansion. We demonstrate how this framework can be applied to Non-Rigid Structure from Motion and leads to simpler explanations of the same data. Compared to existing methods run on the same data, our approach has up to half the reconstruction error, and is more robust to over-fitting and outliers.

Reliable automatic alignment of tomographic projection data by passive auto-focus

Abstract: Purpose: The authors present a robust algorithm that removes the blurring and double-edge artifacts in high-resolution computed tomography (CT) images that are caused by misaligned scanner components. This alleviates the time-consuming process of physically aligning hardware, which is of particular benefit if components are moved or swapped frequently. Methods: The proposed method uses the experimental data itself for calibration. A parameterized model of the scanner geometry is constructed and the parameters are varied until the sharpest 3D reconstruction is found. The concept is similar to passive auto-focus algorithms of digital optical instruments. The parameters are used to remap the projection data from the physical detector to a virtual aligned detector. This is followed by a standard reconstruction algorithm, namely the Feldkamp algorithm. Feldkamp et al.[J. Opt. Soc. Am. A 1, 612-619 (1984)]. Results: An example implementation is given for a rabbit liver specimen that was collected with a circular trajectory. The optimal parameters were determined in less computation time than that for a full reconstruction. The example serves to demonstrate that (a) sharpness is an appropriate measure for projection alignment, (b) our parameterization is sufficient to characterize misalignments for cone-beam CT, and (c) the procedure determines parameter values with sufficientmore » precision to remove the associated artifacts. Conclusions: The algorithm is fully tested and implemented for regular use at The Australian National University micro-CT facility for both circular and helical trajectories. It can in principle be applied to more general imaging geometries and modalities. It is as robust as manual alignment but more precise since we have quantified the effect of misalignment.« less

Fusing Multiview and Photometric Stereo for 3D Reconstruction under Uncalibrated Illumination

Abstract: We propose a method to obtain a complete and accurate 3D model from multiview images captured under a variety of unknown illuminations. Based on recent results showing that for Lambertian objects, general illumination can be approximated well using low-order spherical harmonics, we develop a robust alternating approach to recover surface normals. Surface normals are initialized using a multi-illumination multiview stereo algorithm, then refined using a robust alternating optimization method based on the l1 metric. Erroneous normal estimates are detected using a shape prior. Finally, the computed normals are used to improve the preliminary 3D model. The reconstruction system achieves watertight and robust 3D reconstruction while neither requiring manual interactions nor imposing any constraints on the illumination. Experimental results on both real world and synthetic data show that the technique can acquire accurate 3D models for Lambertian surfaces, and even tolerates small violations of the Lambertian assumption.

Realtime multibody visual SLAM with a smoothly moving monocular camera

Abstract: This paper presents a realtime, incremental multibody visual SLAM system that allows choosing between full 3D reconstruction or simply tracking of the moving objects. Motion reconstruction of dynamic points or objects from a monocular camera is considered very hard due to well known problems of observability. We attempt to solve the problem with a Bearing only Tracking (BOT) and by integrating multiple cues to avoid observability issues. The BOT is accomplished through a particle filter, and by integrating multiple cues from the reconstruction pipeline. With the help of these cues, many real world scenarios which are considered unobservable with a monocular camera is solved to reasonable accuracy. This enables building of a unified dynamic 3D map of scenes involving multiple moving objects. Tracking and reconstruction is preceded by motion segmentation and detection which makes use of efficient geometric constraints to avoid difficult degenerate motions, where objects move in the epipolar plane. Results reported on multiple challenging real world image sequences verify the efficacy of the proposed framework.

Rectification and 3D reconstruction of curved document images

Abstract: Distortions in images of documents, such as the pages of books, adversely affect the performance of optical character recognition (OCR) systems. Removing such distortions requires the 3D deformation of the document that is often measured using special and precisely calibrated hardware (stereo, laser range scanning or structured light). In this paper, we introduce a new approach that automatically reconstructs the 3D shape and rectifies a deformed text document from a single image. We first estimate the 2D distortion grid in an image by exploiting the line structure and stroke statistics in text documents. This approach does not rely on more noise-sensitive operations such as image binarization and character segmentation. The regularity in the text pattern is used to constrain the 2D distortion grid to be a perspective projection of a 3D parallelogram mesh. Based on this constraint, we present a new shape-from-texture method that computes the 3D deformation up to a scale factor using SVD. Unlike previous work, this formulation imposes no restrictions on the shape (e.g., a developable surface). The estimated shape is then used to remove both geometric distortions and photometric (shading) effects in the image. We demonstrate our techniques on documents containing a variety of languages, fonts and sizes.

