Projective Reconstruction Research Articles

GEMVS: a novel approach for automatic 3D reconstruction from uncalibrated multi-view Google Earth images using multi-view stereo and projective to metric 3D homography transformation

ABSTRACT This paper proposes a novel approach for automatic 3D surface reconstruction from uncalibrated and multi-view Google Earth images by using a multi-view stereo method and 3D projective to metric transformation. Without the Rational Polynomial Coefficients, it is impossible to obtain the metric reconstruction of the 3D surface from multi-view satellite images. We solve the uncalibrated multi-view satellite image problem by employing a multi-view stereo vision technique followed by a projective to metric transformation. The virtual pose parameters of the satellite images are obtained by using COLMAP, and the virtual 3D projective reconstruction is done by using EnSoft3D. For projective to metric transformation, we propose to employ 3D homography transformation. Eight 3D correspondence pairs on the viewing frustums between the virtual reference camera and the ideal nadir camera are used to derive a 3D homography matrix. Using the 3D homography matrix, we finally obtain the metric reconstruction of 3D surface up to an unknown height scale in a reference coordinate system of the Google Earth desktop software. Experiments are done in several world locations on Google Earth including building and vegetation areas. Reconstruction error analysis with the Data Fusion Contest 19 dataset is also presented. The average of MAE and RMSE of five tile regions in the dataset are 1.596 m and 2.083 m, respectively.

Development of a muon tomography application with Micromegas detectors

The application of muon tomography method in small scale, for the imaging of a five-centimeter side lead cube, is being examined in the present work. The representation of the object is being achieved by using the transmission muography technique, in which the “free-sky” muon flux is compared to the muon flux measured within the acceptance of the detector. This comparison yields information about the absorption of the muons as they pass through the object under investigation. Also, a projective reconstruction method called “Back Projection” is tested by being applied on the data, providing information about the location of the object and its dimensions. This project has been carried out within the frame of EKATY programme, which aims to the innovative imaging of the subsurface of archaeological sites and the interior of structural elements of monuments in three and four dimensions.

3D SURFACE RECONSTRUCTION FROM MULTI-VIEW AND MULTI-DATE GOOGLE EARTH SATELLITE IMAGES WITH 3D HOMOGRAPHY-BASED PROJECTIVE RECONSTRUCTION

Abstract. In this paper, we propose the 3D surface reconstruction scheme using multi-view and multi-date Google Earth (GE) satellite images. Multi-view stereo matching (MVS) scheme is one of the methods for reconstructing dense 3D surface based on multi-view images and corresponding camera pose geometry. If many views are input, MVS can estimate the disparity (depth) by matching pixels. However, the common users are not always possible to obtain both multi-view satellite images and the camera geometry (such as Rational Polynomial Camera) in various earth regions. Instead, the GE provides multi-view and multi-date satellite images of earth regions. Therefore, the goal of the proposed method is to perform a 3D surface reconstruction using the GE satellite image. We suppose that the GE satellite image is a pinhole camera model, and the camera pose geometry is estimated using the perspective projection model (PPM) based structure from the motion (SfM) method. Then the 3D surface is reconstructed and fusion using the MVS method. However, the GE satellite image is a transformed pseudo-orthoimage for integration into the raster image. For this reason, the camera pose geometry is inaccurately computed in the SfM process. Thus, the high-rise structures in the reconstructed 3D surface are distorted (distorted hexahedral 3D space). Importantly, the satellite image is a weak PPM and it can express the orthographic projection model. Therefore, we compute 3D homography for transforming between distorted hexahedral space to orthographic cuboid space. Then, the distorted 3D surface is transformed using a projective reconstruction based on 3D homography. The transformed 3D surface has the correct shape in the orthographic projection model. The advantage of the proposed method is that the 3D surface of various earth regions is reconstructed using simply accessible GE satellite images. And the transformed 3D surface is reconstructed into orthographic projection model space, thus the orthoimage can be generated using projection.

