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The unceasing quest for a profound comprehension of the Earth system propels the continuous evolution of novel methods for Earth observation. Of these, the Lagrange points situated in the cislunar space proffer noteworthy prospects for space-based Earth observation. Although extant research predominantly centers on Moon-based Earth observation and the L1 point within the Sun-Earth system, the realm of cislunar space remains relatively unexplored. This paper scrutinizes the overarching characteristics of the L1 point within the Earth-Moon system concerning Earth observation. A pivotal enhancement is introduced through the incorporation of the halo orbit. This research comprehensively analyzes the relative motion between the halo orbiter and the Earth, achieved via orbit determination within a rotating coordinate system, followed by a transformation into the Earth coordinate system. Subsequently, numerical simulations employing ephemeris data unveil the observing geometry and Earth observation characteristics, encompassing the distribution of nadir points, viewing angles, and the spatiotemporal ground coverage. As a point of reference, we also present a case study involving a Moon-based platform. Our findings reveal that the motion of the halo orbit, perpendicular to the lunar orbital plane, results in a broader range of nadir point latitudes, which can extend beyond 42°N/S, contingent upon the orbit's size. Additionally, it manifests a more intricate latitude variation, characterized by the bimodal peaks of the proposed temporal complexity curve. The viewing angles and the spatiotemporal ground coverage closely resemble those of Moon-based platforms, with a marginal enhancement in coverage frequency for polar regions. Consequently, it can be deduced that the Earth observation characteristics of the L1 point within the Earth-Moon system bear a close resemblance to those of Moon-based platforms. Nevertheless, considering the distinct advantages of Moon-based platforms, the lunar surface remains the paramount choice, boasting the highest potential for Earth observation within cislunar space. In summation, this study demonstrates the Earth observation characteristics of the L1 point within the Earth-Moon system, emphasizing the distinctions between this and Moon-based platforms. [ABSTRACT FROM AUTHOR]

Camera imaging through refractive interfaces is a crucial issue in photogrammetric measurements. Most past studies adopted numerical optimization algorithms based on refractive ray tracing procedures. In these studies, the camera and interface parameters are usually calculated iteratively with numerical optimization algorithms. Inappropriate initial values can cause iterations to diverge. Meanwhile, these iterations cannot efficiently reveal the accurate nature of refractive imaging. Therefore, obtaining camera calibration results that are both flexible and physically interpretable continues to be challenging. Consequently, in this study, we modeled refractive imaging by employing ray transfer matrix analysis. Subsequently, we deduced an analytical refractive imaging (ARI) equation that explicitly describes the refractive geometry in a matrix form. Although this equation is built upon the paraxial approximation, we executed a numerical experiment that shows that the developed analytical equation can accurately illustrate refractive imaging with a considerable object distance and a slightly tilted angle of the flat interface. This ARI equation can be used to define the expansion center and the normal vector of the flat interface. Finally, we also propose a flexible measurement method to determine the orientation of the flat interface, wherein the orientation can be measured rather than calculated by iterative procedures. • Proposed an Analytical Refractive Imaging equation that shows the projection of a 3D point onto a 2D image point through a flat interface. • Derived the form of the expansion center and presented a simple calibration method to determine the direction of the refracted interface. • The equation and calibration method offer precise optical measurement alternatives for refracted vision calibration issues. [ABSTRACT FROM AUTHOR]

Moon-based synthetic aperture radar (SAR) offers unprecedented temporal and spatial coverage. Its repeat-pass interferometry is expected to play a substantial role in earth science because of its large-scale, long-term, near 24.8 h revisit period, and stable earth observation ability. However, it faces a greater challenge when the signal passes through the ionosphere compared with the low Earth orbit (LEO) satellite. In this study, we constructed a total electron content (hereafter referred to as TEC) calculation model for the propagation path of a moon-based SAR signal based on International reference ionosphere model and moon-based SAR interferometry (InSAR) geometry. Subsequently, the ionospheric delay at various carrier frequencies was quantitatively evaluated under different time baseline types. The results show that the interferometric phase space gradient caused by ionospheric can reach ten times that of LEO SAR satellites with superposition of diurnal and seasonal ionospheric variations. In addition, this problem in the observation area with a large incident angle is more severe, which limits the effective swath width of moon-based repeat-pass InSAR. The ionospheric delay effects can be avoided to some extent by selecting the interference combination at nighttime or approaching the solar altitude angle. To highlight the large-scale ground deformation information in most cases and give full play to the long-term and stable observation advantages of the moon-based platform, accurate ionospheric correction or compensation must be considered.