Multiple-Camera Instrumentation of a Single Point Incremental Forming Process Pilot for Shape and 3D Displacement Measurements: Methodology and Results

Abstract: A multiple-camera system (more than two cameras) has been developed to measure the shape variations and the 3D displacement field of a sheet metal part during a Single Point Incremental Forming (SPIF) operation. The modeling of the multiple-camera system and the calibration procedure to determine its parameters are described. The sequence of images taken during the forming operation is processed using a multiple-view Digital Image Correlation (DIC) method and the 3D reconstruction of the part shape is obtained using a Sparse Bundle Adjustment (SBA) method. Two experiments that demonstrate the potentiality of the method are described.

An introduction to image-based 3D surface reconstruction and a survey of photometric stereo methods

Abstract: This paper provides an introduction to photometric methods for image-based 3D shape reconstruction and a survey of photometric stereo techniques. We begin with taxonomy of active and passive shape acquisition techniques. Then we describe the methodical background of photometric 3D reconstruction, define the canonical setting of photometric stereo (Lambertian surface reflectance, parallel incident light, known illumination direction, known surface albedo, absence of cast shadows), discuss the 3D reconstruction of surfaces from local gradients, summarize the concept of the bidirectional reflectance distribution function (BRDF), and outline several important empirically and physically motivated reflectance models. We provide a detailed treatment of several generalizations of the canonical setting of photometric stereo, namely non-distant light sources, unknown illumination directions, and, in some detail, non-Lambertian surface reflectance functions. An important special case is purely specular reflections, where an extended light source allows capturing a surface that consists of perfectly specular surface patches. Linear combinations of purely Lambertian and purely specular reflectance components are favorably used for reconstructing smooth surfaces and also human skin. Nonuniform surface reflectance properties are estimated based on a simultaneous 3D reconstruction and determination of the locally variable parameters of the reflectance function based on a multitude of images. Assuming faceted surfaces, the effective resolution of the 3D reconstruction result can be increased to some extent beyond that of the underlying images. Other approaches separate specular and diffuse reflectance components based on polarization data or color information. The specular reflections can be used additionally to estimate the direction from which the surface is illuminated. Finally, we describe methods to combine photometric 3D reconstruction techniques with active and passive triangulation-based approaches.

Online 3D reconstruction using convex optimization

Abstract: We present a system that is capable of interactively reconstructing a scene from a single live camera. We use a dense volumetric representation of the surface, which means there are no constraints concerning the 3D-scene topology. Reconstruction is based on range image fusion using a total variation formulation, where the surface is represented implicitly by a signed distance function. The final 3D-model is obtained by minimizing a global convex energy and extracting the zero level-set of the solution. The whole reconstruction process is designed to be online. Users can constantly inspect the current reconstruction and adapt camera movement to get the desired amount of detail for specific parts of the reconstructed scene.

Three-dimensional photoacoustic tomography based on the focal-line concept

Abstract: A full ring ultrasonic array-based photoacoustic tomography system was recently developed for small animal brain imaging. The 512-element array is cylindrically focused in the elevational direction, and can acquire a two-dimensional (2D) image in 1.6 s. In this letter, we demonstrate the three-dimensional (3D) imaging capability of this system. A novel 3D reconstruction algorithm was developed based on the focal-line concept. Compared to 3D images acquired simply by stacking a series of 2D images, the 3D focal-line reconstruction method renders images with much less artifacts, and improves the elevational resolution by 30% and the signal-to-noise ratio by two times. The effectiveness of the proposed algorithm was first validated by numerical simulations and then demonstrated with a hair phantom experiment and an ex vivo mouse embryo experiment.

Multi-view 3D reconstruction for scenes under the refractive plane with known vertical direction

Abstract: Images taken from scenes under water suffer distortion due to refraction. While refraction causes magnification with mild distortion on the observed images, severe distortions in geometry reconstruction would be resulted if the refractive distortion is not properly handled. Different from the radial distortion model, the refractive distortion depends on the scene depth seen from each light ray as well as the camera pose relative to the refractive surface. Therefore, it's crucial to obtain a good estimate of scene depth, camera pose and optical center to alleviate the impact of refractive distortion. In this work, we formulate the forward and back projections of light rays involving a refractive plane for the perspective camera model by explicitly modeling refractive distortion as a function of depth. Furthermore, for cameras with an inertial measurement unit (IMU), we show that a linear solution to the relative pose and a closed-form solution to the absolute pose can be derived with known camera vertical directions. We incorporate our formulations with the general structure from motion framework followed by the patch-based multiview stereo algorithm to obtain a 3D reconstruction of the scene. We show through experiments that the explicit modeling of depth-dependent refractive distortion physically leads to more accurate scene reconstructions.