Locality-Adaptive Structured Dictionary Learning for Cross-Domain Recognition

Dictionary learning has achieved remarkable success on a wide range of machine learning-based applications. In this paper, a locality-adaptive structured dictionary learning (LASDL) algorithm for cross-domain recognition is proposed. In the LASDL, a projective structured double reconstruction strategy is developed to train class-oriented sub-dictionaries from the specific classes of cross-domain samples. The strategy benefits to make full advantage of the discriminative information of cross-domain data and bridge the distribution divergence between two different domains. Meanwhile, an adaptive geometrical structure preserving function is designed to not only preserve the local manifold structures spanned by the representation coefficient spaces of the source and target domains, but also impose a constraint that the coefficients should keep closer to their class centers, which is propitious to reduce the distribution divergence and make the representation more accurate. With the structured linear coding technique, the final cross-domain recognition can be efficiently performed by determining class-specific reconstruction error. The optimization of the proposed LASDL model can be efficiently solved by simple least square method and alternating direction method of multipliers (ADMM) algorithm. Extensive experimental results validate the superiority of the proposed algorithm in contrast to other state-of-the-art predecessors.

An Improved Wave Velocity Model for Acoustic Emission Source Localization in Heterogeneous Rock Materials with Unknown Inclusions

The accuracy of locating acoustic emission (AE) source location is closely related to the reasonability of the adopted wave velocity model. However, it is literally hard to obtain an accurate wave velocity model for a heterogeneous rock material due to its inner invisible inclusions and local defects, making the AE source localization very challenging. To obtain a more appropriate wave velocity model for the heterogeneous rock material having unknown inclusions, in this study the projective reconstruction method (PRM) was utilized to determine the wave velocity model. Because the PRM is irrelevant to the continuous assumption, the proposed wave velocity model can well reflect the discontinuous characteristics of the real wave velocity field in rock materials. Then, the proposed wave velocity model was incorporated into an arrival time-based governing equation to locate the AE source. To demonstrate the effectiveness of the proposed method in improving the AE source location accuracy and monitoring the rock failure process, lead-break tests and three-point bending tests were conducted on the composite rock and rock-like specimens, respectively. Results show that the improved wave velocity model obtained by the PRM can significantly improve the accuracy of AE source location in the heterogeneous rock material with unknown inclusions.

Algorithm of 3D Virtual Reconstruction of Ancient Buildings in Qing Dynasty Based on Image Sequence

Aiming at the problem of low accuracy and poor integrity of traditional Qing Dynasty ancient architecture 3D virtual reconstruction algorithm, a 3D virtual reconstruction algorithm of Qing Dynasty ancient architecture based on image sequence is proposed. Acquire the sequence images of ancient buildings in the Qing Dynasty through the pinhole camera model, analyze the projective space and reconstruction space of the sequence images, redefine the similarity measurement coefficient according to the improved 2DPCA-SIFT feature matching algorithm, match the feature points of the ancient architecture images in the Qing Dynasty, and use random sampling to be consistent. The algorithm solves the basic matrix, removes the interference error in the image reconstruction process, and realizes the design of the three-dimensional reconstruction algorithm through image sequence fusion. The experimental results show that, compared with the existing methods, the completeness of the three-dimensional virtual reconstruction 3D model of ancient Qing Dynasty buildings constructed by the designed algorithm is 87.26% on average, and the completeness and accuracy of the 3D model construction of the subparts of the ancient Qing Dynasty buildings of this method are better. The height of the building fully shows that the designed building has good performance in the construction of the three-dimensional model of ancient buildings in the Qing Dynasty.

A linear method for camera pair self-calibration

We examine 3D reconstruction in unordered sets of uncalibrated images. We introduce a linear method to self-calibrate and find the metric reconstruction of a camera pair. We assume unknown and varying focal lengths but otherwise known internal camera parameters and a known projective reconstruction of the camera pair. We recover two possible camera configurations in space and use the Cheirality condition, that all 3D scene points are in front of both cameras, to disambiguate the solution. Towards identifying camera configurations that would perplex solution disambiguation, we show in two Theorems, first that the two solutions are in mirror positions and then the relations between their viewing directions. We validate our approach in synthetic and real scenes. In camera pair self-calibration and metric reconstruction, our method performs on par (median rotation error ΔR=3.49°) with the standard approach of Kruppa equations followed by 5P algorithm (ΔR=3.77°). We get realistic multi-view reconstructions, using numerous camera pair metric reconstructions generated by our linear method, rotation-averaging algorithms and a novel method to average focal length estimates.