In man-made environments, most of the objects and structures are organized in the form of orthogonal and parallel planes. These planes can be approximated by an Atlanta world assumption, in which the normals of planes can be represented by Atlanta frames. The Atlanta world assumption has one vertical frame and multiple horizontal frames. Conventionally, given a set of inputs such as surface normals, the Atlanta frame estimation problem can be solved by a branch-and-bound (BnB) algorithm. However, the runtime of the BnB algorithm will increase greatly when the dimensionality (i.e., the number of horizontal frames) increases. In this paper, we estimate only the vertical direction, instead of all Atlanta frames at once. Accordingly, we propose a vertical direction estimation method by considering the relationship between the vertical frame and horizontal frames. Concretely, our approach employs a BnB algorithm to search the vertical direction, thereby guaranteeing global optimality without requiring prior knowledge of the number of Atlanta frames. In order to guarantee convergence, four novel bounds are investigated, by mapping a 3D hemisphere to a 2D region. We verify the feasibility of the proposed method using various challenging synthetic and real-world data. [ABSTRACT FROM AUTHOR]

The spatiotemporal coverage of a Moon-based synthetic aperture radar (SAR) is analyzed based on the imaging geometry, upon which the spatial coverage and image formulation rely. The distance from the Earth to the Moon-based SAR and bounds of the grazing and azimuthal angles jointly determine the coverage area on the Earth’s surface. Meanwhile, the ground coverage of the Moon-based SAR is determined by the bounds of the grazing and azimuthal angles and geographic coordinates of the nadir point at a specified time. Moreover, the temporal variation in the spatial coverage is pertinent to the temporally varying nadir point of the Moon-based SAR on the Earth’s surface. Furthermore, numerical simulations using the lunar ephemeris data are carried out to complement the analysis and to illustrate the spatiotemporal coverage. Finally, a guideline for the optimal site selection of a Moon-based SAR is proposed. In conclusion, a Moon-based SAR has the potential to perform long-term, continuous Earth observations on a global scale to enhance our capability to understand the planet. [ABSTRACT FROM AUTHOR]

We present here a comprehensive imaging theory about cone mirrors in a single-view-point (SVP) configuration and show that an SVP cone mirror catadioptric system is not only practical but also has unique advantages for certain applications. We show its merits and weaknesses and how to build a workable system.

Estimating the 6-DoF pose of a camera from a single image relative to a 3D point-set is an important task for many computer vision applications. Perspective-n-point solvers are routinely used for camera pose estimation, but are contingent on the provision of good quality 2D–3D correspondences. However, finding cross-modality correspondences between 2D image points and a 3D point-set is non-trivial, particularly when only geometric information is known. Existing approaches to the simultaneous pose and correspondence problem use local optimisation, and are therefore unlikely to find the optimal solution without a good pose initialisation, or introduce restrictive assumptions. Since a large proportion of outliers and many local optima are common for this problem, we instead propose a robust and globally-optimal inlier set maximisation approach that jointly estimates the optimal camera pose and correspondences. Our approach employs branch-and-bound to search the 6D space of camera poses, guaranteeing global optimality without requiring a pose prior. The geometry of SE(3) is used to find novel upper and lower bounds on the number of inliers and local optimisation is integrated to accelerate convergence. The algorithm outperforms existing approaches on challenging synthetic and real datasets, reliably finding the global optimum, with a GPU implementation greatly reducing runtime. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to control the pose of a camera mounted on a two-axis gimbal system for visual servoing applications. In these applications, the camera should be stable while its line-of-sight points at a target located within the camera’s field of view. One of the most challenging aspects of these systems is the coupling in the gimbal kinematics as well as the imaging geometry. Such factors must be considered in the control system design process to achieve better control performances. The novelty of this study is that the couplings in both mechanism’s kinematics and imaging geometry are decoupled simultaneously by a new technique, so popular control methods can be easily implemented, and good tracking performances are obtained. The proposed control configuration includes a calculation of the gimbal’s desired motion taking into account the coupling influence, and a control law derived by the backstepping procedure. Simulation and experimental studies were conducted, and their results validate the efficiency of the proposed control system. Moreover, comparison studies are conducted between the proposed control scheme, the image-based pointing control, and the decoupled control. This proves the superiority of the proposed approach that requires fewer measurements and results in smoother transient responses.

