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Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maintained when certain conditions are satisfied, and the physics-based nature is also kept. Although some works applied implicit PDEs to 3D surface reconstruction from images, there is little work on exploiting the explicit solutions of PDE to this topic, which is more efficient and accurate. In this paper, we propose a new method to apply the explicit solutions of a fourth-order partial differential equation to surface reconstruction from multi-view images. The method includes two stages: point clouds data are extracted from multi-view images in the first stage, which is followed by PDE-based surface reconstruction from the obtained point clouds data. Our computational experiments show that the reconstructed PDE surfaces exhibit good quality and can recover the ground truth with high accuracy. A comparison between various solutions with different complexity to the fourth-order PDE is also made to demonstrate the power and flexibility of our proposed explicit PDE for surface reconstruction from images.

We propose and demonstrate a simple, low-cost, three-dimensional (3D) shape acquisition method for transparent 3D printed microscopic objects. Our method uses ultraviolet (UV) illumination to obtain high-contrast silhouette images of transparent 3D printed polymer objects. Multiple silhouette images taken from different viewpoints make it possible to reconstruct the 3D shape of this transparent object. A 3D shape acquisition system consisting of a UV light-emitting diode, charge-coupled device camera and a rotation stage was constructed and used to successfully reconstruct the 3D shape of a transparent bunny model produced using micro-stereolithography. In addition, 3D printed pillar array models, with different diameters on the order of several hundred micrometers, were reconstructed. This method will be a promising tool for the 3D shape reconstruction of transparent 3D objects on both the micro- and macro-scale by changing the imaging lens.

Single-shot 3D imaging and shape reconstruction has seen a surge of interest due to the ever-increasing evolution in sensing technologies. In this paper, a robust single-shot 3D shape reconstruction technique integrating the structured light technique with the deep convolutional neural networks (CNNs) is proposed. The input of the technique is a single fringe-pattern image, and the output is the corresponding depth map for 3D shape reconstruction. The essential training and validation datasets with high-quality 3D ground-truth labels are prepared by using a multi-frequency fringe projection profilometry technique. Unlike the conventional 3D shape reconstruction methods which involve complex algorithms and intensive computation to determine phase distributions or pixel disparities as well as depth map, the proposed approach uses an end-to-end network architecture to directly carry out the transformation of a 2D image to its corresponding 3D depth map without extra processing. In the approach, three CNN-based models are adopted for comparison. Furthermore, an accurate structured-light-based 3D imaging dataset used in this paper is made publicly available. Experiments have been conducted to demonstrate the validity and robustness of the proposed technique. It is capable of satisfying various 3D shape reconstruction demands in scientific research and engineering applications.

Precise knowledge of the 3D shape of clinical crowns is crucial for the treatment of malocclusion problems as well as several endodontic procedures. While computed tomography would present such information, it is believed there is no threshold radiation dose below which it is considered safe. In this study, the authors propose an appearance based approach which allows for the reconstruction of plausible human jaw 3D models given a single optical image with unknown illumination. Appearance bases are analytically constructed using the frequency-based representation of the irradiance equation while incorporating prior information about natural illumination and teeth reflectance. The inherent relation between the photometric information and the underlying 3D shape is formulated as a statistical model where the coupled effect of illumination and reflectance is modelled using the Helmholtz hemispherical harmonics-based irradiance harmonics whereas the principle component regression is deployed to carry out the estimation of 3D shapes. The authors' approach relaxes limiting assumptions of conventional shape-from-shading approaches while being able to reconstruct tooth occlusal surface with challenging conditions, such as scattered specular spots and significant changes in colour and albedo characteristics resulting from tooth filling. Vis-à-vis dental applications, the results demonstrate a significant increase in accuracy in favour of the proposed approach.

Current-voltage measurements in electrical impedance tomography (EIT) can be partially ordered with respect to definiteness of the associated self-adjoint Neumann-to-Dirichlet operators. With this ordering, a pointwise larger conductivity leads to smaller current-voltage measurements, and smaller conductivities lead to larger measurements. We present a converse of this simple monotonicity relation and use it to solve the shape reconstruction (a.k.a. inclusion detection) problem in EIT. The outer shape of a region where the conductivity differs from a known background conductivity can be found by simply comparing the measurements to that of smaller or larger test regions. [PUBLICATION ABSTRACT]

We present parallel single-pixel imaging (PSI), a photography technique that captures light transport coefficients and enables the separation of direct and global illumination, to achieve 3D shape reconstruction under strong global illumination. PSI is achieved by extending single-pixel imaging (SI) to modern digital cameras. Each pixel on an imaging sensor is considered an independent unit that can obtain an image using the SI technique. The obtained images characterize the light transport behavior between pixels on the projector and the camera. However, the required number of SI illumination patterns generally becomes unacceptably large in practical situations. We introduce local region extension (LRE) method to accelerate the data acquisition of PSI. LRE perceives that the visible region of each camera pixel accounts for a local region. Thus, the number of detected unknowns is determined by local region area, which is extremely beneficial in terms of data acquisition efficiency. PSI possesses several properties and advantages. For instance, PSI captures the complete light transport coefficients between the projector–camera pair, without making specific assumptions on measured objects and without requiring special hardware and restrictions on the arrangement of the projector–camera pair. The perfect reconstruction property of LRE can be proven mathematically. The acquisition and reconstruction stages are straightforward and easy to implement in the existing projector–camera systems. These properties and advantages make PSI a general and sound theoretical model to decompose direct and global illuminations and perform 3D shape reconstruction under global illumination.