Radioactive Source Localisation via Projective Linear Reconstruction.

Radiation mapping, through the detection of ionising gamma-ray emissions, is an important technique used across the nuclear industry to characterise environments over a range of length scales. In complex scenarios, the precise localisation and activity of radiological sources becomes difficult to determine due to the inability to directly image gamma photon emissions. This is a result of the potentially unknown number of sources combined with uncertainties associated with the source-detector separation—causing an apparent ‘blurring’ of the as-detected radiation field relative to the true distribution. Accurate delimitation of distinct sources is important for decommissioning, waste processing, and homeland security. Therefore, methods for estimating the precise, ‘true’ solution from radiation mapping measurements are required. Herein is presented a computational method of enhanced radiological source localisation from scanning survey measurements conducted with a robotic arm. The procedure uses an experimentally derived Detector Response Function (DRF) to perform a randomised-Kaczmarz deconvolution from robotically acquired radiation field measurements. The performance of the process is assessed on radiation maps obtained from a series of emulated waste processing scenarios. The results demonstrate a Projective Linear Reconstruction (PLR) algorithm can successfully locate a series of point sources to within 2 cm of the true locations, corresponding to resolution enhancements of between 5× and 10×.

Critical hypersurfaces and instability for reconstruction of scenes in high dimensional projective spaces

In the context of multiple view geometry, images of static scenes are modeled as linear projections from a projective space ℙ3 to a projective plane ℙ2 and, similarly, videos or images of suitable dynamic or segmented scenes can be modeled as linear projections from ℙk to ℙh, with k > h ≥ 2. In those settings, the projective reconstruction of a scene consists in recovering the position of the projected objects and the projections themselves from their images, after identifying many enough correspondences between the images. A critical locus for the reconstruction problem is a configuration of points and of centers of projections, in the ambient space, where the reconstruction of a scene fails. Critical loci turn out to be suitable algebraic varieties. In this paper we investigate those critical loci which are hypersurfaces in high dimension complex projective spaces, and we determine their equations. Moreover, to give evidence of some practical implications of the existence of these critical loci, we perform a simulated experiment to test the instability phenomena for the reconstruction of a scene, near a critical hypersurface.

NRSfPP: non-rigid structure-from-perspective projection

A state-of-the-art algorithm for perspective projection reconstruction of non-rigid surfaces from single-view and realistic videos is proposed. It overcomes the limitations arising from the usage of orthographic camera model and also the complexity and non-linearity issues of perspective projection equation. Unlike traditional non-rigid structure-from-motion (NRSfM) methods, which have been studied only on synthetic datasets and controlled lab environments that require some prior constraints (such as manually segmented objects, limited rotations and occlusions, and full-length trajectories); the proposed method can be used in realistic video sequences. In addition, contrary to previous methods that use multiple cameras with different relative viewing angles, only a single-view video is required to reconstruct the 3D structures. By only using the 2D frames of incoming video stream, the proposed method extracts the projective depth coefficients of each point in each input frame, rotation matrix, translation vector, varying camera parameters (such as focal lengths for each input frame), and finally reconstructs the 3D deformable shape. Due to the high number of unknowns, the problem has been divided into two parts of projective depth coefficients extraction and 3D shape reconstruction. Perspective reconstruction of non-rigid surfaces has been extended to be certainly converged which leads to a significant increase in execution frequency of the iterated algorithm that has been presented for projective depth coefficients extraction. As such, it produces promising results for perspective projection reconstruction of non-rigid surfaces from single-view and realistic videos. The accuracy and robustness of the proposed method is demonstrated quantitatively on synthetic data and qualitatively on real image sequences. The experimental results show that NRSfPP provides the state-of-the-art results and resolves the failures of previous approaches by eliminating all of the predefined situations and constraints of applying perspective projection as the camera model.