Objectives: The objective was to evaluate a visible-light-transillumination (using Digital Imaging Fiber-Optic Transillumination machine: DIFOTI) method using occlusal view (DIFOTI-occl), axial view (buccal and lingual: DIFOTI-axial), and combination of all views (DIFOTI-all) for detecting non-cavitated approximal caries and to compare its performance to visual examination (International Caries Detection and Assessment System: ICDAS). Materials and methods: Thirty extracted human premolars were selected (sound to lesions into the outer one-third of the dentine) based on micro-computed tomography (μ-CT). Teeth were mounted in a custom-made device to simulate approximal contact. DIFOTI (Electro-Optical Sciences Inc., Irvington, NY, USA) images were obtained from the occlusal, buccal, and lingual views. DIFOTI image and ICDAS examinations were performed and repeated by three trained/calibrated examiners. Sensitivity, specificity, area under receiver operating characteristics curve (Az), inter- and intra-class correlation coefficients (ICCs), and correlation were determined. Results: Sensitivity/specificity was for DIFOTI-occl: 0.42/0.75, DIFOTI-axial: 0.86/0.93, DIFOTI-all: 0.91/0.69, and for ICDAS: 0.89/0.83. Az for DIFOTI-occl was significantly lower than that of DIFOTI-axial (p < 0.001), DIFOTI-all (p = 0.002), and ICDAS (p = 0.005). Spearman correlation coefficients with μ-CT for DIFOTI-occl (r = 0.39) showed weak association, while DIFOTI-axial (r = 0.80), DIFOTI-all (r = 0.91), and ICDAS (r = 0.90) showed moderate association. ICCs for intra-examiner repeatability/inter-examiner agreement were for DIFOTI-occl (0.64/0.58), DIFOTI-axial (0.92/0.89), DIFOTI-all (0.85/0.83), and ICDAS (0.79/0.72). Conclusions: The results of the current in vitro study suggest that, for detection of non-cavitated approximal caries lesions, DIFOTI performs better using axial than occlusal view. Clinical relevance: Approximal non-cavitated caries detection is challenging. DIFOTI can observe images from occlusal-, buccal-, and lingual views. DIFOTI and visual (ICDAS) examinations of buccal- and lingual- and all-views are more suitable than those of occlusal view for a detection of non-cavitated approximal caries. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the dependency of oil spill observations in polarimetric SAR data on imaging geometry, i.e., on incidence angle and look direction relative to the wind. The study is based on quad-polarization data acquired by the Uninhabited Aerial Vehicle Synthetic Aperture Radar over experimental oil slicks under relatively high winds of 10–12 m/s over an 8-hour period. The data is collected over a wide range of incidence angles and alternates between looking upwind (UW) and downwind (DW). The unique time series enables a detailed study of the behavior of multipolarization parameters over clean sea and oil slicks under varying imaging geometry to be carried out for the first time. For clean sea backscatter, our findings are in agreement with previous studies, showing decreasing backscatter as the incidence angle increases and from UW to DW, with the highest sensitivity in the HH channel. We also find similar variations in oil covered areas. The results suggest that the oil slick backscatter is slightly more sensitive to the relative wind direction than the clean sea, and higher oil-sea damping ratios are found in DW than in UW cases, particularly in the HH channel. All multipolarization features investigated have some degree of dependency on imaging geometry. The lowest sensitivities are found in the magnitude of the copolarization correlation coefficient, the standard deviation of the copolarized phase difference, the polarization difference, the mean scattering angle and the entropy. Several features clearly change behavior when the signal approaches the sensor noise floor, and we find that the measurements and derived parameters may be affected at even higher signal-to-noise ratio (SNR) levels than previously proposed, i.e., closer to 7–9 dB above the sensor noise floor. Overall, the polarization difference is clearly identified as the most interesting parameter for oil spill observation, producing high oil-sea contrast in addition to low sensitivity to imaging geometry. The results show that both the relative wind direction and the incidence angle, in combination with the SNR, should be taken into account when developing operational methods based on multipolarization SAR data. [ABSTRACT FROM AUTHOR]