Majority of current research focuses on a single static object reconstruction from a given pointcloud. However, the existing approaches are not applicable to real world applications such as dynamic and morphing scene reconstruction. To solve this, we propose a novel two-tiered deep neural network architecture, which is capable of reconstructing self-obstructed human-like morphing shapes from a depth frame in conjunction with cameras intrinsic parameters. The tests were performed using on custom dataset generated using a combination of AMASS and MoVi datasets. The proposed network achieved Jaccards’ Index of 0.7907 for the first tier, which is used to extract region of interest from the point cloud. The second tier of the network has achieved Earth Mover’s distance of 0.0256 and Chamfer distance of 0.276, indicating good experimental results. Further, subjective reconstruction results inspection shows strong predictive capabilities of the network, with the solution being able to reconstruct limb positions from very few object details.

The technical challenge of balancing radiant illuminance and the angular diameter of the simulated sun remains unsolved, preventing the realization of a solar simulator with both a 32' angular diameter and a solar constant irradiance. This paper proposes a direct solar radiation simulation method using grating anomalous dispersion and a technological implementation scheme. This new architecture consists of a spectrally modulated optical engine, a diffractive combining system, and a multi-aperture imaging reconstruction system. We designed an optical system for simulating direct solar radiation, which achieves a high degree of reproducibility of natural direct solar radiation characteristics. The performance of this system was verified through simulation, with the results indicating that the solar direct radiation simulator achieves an angular diameter of 31.7' while maintaining radiant illuminance above a solar constant. Additionally, the system spectral match to both the extraterrestrial (AM0G) and terrestrial global (AM1.5G) solar spectra, along with its uniformity, complies with an A+ grade. The studied direct solar radiation simulation is currently the only instrument capable of achieving a solar constant of an angular diameter less than 32'. This research revolutionizes the structure and principle of the traditional solar simulator, makes up for the deficiencies of the existing solar simulation technology, further improves the theoretical system of solar direct radiation simulation, and has far-reaching scientific significance for the development and application of solar simulation technology.

Shape reconstruction and rotation axis estimation of small bodies essential for both engineering applications and scientific investigations. This paper presents a Structure-from-Motion-based (SFM) method for small body shape reconstruction and rotation axis estimation. The method enables fast and autonomous estimation of shape and rotation axis at relatively large distances during the approach phase with a limited number of images. Using near-hovering observations, sequential image poses are estimated via incremental SFM. The normal vector of the plane where the fitted space circle is located is identified as the small body’s rotation axis and transformed into the small body-centered J2000 inertial coordinate system. A global shape model is then generated through dense stereo matching. The proposed method is evaluated using both simulated and real mission data. A total of 75 simulation cases are designed, accounting for sun phase angle, approach angle, small body shape, and image count per rotation period. Results show that over 95% of cases achieve a rotation axis estimation error below 5°. When tens of images are captured per rotation period, the rotation axis can be estimated within minutes. Validation with OSIRIS-REx mission data for Bennu yields a rotation axis estimation error of approximately 1°, while dense reconstruction shows an average deviation of 2.55 m compared to the SPC shape model. These findings demonstrate the method’s effectiveness and suitability for small body exploration.

Shape-sensing optical fibers have become increasingly important in applications requiring flexible navigation, spatial awareness, and deformation monitoring. Fiber Bragg Grating (FBG) sensors inscribed in multi-core optical fibers have been democratized over the years and nowadays offer a compact and robust platform for shape reconstruction. In this work, we propose a novel, computationally efficient method for determining the 3D tip position of a bent multi-core FBG-based optical fiber using a second-order polynomial approximation of the fiber’s shape. The method begins with a calibration procedure, where polynomial coefficients are fitted for known bend configurations and subsequently modeled as a function of curvature using exponential decay functions. This allows for real-time estimation of the fiber tip position from curvature measurements alone, with no need for iterative numerical solutions or high processing power. The method was validated using miniaturized test structures and achieved sub-millimeter accuracy (<0.1 mm) over a 4.5 mm displacement range. Its simplicity and accuracy make it suitable for embedded or edge-computing applications in confined navigation, structural inspection, and medical robotics.