Critical loci in computer vision and matrices dropping rank in codimension one

Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable 4×3 matrices, N, of linear forms. Such loci are classified in this paper, in the case in which N drops rank in codimension one, giving rise to reducible varieties. This rests on the complete classification of matrices of size (n+1)×n for n≤3, which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally. The classification of special matrices as above is also leveraged to study degenerate critical loci for suitable projections from P3.

An automatic three-dimensional geological engineering modeling method based on tri-prism

The three-dimensional geological engineering model representing the coupling relationship between geological engineering objects is the major focus of researches on three-dimensional geoscience modeling. However, a large number of challenging interactive human-computer operations is still essential in the current geological engineering modeling methods. In order to achieve full automation, a new automatic geological engineering modeling method is systematically studied and proposed in this paper. The method uses TP (Tri-Prism) volume featured by vertical side edge as the modeling primitive. First, the three-dimensional geological model which characterizes the complete interior structure and topology of the geological object is constructed based on borehole data, and the engineering model is constructed by sequential section modeling approach. The geological model and the engineering model are treated as the base model and constraint model respectively for integration. Then, the coupling of geological and engineering models is achieved by the efficient “body-surface” intersection algorithm and projective reconstruction algorithm for TP-based model with its intraformational projective characteristic. Finally, the geological engineering model is automatically reconstructed through this workflow. The experiment demonstrates that the proposed method could build seamless three-dimensional volumetric geological engineering model fully automatically and all features of TP-based volumetric model are still maintained within the model, which satisfies the requirement for volumetric model analysis.

Projective Double Reconstructions Based Dictionary Learning Algorithm for Cross-Domain Recognition.

Dictionary learning plays a significant role in the field of machine learning. Existing works mainly focus on learning dictionary from a single domain. In this paper, we propose a novel projective double reconstructions (PDR) based dictionary learning algorithm for cross-domain recognition. Owing the distribution discrepancy between different domains, the label information is hard utilized for improving discriminability of dictionary fully. Thus, we propose a more flexible label consistent term and associate it with each dictionary item, which makes the reconstruction coefficients have more discriminability as much as possible. Due to the intrinsic correlation between cross-domain data, the data should be reconstructed with each other. Based on this consideration, we further propose a projective double reconstructions scheme to guarantee that the learned dictionary has the abilities of data itself reconstruction and data crossreconstruction. This also guarantees that the data from different domains can be boosted mutually for obtaining a good data alignment, making the learned dictionary have more transferability. We integrate the double reconstructions, label consistency constraint and classifier learning into a unified objective and its solution can be obtained by proposed optimization algorithm that is more efficient than the conventional l1 optimization based dictionary learning methods. The experiments show that the proposed PDR not only greatly reduces the time complexity for both training and testing, but also outperforms over the stateof- the-art methods.

Projective Reconstruction in Algebraic Vision

AbstractWe discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

Critical Loci for Two Views Reconstruction as Quadratic Transformations Between Images

In this paper, the effect of the existence of a critical set for the projective reconstruction of a scene in $${{\mathbb {P}}}^{3}$$ from two views is analyzed directly on the image planes. Corresponding points, which are images of critical points, are linked by a birational map between the two planes which is a quadratic transformation. This transformation is explicitly described and used to investigate the instability phenomena for reconstruction with a new approach.

Abstract: A Clinical Trial for Three-Dimensional Vascular Mapping of Anterolateral Thigh Flap Distally-Branching Perforator Vessels Based on Photoacoustic Tomography: The Protocol and Preliminary Results