This paper proposes a robust feature-based mosaicking method that can handle images obtained by lightweight unmanned aerial vehicles (UAVs). The imaging geometry of small UAVs can be characterized by unstable flight attitudes and low flight altitudes. These can reduce mosaicking performance by causing insufficient overlaps, tilted images, and biased tiepoint distributions. To solve these problems in the mosaicking process, we introduce the tiepoint area ratio (TAR) as a geometric stability indicator and orthogonality as an image deformation indicator. The proposed method estimates pairwise transformations with optimal transformation models derived by geometric stability analysis between adjacent images. It then estimates global transformations from optimal pairwise transformations that maximize geometric stability between adjacent images and minimize mosaic deformation. The valid criterion for the TAR in selecting an optimal transformation model was found to be about 0.3 from experiments with two independent image datasets. The results of a performance evaluation showed that the problems caused by the imaging geometry characteristics of small UAVs could actually occur in image datasets and showed that the proposed method could reliably produce image mosaics for image datasets obtained in both general and extreme imaging environments.

Sea surface roughness (SSR) is a key physical parameter in studies of air–sea interactions and the ocean dynamics process. The SSR quantitative inversion model based on multi-angle sun glitter (SG) images has been proposed recently, which will significantly promote SSR observations through multi-angle remote-sensing platforms. However, due to the sensitivity of the sensor view angle (SVA) to SG, it is necessary to determine the optimal imaging angle and their combinations. In this study, considering the design optimization of imaging geometry for multi-angle remote-sensing platforms, we have developed an error transfer simulation model based on the multi-angle SG remote-sensing radiation transmission and SSR estimation models. We simulate SSR estimation errors at different imaging geometry combinations to evaluate the optimal observation geometry combination. The results show that increased SSR inversion accuracy can be obtained with SVA combinations of 0° and 20° for nadir- and backward-looking SVA compared with current combinations of 0° and 27.6°. We found that SSR inversion prediction error using the proposed model and actual SSR inversion error from field buoy data are correlated. These results can provide support for the design optimization of imaging geometry for multi-angle ocean remote-sensing platforms.

In real applications, a pinhole camera capturing objects through a planar parallel transparent plate is frequently employed. Due to the refractive effects of the plate, such an imaging system does not comply with the conventional pinhole camera model. Although the system is ubiquitous, it has not been thoroughly studied. This paper aims at presenting a simple virtual camera model, called a plate refractive camera model, which has a form similar to a pinhole camera model and can efficiently model refractions through a plate. The key idea is to employ a pixel-wise viewpoint concept to encode the refraction effects into a pixel-wise pinhole camera model. The proposed camera model realizes an efficient forward projection computation method and has some advantages in applications. First, the model can help to compute the caustic surface to represent the changes of the camera viewpoints. Second, the model has strengths in analyzing and rectifying the image caustic distortion caused by the plate refraction effects. Third, the model can be used to calibrate the camera's intrinsic parameters without removing the plate. Last but not least, the model contributes to putting forward the plate refractive triangulation methods in order to solve the plate refractive triangulation problem easily in multiviews. We verify our theory in both synthetic and real experiments. [ABSTRACT FROM AUTHOR]