Gradient Flows for Optimizing Triangular Mesh-based Surfaces: Applications to 3D Reconstruction Problems Dealing with Visibility

Abstract: This article tackles the problem of using variational methods for evolving 3D deformable surfaces. We give an overview of gradient descent flows when the shape is represented by a triangular mesh-based surface, and we detail the gradients of two generic energy functionals which embody a number of energies used in mesh processing and computer vision. In particular, we show how to rigorously account for visibility in the surface optimization process. We present different applications including 3D reconstruction from multiple views for which the visibility is fundamental. The gradient correctly takes into account the visibility changes that occur when a surface moves; this forces the contours generated by the reconstructed surface to match with the apparent contours in the input images.

Automated articulated structure and 3D shape recovery from point correspondences

Abstract: In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based articulated motion. We decompose a set of point tracks into rigid-bodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the regions of overlap. This allows us to formulate the problem of 3D reconstruction as one of model assignment, where each model corresponds to the motion and shape parameters of an articulated body part. We show how this labelling can be optimised using a combination of pre-existing graph-cut based inference, and robust structure from motion factorization techniques. The strength of our approach comes from viewing both the decomposition into parts, and the 3D reconstruction as the optimisation of a single cost function, namely the image re-projection error. We show results of full 3D shape recovery on challenging real-world sequences with one or more articulated bodies, in the presence of outliers and missing data.

Procedural 3D Building Reconstruction Using Shape Grammars and Detectors

Abstract: We propose a novel grammar-driven approach for reconstruction of buildings and landmarks. Our approach complements Structure-from-Motion and image-based analysis with a 'inverse' procedural modeling strategy. So far, procedural modeling has mostly been used for creation of virtual buildings, while the inverse approaches typically focus on reconstruction of single facades. In our work, we reconstruct complete buildings as procedural models using template shape grammars. In the reconstruction process, we let the grammar interpreter automatically decide on which step to take next. The process can be seen as instantiating the template by determining the correct grammar parameters. As an example, we have chosen the reconstruction of Greek Doric temples. This process significantly differs from single facade segmentation due to the immediate need for 3D reconstruction.

Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization

Abstract: Recent works have demonstrated that three-dimensional (3D) object reconstruction is possible from integral images captured in severely photon starved conditions. In this paper we propose an iterative approach to implement a maximum likelihood expectation maximization estimator with several types of regularization for 3D reconstruction from photon counting integral images. We show that the proposed algorithms outperform the previously reported approaches for photon counting 3D integral imaging reconstruction. To the best of our knowledge, this is the first report on using iterative statistical reconstruction techniques for 3D photon counting integral imaging.

Event-based stereo matching approaches for frameless address event stereo data

Abstract: In this paper we present different approaches of 3D stereo matching for bio-inspired image sensors. In contrast to conventional digital cameras, this image sensor, called Silicon Retina, delivers asynchronous events instead of synchronous intensity or color images. The events represent either an increase (on-event) or a decrease (off-event) of a pixel's intensity. The sensor can provide events with a time resolution of up to 1ms and it operates in a dynamic range of up to 120dB. In this work we use two silicon retina cameras as a stereo sensor setup for 3D reconstruction of the observed scene, as already known from conventional cameras. The polarity, the timestamp, and a history of the events are used for stereo matching. Due to the different information content and data type of the events, in comparison to conventional pixels, standard stereo matching approaches cannot directly be used. Thus, we developed an area-based, an event-image-based, and a time-based approach and evaluated the results achieving promising results for stereo matching based on events.

Dense one-shot 3D reconstruction by detecting continuous regions with parallel line projection

Abstract: 3D scanning of moving objects has many applications, for example, marker-less motion capture, analysis on fluid dynamics, object explosion and so on. One of the approach to acquire accurate shape is a projector-camera system, especially the methods that reconstructs a shape by using a single image with static pattern is suitable for capturing fast moving object. In this paper, we propose a method that uses a grid pattern consisting of sets of parallel lines. The pattern is spatially encoded by a periodic color pattern. While informations are sparse in the camera image, the proposed method extracts the dense (pixel-wise) phase informations from the sparse pattern. As the result, continuous regions in the camera images can be extracted by analyzing the phase. Since there remain one DOF for each region, we propose the linear solution to eliminate the DOF by using geometric informations of the devices, i.e. epipolar constraint. In addition, solution space is finite because projected pattern consists of parallel lines with same intervals, the linear equation can be efficiently solved by integer least square method. In this paper, the formulations for both single and multiple projectors are presented. We evaluated the accuracy of correspondences and showed the comparison with respect to the number of projectors by simulation. Finally, the dense 3D reconstruction of moving objects are presented in the experiments.

