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Three-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.

Aim: Three-dimensional facial imaging systems are a useful tool that is gradually replacing two-dimensional imaging and traditional anthropometry with calipers. In this varied and growing landscape of new devices, Canfield (Canfield Scientific, Parsippany, NJ, USA) has proposed a series of static and portable 3D imaging systems. The aim of this systematic review was to evaluate the current literature regarding the validation of Canfield’s Vectra imaging systems. Materials and Methods: A search strategy was developed on electronic databases including PubMed, Web of Science and Scopus by using specific keywords. After the study selection phase, a total of 10 articles were included in the present review. Results: A total of 10 articles were finally included in the present review. For six articles, we conducted a validation of the Vectra static devices, focusing especially on the Vectra M5, Vectra M3 and Vectra XT. For four articles, we validated the Vectra H1 portable system. Conclusions: All of the reviewed articles concluded that Canfield’s Vectra 3D imaging systems are capable of capturing accurate and reproducible stereophotogrammetric images. Minor errors were reported, particularly in the acquisition of the perioral region, but all the evaluated devices are considered to be valid and accurate tools for clinicians.

A refractive lens is one of the simplest, most cost-effective and easily available imaging elements. Given a spatially incoherent illumination, a refractive lens can faithfully map every object point to an image point in the sensor plane, when the object and image distances satisfy the imaging conditions. However, static imaging is limited to the depth of focus, beyond which the point-to-point mapping can only be obtained by changing either the location of the lens, object or the imaging sensor. In this study, the depth of focus of a refractive lens in static mode has been expanded using a recently developed computational reconstruction method, Lucy-Richardson-Rosen algorithm (LRRA). The imaging process consists of three steps. In the first step, point spread functions (PSFs) were recorded along different depths and stored in the computer as PSF library. In the next step, the object intensity distribution was recorded. The LRRA was then applied to deconvolve the object information from the recorded intensity distributions during the final step. The results of LRRA were compared with two well-known reconstruction methods, namely the Lucy-Richardson algorithm and non-linear reconstruction.

Background Quantitative biomarkers of facial skin aging were investigated in 109 healthy Asian female volunteers, aged 20 to 70 years. Materials and Methods In vivo 3D Line‐field Confocal Optical Coherence Tomography (LC‐OCT) imaging, enhanced by Artificial Intelligence (AI)‐based quantification algorithms, was utilized to compute various metrics, including stratum corneum thickness (SC), viable epidermal (VE) thickness, and Dermal‐Epidermal Junction (DEJ) undulation along with cellular metrics for the temple, cheekbone, and mandible. Results Comparison with data from a cohort of healthy Caucasian volunteers revealed similarities in the variations of stratum corneum and viable epidermis layers, as well as cellular shape and size with age in both ethnic groups. However, specific findings emerged, such as larger, more heterogeneous nuclei in both layers, demonstrated by an increase in nuclei volume and their standard deviation, and increased network atypia, all showing significant age‐related variations. Caucasian females exhibited a flatter and more homogeneous epidermis, evidenced by a decreased standard deviation of the number of layers, and a less dense cellular network with fewer cells per layer, indicated by a decrease in cell surface density. Conclusion Ethnicity‐wise comparisons highlighted distinct biological features specific to each population. Asian individuals showed significantly higher DEJ undulation, higher compactness, and lower cell network atypia compared to their Caucasian counterparts across age groups. Differences in stratum corneum and viable epidermal thickness on the cheekbone were also significant. LC‐OCT 3D imaging provides valuable insights into the aging process in different populations and underscores inherent biological differences between Caucasian and Asian female volunteers.

An image fusion method has been proposed for plant images taken using a two-dimensional (2D) camera and three-dimensional (3D) portable lidar for obtaining a 3D distribution of physiological and biochemical plant properties. In this method, a 2D multispectral camera with five bands (475–840 nm) and a 3D high-resolution portable scanning lidar were applied to three sets of sample trees. After producing vegetation index (VI) images from multispectral images, 3D point cloud lidar data were projected onto the 2D plane based on perspective projection, keeping the depth information of each of the lidar points. The VI images were 2D registered to the lidar projected image based on the projective transformation and VI 3D point cloud images were reconstructed based on the depth information. Based on the relationship between the VI values and chlorophyll contents taken by a soil and plant analysis development (SPAD)-502 plus chlorophyll meter, 3D distribution images of the chlorophyll contents were produced. Similarly, a thermal 3D image for a sample was also produced. The resultant chlorophyll distribution images offered vertical and horizontal distributions, and those for each orientation for each sample, showing the spatial variability of the distribution and the difference between the samples.