Before applying change detection, high resolution SAR (Synthetic Aperture Radar) imagery benefits from advanced denoising mechanisms to preserve details and minimize speckle. We propose a change detector based on a MCA (Morphological Components Analysis) of a difference image (DI). With MCA, the data is decomposed into image features utilizing sparse representations of the image content. By introducing a priori knowledge of the content of the scenes, and exploiting shape information corresponding to the changes provided by MCA, we can significantly improve performance under adverse conditions, such as inconsistent acquisition geometries. [ABSTRACT FROM AUTHOR]

Catadioptric systems consist of the combination of lenses and mirrors. From them, central panoramic systems stand out because they provide a unique effective viewpoint, leading to the well-known unifying theory for central catadioptric systems. This paper considers catadioptric systems consisting of a conical mirror and a perspective camera. Although a system with conical mirror does not possess a single projection point, it has some advantages as the cone is a very simple shape to produce, it has higher resolution in the peripheral, and adds less optical distortion to the images. The contributions of this work are the model of this non-central system by means of projective mappings from a torus to a plane, the procedure to calibrate this system, and the definition of the conical fundamental matrix with a role similar to that of perspective cameras. Additionally, a procedure to compute the relative motion between two views from the conical fundamental matrix is presented. The proposal is illustrated with simulations and real experiments. [ABSTRACT FROM AUTHOR]

The efficiency of interior orientation parameters (IOPs) and exterior orientation parameters (EOPs) of the Satellite Pour l'Observation de la Terre 5 (SPOT-5) has been investigated with respect to georeferencing accuracy. A couple of SPOT-5 high-resolution geometric panchromatic level-1A stereoimages with 5-m ground sampling distance covering Zonguldak (Turkey) test field were used for this purpose using orientation parameters provided by metadata files. Ground control points are obtained by Global Positioning System observations. For the purpose of establishing geometric relationship between image and ground coordinate systems, an orbit-attitude parametric model has been used considering imaging geometry of sensor and ephemeris data of satellite. Adjustment consisting of the Gauss-Helmert model was performed in pre- and bundle-adjustment steps. Analyses show that the most efficient parameters are IOPs defined by look angles while EOPs are not significant on the accuracy. The validation of the EOPs and the correlation among IOPs and EOPs are also statistically analyzed. Different variations of point distribution and EOP configurations were preferred, achieving the georeferencing accuracies as ~ ±1 m and ~ ± 5 m at control and check points, respectively. All computations are performed via the developed program package called GeoSpot in Matlab platform. [ABSTRACT FROM PUBLISHER]

We proposed a novel rotation-invariant feature based passive ranging algorithm to estimate the distance of an imaged non-cooperation target to camera. This improved algorithm avoids sometimes occurrence of physically unreasonable results in solving the existing quartic equation, such as the happening of complex or negative value. This method uses three matched points in two adjacent frames of an image sequence to extract depth-dependent line features of the target. With this line features combination of the observer's displacement and imaging directions, a quadratic equation was build to estimate the distance. Analysis shows that the proposed new passive ranging equation would be solvable when the observer is with non-zero displacement in adjacent sampling instances. Our reduced-model experiment also demonstrates that the proposed algorithm is not only simple and feasible but also with a relative ranging error no more than 4 per cent in most cases. [ABSTRACT FROM AUTHOR]

The high resolution of digital cameras has made single-shot, single-sensor acquisition of light fields feasible, though considerable design effort is still necessary in order to construct the necessary collection of optical elements for particular acquisition scenarios. This paper explores a pipeline for designing, fabricating and utilizing faceted mirror arrays which simplifies this task. The foundation of the pipeline is an interactive tool that automatically optimizes for mirror designs while exposing to the user a set of intuitive parameters for light field quality and manufacturing constraints. We investigate two manufacturing processes for automatic fabrication of the resulting designs: one is based on CNC milling, polishing, and plating of one solid work piece, while the other involves assembly of CNC-cut mirror facets. We demonstrate results for refocusing in a macro photography scenario. In addition, we observe that traditional photographic parameters take novel roles in the faceted mirror array setup and discuss their influence. [ABSTRACT FROM AUTHOR]