Single-camera panoramic stereo imaging system with a fisheye lens and a convex mirror

Abstract: This paper presents a panoramic stereo imaging system which uses a single camera coaxially combined with a fisheye lens and a convex mirror. It provides the design methodology, trade analysis, and experimental results using commercially available components. The trade study shows the design equations and the various tradeoffs that must be made during design. The system’s novelty is that it provides stereo vision over a full 360-degree horizontal field-of-view (FOV). Meanwhile, the entire vertical FOV is enlarged compared to the existing systems. The system is calibrated with a computational model that can accommodate the non-single viewpoint imaging cases to conduct 3D reconstruction in Euclidean space.

Decomposition of Complex Line Drawings with Hidden Lines for 3D Planar-Faced Manifold Object Reconstruction

Abstract: Three-dimensional object reconstruction from a single 2D line drawing is an important problem in computer vision. Many methods have been presented to solve this problem, but they usually fail when the geometric structure of a 3D object becomes complex. In this paper, a novel approach based on a divide-and-conquer strategy is proposed to handle the 3D reconstruction of a planar-faced complex manifold object from its 2D line drawing with hidden lines visible. The approach consists of four steps: 1) identifying the internal faces of the line drawing, 2) decomposing the line drawing into multiple simpler ones based on the internal faces, 3) reconstructing the 3D shapes from these simpler line drawings, and 4) merging the 3D shapes into one complete object represented by the original line drawing. A number of examples are provided to show that our approach can handle 3D reconstruction of more complex objects than previous methods.

Detailed reconstruction of 3D plant root shape

Abstract: We study the 3D reconstruction of plant roots from multiple 2D images. To meet the challenge caused by the delicate nature of thin branches, we make three innovations to cope with the sensitivity to image quality and calibration. First, we model the background as a harmonic function to improve the segmentation of the root in each 2D image. Second, we develop the concept of the regularized visual hull which reduces the effect of jittering and refraction by ensuring consistency with one 2D image. Third, we guarantee connectedness through adjustments to the 3D reconstruction that minimize global error. Our software is part of a biological phenotype/genotype study of agricultural root systems. It has been tested on more than 40 plant roots and results are promising in terms of reconstruction quality and efficiency.

3D motion reconstruction for real-world camera motion

Abstract: This paper addresses the problem of 3D motion reconstruction from a series of 2D projections under low reconstructibility. Reconstructibility defines the accuracy of a 3D reconstruction from 2D projections given a particular trajectory basis, 3D point trajectory, and 3D camera center trajectory. Reconstructibility accuracy is inherently related to the correlation between point and camera trajectories. Poor correlation leads to good reconstruction, high correlation leads to poor reconstruction. Unfortunately, in most real-world situations involving non-rigid objects (e.g. bodies), camera and point motions are highly correlated (i.e., slow and smooth) resulting in poor reconstructibility. In this paper, we propose a novel approach for 3D motion reconstruction of non-rigid body motion in the presence of real-world camera motion. Specifically we: (i) propose the inclusion of a small number of keyframes in the video sequence from which 3D coordinates are inferred/estimated to circumvent ambiguities between point and camera motion, and (ii) employ a L 1 penalty term to enforce a spar-sity constraint on the trajectory basis coefficients so as to ensure our reconstructions are consistent with the natural compressibility of human motion. We demonstrate impressive 3D motion reconstruction for 2D projection sequences with hitherto low reconstructibility.

Incremental free-space carving for real-time 3D reconstruction

Abstract: Almost all current multi-view methods are slow, and thus suited to offline reconstruction. This paper presents a set o f heuristic space-carving algorithms with a focus on speed over detail. The algorithms discretize space via the 3D Delaunay triangulation, and they carve away the volumes that violate free-space or visibility constraints. Whereas sim ilar methods exist, our algorithms are fast and fully incrementa l. They encompass a dynamic event-driven approach to reconstruction that is suitable for integration with online SLAM or Structure-from-Motion. We integrate our algorithms with PTAM [ 12], and we realize a complete system that reconstructs 3D geometry from video in real-time. Experiments on typical real-world inpu ts demonstrate online performance with modest hardware. We provide run-time complexity analysis and show that the perevent processing time is independent of the number of images previously processed: a requirement for real-time operation on lengthy image sequences.