BACKGROUND: Thin free flaps are challenging procedures. In particular, the failure of thin anterolateral thigh (ALT) flaps is reported to be associated with the distal branching pattern of the perforator vessels. In a previous study, we demonstrated the feasibility of using photoacoustic tomography (PAT) to identify ALT perforators and their branching patterns in the subcutaneous layer, especially those in oblique or horizontal orientations.1 In this paper, we present the protocol and preliminary results of a clinical trial for three-dimensional vascular mapping of the distal ALT perforators using PAT imaging. METHODS: Patients for whom reconstructive surgery using an ALT flap was planned were recruited. Four days before the operation, the bilateral anterolateral aspects of the mid-thigh were examined by PAT. The perforator orientation, as determined by ultrasound, was marked with red ink. The body surface was marked every 4 cm with purple ink. The acquired data were processed three-dimensionally using a laboratory-made imaging software program. The depth of the visualized perforator vessels and the distal networks were distinguished based on the color gradation. The body surface markings were preserved until the operation day using a film sheet. Two days before the operation, the three-dimensional vascular data were converted into a two-dimensional vascular map using a projective image reconstruction technique. A semi-automated normal vector detection method and curvature approximation were applied to maintain accuracy. The depth was indicated by color gradation on a sterilized transparent sheet. The mapping sheet was attached to the patient’s thigh before the operation. The skin incision was performed with cutting the transparent mapping sheet. The stem portion of the perforator vessels was evaluated at the level of fascia lata. RESULTS: The first clinical trial involved a 32-year-old male patient with a malignant chest-wall tumor. Each PAT scan took approximately 5 minutes per thigh. The perforator vessels were visualized at the expected points by ultrasonography. A two-dimensional vascular mapping sheet was prepared by drawing the courses of the subcutaneous micro-vessels using projection mapping. Our computing technique projected the trajectories of the vessels in the subcutaneous layer onto a two-dimensional transparent sheet and showed the depth by color gradation. The stem portion of the perforator vessels, as estimated by PAT, was correlated with the operative findings at the points that penetrated the fascia. CONCLUSION: The first clinical trial protocol revealed the efficacy of PAT in creating a three-dimensional vascular map of the anterolateral thigh in the clinical setting.

Revisiting Projective Structure from Motion: A Robust and Efficient Incremental Solution.

This paper presents a solution to the Projective Structure from Motion (PSfM) problem able to deal efficiently with missing data, outliers and, for the first time, large scale 3D reconstruction scenarios. By embedding the projective depths into the projective parameters of the points and views, we decrease the number of unknowns to estimate and improve computational speed by optimizing standard linear Least Squares systems instead of homogeneous ones. In order to do so, we show that an extension of the linear constraints from the Generalized Projective Reconstruction Theorem can be transferred to the projective parameters, ensuring also a valid projective reconstruction in the process. We use an incremental approach that, starting from a solvable sub-problem, incrementally adds views and points until completion with a robust, outliers free, procedure. To prevent error accumulation, a refinement based on alternation between new estimations of views and points is used. This can also be done with constrained non-linear optimization. Experiments with simulated data shows that our approach is performing well, both in term of the quality of the reconstruction and the capacity to handle missing data and outliers with a reduced computational time. Finally, results on real datasets shows the ability of the method to be used in medium and large scale 3D reconstruction scenarios with high ratios of missing data (up to 98 percent).

Efficient regional single-pixel imaging for multiple objects based on projective reconstruction theorem

Single-pixel imaging (SPI) is a novel imaging method with a non-spatial detector that is utilized when imaging. SPI exhibits numerous advantages but is time-consuming and ineffective. This paper proposes an efficient regional SPI (ERSI) based on projective reconstruction theorem. The main idea of ERSI is locating object regions first and then adaptively project patterns only on these regions. The ERSI is considerably more efficient than traditional SPI because the former disregards background information. Experiments verified that ERSI shortens the time consumed for SPI to approximately 10% if the scene contains several small objects.

The Object’s Reconstruction of CT Detection Based on Filtered Back Projection Algorithm

Now the most scholars will use parallel beam projection reconstruction algorithm to study CT inspection system to reduction the object. By using these algorithms, for CT system detect reduction target image is not clear, stellate lines occurs on the projective reconstruction object artifact, leads to the serious distortion. This article mainly focuses on the improvement of the precision in the detection of the CT system. The first image of the CT system we get is the projection of the object, then the projection is processed with a one-dimensional filter by using Matlab, we can get reconstructed projection. The resulting image is more restored and clearer than without processing in a filter. We use this theory to a specific CT system test and the use of the theory methods to rebuild the absorption rate, clear graphics of object, found that the image after filtering is more accurate and clear.

Robust 3D Projective Reconstruction by Learning

Robust 3D Projective Reconstruction by Learning