Circular-aperture synthetic aperture radar (SAR) imaging has been evaluated using the airborne very high frequency (VHF) band Coherent All RAdio BAnd Sensing (CARABAS)-II system (20-90 MHz). Images, as well as results, from detection of vehicles in dense forest concealment have been compared with linear-aperture SAR. Circular-aperture SAR imaging provides higher image resolution and increased object information, but complexity of signal processing and requirements on imaging geometry accuracy increases. The latter is, however, partly mitigated by using low frequencies in the VHF band. A high-quality digital elevation model is used to ensure high-quality image focusing and to avoid distorting object shape. Contrast optimization is used to reduce global focusing errors. The image resolution is observed to be about 1 m2 in agreement with theoretical predictions. Detection performance has been evaluated using image data from a full circular synthetic aperture, i.e., 360° of aspect angle variation. Results, both for single-pass detection (SPD) and change detection (CD), show a considerable advantage compared with detection based on linear-aperture SAR. The detection probability for SPD increases from 0.4 to 0.8 at a false-alarm rate (FAR) of 30/km2. For CD, the detection probability increases from 0.7 to 0.9 at a FAR of 2/km2. [ABSTRACT FROM AUTHOR]

The precision of georeferencing of pushbroom satellite images without using ground control points is estimated. The study includes what-if scenarios for various precisions of star trackers, GPS receivers, image acquisition timing, interior camera parameters, and digital elevation model (DEM). Moreover, the effects of satellite altitude and sensor positions on the pushbroom array are also taken into account. The probability distribution function of the input parameters is determined by considering the sensor characteristics, environmental effects, and assumptions. The precision of the georeferenced coordinates is estimated by Monte Carlo simulation and differential sensitivity analysis. The analyses provide the most probable georeferenced coordinates and their precision for a certain precision of sensors and imaging geometry. The study is conducted based on the BilSAT orbit and SPOT 5 and Landsat optical system characteristics. An Shuttle Radar Topography Mission (SRTM) DEM and a DEM obtained from stereo images are used in georeferencing. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of factorization-based 3D reconstruction from uncalibrated image sequences. Previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection. The affine approximation is widely adopted due to its simplicity, whereas the extension to perspective model suffers from recovering projective depths. To fill the gap between simplicity of affine and accuracy of perspective model, we propose a quasi-perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework. The novelty and contribution of this paper are as follows. Firstly, under the assumption that the camera is far away from the object with small lateral rotations, we prove that the imaging process can be modeled by quasi-perspective projection, which is more accurate than affine model from both geometrical error analysis and experimental studies. Secondly, we apply the model to establish a framework of rigid and nonrigid factorization under quasi-perspective assumption. Finally, we propose an Extended Cholesky Decomposition to recover the rotation part of the Euclidean upgrading matrix. We also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely. The proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed. [ABSTRACT FROM AUTHOR]

Accurate measurement of the position' of features in an image is subject to a fundamental compromise: The features must be both small, to limit the effect of nonlinear distortions, and large, to limit the effect of noise and discretization. This constrains both the accuracy and the robustness of image measurements, which play an important role in geometric camera calibration as well as in all subsequent measurements based on that calibration. In this paper, we present a new geometric camera calibration technique that exploits the complete camera model during the localization of control markers, thereby abolishing the marker size compromise. Large markers allow a dense pattern to be used instead of a simple disc, resulting in a significant increase in accuracy and robustness. When highly planar markers are used, geometric camera calibration based on synthetic images leads to true errors of 0.002 pixels, even in the presence of artifacts such as noise, illumination gradients, compression, blurring, and limited dynamic range. The camera parameters are also accurately recovered, even for complex camera models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable is it that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate correspondence pair? If we knew the true fundamental matrix, the answer would be trivial but in reality we do not know it because of estimation errors. So, as an independent point in the first view is given, we will show we may compute the point-probability-density function, termed as the epipolar pdf, for the epipolar line points in the second view that describes the current level of knowledge of the epipolar geometry between the views. This point–point-probability-density relation is a probabilistic form of the epipolar constraint that also approaches the true point–line relation as the number of training correspondences tends to infinity. In this paper, we will also show that the eigenvectors of the epipolar line covariance matrix have certain interpretations on the image plane, of which one is the previously observed, narrowest point of the epipolar envelope. The results of this paper are important since the uncertainty of the epipolar constraint can be now taken into account in a sound way in applications. [Copyright &y& Elsevier]