Polarization 3D imaging is a passive, monocular, long-distance 3D imaging technology. Compared with traditional 3D imaging methods, it has many advantages, such as its lack of need for a light source, lack of need for image matching, and ability to achieve 3D imaging using only a single image. In this study, the principle of polarization 3D imaging was introduced. In the design process of a polarization 3D imager, the acquisition method for obtaining polarization information, the extinction ratio, the spatial resolution, and the refractive index of objects was introduced in detail. The influence of these key factors on the accuracy of polarization 3D imaging was analyzed. Taking the limitations of a small satellite payload into account, specific indicators such as multi-aperture polarized imaging, a 10,000:1 extinction ratio, and a spatial resolution of 30 m were designed. The implementation and functions of the polarization 3D imager were elaborated upon, and optical systems and polarizing devices were developed. Finally, by utilizing the image data obtained by the polarization 3D imager, polarization 3D imaging of real ground objects was obtained. The accuracy of the polarization 3D imaging inversion was approximately twice the spatial resolution. These research results lay the technical foundations for the development and practical application of polarization 3D imaging technology and instruments.

We consider the 3D coefficient inverse problem for parabolic wave equation. It involves determining the spatial distribution of refractive and absorption indices by processing phase diffraction patterns obtained by irradiating an object with a set of Gaussian beams. Unlike tomography and ptychography, rotation or scanning of the sample is not required. The problem is solved by expanding the wave field and the complex dielectric constant ε r → over the full set of Gaussian beam functions. To determine ε r → , we obtain a nonlinear matrix equation. The condition of its solvability allows the selection of sampling frequencies by coordinates in accordance with the practical task.

Imaging using millimeter waves (MMW) and terahertz (THz) waves can help inspect hazardous materials hidden beneath clothing in a non-contact and non-invasive manner. A 3D terahertz imaging system for security gate applications in the 275–305 GHz range was developed and experimentally demonstrated to detect concealed objects carried by pedestrians. This system performs 3D measurements by combining depth detection using frequency-modulated continuous wave (FM-CW) radar, vertical scanning of the detection spot using a 1D high-speed mechanical beam scanner, and horizontal movement of the irradiated area and detection spot as the pedestrian walks. The high-speed beam scanner comprises an F-Theta telecentric lens and a polygon mirror. It has a vertical line scan rate of 142 lines/s and spatial resolution of ~10 mm, consistent with the design value, and a depth resolution of ~7 mm, which is 40% larger than the theoretical value estimated from the FM-CW radar principle. The depth-dependent lateral distortion in 3D images, known as telecentricity, measured using the body scanner imaging system, was also evaluated. Consequently, images with the same magnification were obtained at a range of more than 500 mm of focus depth. Finally, the detection of concealed objects carried by pedestrians was demonstrated, showing that the system can work for a pedestrian walking at speeds from 4 km/h to 7 km/h.

Background and objectives: This study aimed to evaluate the effectiveness of decompression on jaw cysts according to various parameters by volumetric analysis using three-dimensional computed tomography. Materials and methods: Fifty patients who underwent surgical decompression of the jaw cystic lesion were selected, and their preoperative and postoperative computed tomography results between 3 and 27 months were collected. Volumetric analysis was performed to evaluate any differences in the rate of volumetric change according to the sex, age, initial volume of the lesion, duration, location of the lesion, tooth extraction, expansion of the cortical layer, and pathological diagnosis. Multiple linear regression and generalised linear mixed models were used for statistical analyses. Results: The mean reduction rate among all patients was 54.68%. Multiple linear regression analysis revealed that higher reduction rates were associated with a long decompression period, young patient age, and location of the cyst in the posterior maxilla. Generalised linear mixed models revealed that higher reduction rates were associated with a long decompression period and young patient age. Conclusions: Decompression was an effective treatment for reducing the cyst size in all patients. Its effectiveness increased with a long treatment duration, young patient age, and cyst location in the posterior maxilla three-dimensionally.

The cilium, a pivotal organelle crucial for cell signaling and proper cell function, relies on meticulous macromolecular transport from the cytoplasm for its formation and maintenance. While the intraflagellar transport (IFT) pathway has traditionally been the focus of extensive study concerning ciliogenesis and ciliary maintenance, recent research highlights a complementary and alternative mechanism—vesicle-assisted transport (VAT) in cytoplasm to cilium trafficking. Despite its potential significance, the VAT pathway remains largely uncharacterized. This review explores recent studies providing evidence for the dynamics of vesicle-related diffusion and transport within the live primary cilium, employing high-speed super-resolution light microscopy. Additionally, we analyze the spatial distribution of vesicles in the cilium, mainly relying on electron microscopy data. By scrutinizing the VAT pathways that facilitate cargo transport into the cilium, with a specific emphasis on recent advancements and imaging data, our objective is to synthesize a comprehensive model of ciliary transport through the integration of IFT-VAT mechanisms.