The paper presents a new set of axioms of digital topology, which are easily understandable for application developers. They define a class of locally finite (LF) topological spaces. An important property of LF spaces satisfying the axioms is that the neighborhood relation is antisymmetric and transitive. Therefore any connected and non-trivial LF space is isomorphic to an abstract cell complex. The paper demonstrates that in an n-dimensional digital space only those of the ( a, b)-adjacencies commonly used in computer imagery have analogs among the LF spaces, in which a and b are different and one of the adjacencies is the “maximal” one, corresponding to 3 n − 1 neighbors. Even these ( a, b)-adjacencies have important limitations and drawbacks. The most important one is that they are applicable only to binary images. The way of easily using LF spaces in computer imagery on standard orthogonal grids containing only pixels or voxels and no cells of lower dimensions is suggested. [ABSTRACT FROM AUTHOR]

We present here a comprehensive imaging theory about cone mirrors in a single-view-point (SVP) configuration and show that an SVP cone mirror catadioptric system is not only practical but also has unique advantages for certain applications. We show its merits and weaknesses and how to build a workable system. [ABSTRACT FROM AUTHOR]

The goal of this paper is to provide a "self-adaptive" system for real-time range acquisition. Reconstructions are based on a single frame structured light illumination. Instead of using generic, static coding that is supposed to work under all circumstances, system adaptation is proposed. This occurs on-the-fly and renders the system more robust against instant scene variability and creates suitable patterns at startup. A continuous trade-off between speed and quality is made. A weighted combination of different coding cues—based upon pattern color, geometry, and tracking—yields a robust way to solve the correspondence problem. The individual coding cues are automatically adapted within a considered family of patterns. The weights to combine them are based on the average consistency with the result within a small time-window. The integration itself is done by reformulating the problem as a graph cut. Also, the camera-projector configuration is taken into account for generating the projection patterns. The correctness of the range maps is not guaranteed, but an estimation of the uncertainty is provided for each part of the reconstruction. Our prototype is implemented using unmodified consumer hardware only and, therefore, is cheap. Frame rates vary between 10 and 25 fps, dependent on scene complexity. [ABSTRACT FROM AUTHOR]

This paper proposes a visual representation named scene tunnel for capturing urban scenes along routes and visualizing them on the Internet. We scan scenes with multiple cameras or a fish-eye camera on a moving vehicle, which generates a real scene archive along streets that is more complete than previously proposed route panoramas. Using a translating spherical eye, properly set planes of scanning, and unique parallel-central projection, we explore the image acquisition of the scene tunnel from camera selection and alignment, slit calculation, scene scanning, to image integration. The scene tunnels cover high buildings, ground, and various viewing directions and have uniformed resolutions along the street. The sequentially organized scene tunnel benefits texture mapping onto the urban models. We analyze the shape characteristics in the scene tunnels for designing visualization algorithms. After combining this with a global panorama and forward image caps, the capped scene tunnels can provide continuous views directly for virtual or real navigation in a city. We render scene tunnel dynamically by view warping, fast transmission, and flexible interaction. The compact and continuous scene tunnel facilitates model construction, data streaming, and seamless route traversing on the Internet and mobile devices. [ABSTRACT FROM AUTHOR]

It is well known that without any priori knowledge on the scene, camera motion and camera intrinsic parameters, the only constraint between a pair of images is the so-called epipolar constraint, or equivalently its fundamental matrix. For each fundamental matrix, at most two independent constraints on the cameras’ intrinsic parameters are available via the Kruppa equations. Given N images, N( N−1)/2 fundamental matrices appear, and N( N−1) Kruppa constraints are available. However, to our knowledge, a formal proof of how many independent Kruppa constraints exist out of these N( N−1) ones is unavailable in the literature. In this paper, we prove that given N images captured by a pinhole camera with varying parameters and under general motion, the number of independent Kruppa constraints is (5 N−9) ( N > 2), and it is less than that of independent constraints from the absolute quadric by only one. This one-constraint-less property of the Kruppa equations is their inherent deficiency and is independent of camera motion. This deficiency is due to their failure of automatic enforcement of the rank-three-ness on the absolute quadric. [ABSTRACT FROM AUTHOR]

This paper presents a method for calibrating a projector-camera system that consists of multiple projectors (or multiple poses of a single projector), a camera, and a planar screen. We consider the problem of estimating the homography between the screen and the image plane of the camera or the screen-camera homography, in the case where there is no prior knowledge regarding the screen surface that enables the direct computation of the homography. It is assumed that the pose of each projector is unknown while its internal geometry is known. Subsequently, it is shown that the screen-camera homography can be determined from only the images projected by the projectors and then obtained by the camera, up to a transformation with four degrees of freedom. This transformation corresponds to arbitrariness in choosing a two-dimensional coordinate system on the screen surface and when this coordinate system is chosen in some manner, the screen-camera homography as well as the unknown poses of the projectors can be uniquely determined. A noniterative algorithm is presented, which computes the homography from three or more images. Several experimental results on synthetic as well as real images are shown to demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract: We present a method to simultaneously reconstruct cameras, points, lines, degenerate quadrics and full-rank quadrics from a set of n uncalibrated views of a static scene. Our method is based on the use of Bundle Adjustment to refine an initial reconstruction. During the initialization stage, a novel algorithm was proposed for the conic outline correction in n views. Constrains derived from this algorithm were also integrated in the cost function of Bundle Adjustment to help preserve the right topology of the reconstructed quadrics. [Copyright &y& Elsevier]

Abstract: In this paper we present an algorithm for the simultaneous projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using Bundle Adjustment. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. Furthermore, for the reconstruction of quadrics (both full-rank and degenerate) and plane conics, a novel algorithm for the rectification of the outlines projected in n views is presented. Finally, we found out that due to the noise in the data, the global minimum of the classic cost function used in Bundle Adjustment may unfortunately break the topology of the quadrics. Hence, during the iterations of this method, we need to add the constraints to keep the quadrics within acceptable limits to preserve their topology. [Copyright &y& Elsevier]

An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and, subsequently, finding its roots. It is the first algorithm well- suited for numerical implementation that also corresponds to the inherent complexity of the problem. We investigate the numerical precision of the algorithm. We also study its performance under noise in minimal as well as overdetermined cases. The performance is compared to that of the well-known 8 and 7-point methods and a 6-point scheme. The algorithm is used in a robust hypothesize-and- test framework to estimate structure and motion in real-time with low delay. The real-time system uses solely visual input and has been demonstrated at major conferences. [ABSTRACT FROM AUTHOR]

A new approach to camera calibration using vanishing line information for three-dimensional computer vision is proposed. Calibrated parameters include the orientation, the position, the focal length, and the image plane center of a camera. A rectangular parallelepiped is employed as the calibration target to generate three principal vanishing points and then three vanishing lines from the projected image of the parallelepiped. Only a monocular image is required for solving these camera parameters. It is shown that the image plane center is the orthocenter of a triangle formed by the three vanishing lines. From the slopes of the vanishing lines the camera orientation parameters can be determined. The focal length can be computed by the area of the triangle. The camera position parameters can then be calibrated by using related geometric projective relationships. The derived results show the geometric meanings of these camera parameters. The calibration formulas are analytic and simple to compute. Experimental results show the feasibility of the proposed approach for a practical application-autonomous land vehicle guidance. [ABSTRACT FROM AUTHOR]