Imaging Geometry Research Articles

Development of a stereoscopic CT metal artifact management algorithm using gantry angle tilts for head and neck patients.

Dental amalgams are a common source of artifacts in head and neck (HN) images. Commercial artifact reduction techniques have been offered, but are substantially ineffectual at reducing artifacts from dental amalgams, can produce additional artifacts, provide inaccurate HU information, or require extensive computation time, and thus offer limited clinically utility. The goal of this work was to define and validate a novel algorithm and provide a phantom‐based testing as proof of principle. An initial clinical comparison to a vendor's current solution was also performed. The algorithm uses two‐angled CT scans in order to generate a single image set with minimal artifacts posterior to the metal implants. The algorithm was evaluated using a phantom simulating a HN patient with dental fillings. Baseline (no artifacts) geometrical measurements of the phantom were taken in the anterior–posterior, left–right, and superior–inferior directions and compared to the metal‐corrected images using our algorithm to evaluate possible distortion from application of the algorithm. Mean HU numbers were also compared between the baseline scan and corrected image sets. A similar analysis was performed on the vendor's algorithm for comparison. The algorithm developed in this work successfully preserved the image geometry and HU and corrected the CT metal artifacts in the region posterior to the metal. The average total distortion for all gantry angles in the AP, LR, and SI directions was 0.17, 0.12, and 0.14 mm, respectively. The HU measurements showed significant consistency throughout the different reconstructed images when compared to the baseline image sets. The vendor's algorithm also showed no geometrical distortion but performed inferiorly in the HU number analysis compared to our technique. Our novel metal artifact management algorithm, using CT gantry angle tilts, provides a promising technique for clinical management of metal artifacts from dental amalgam.

In-Flight Calibration and Performance of the OSIRIS-REx Touch And Go Camera System (TAGCAMS)

The Touch And Go Camera System (TAGCAMS) is a three-camera-head instrument onboard NASA’s OSIRIS-REx asteroid sample return mission spacecraft. The purpose of TAGCAMS is to facilitate navigation to the target asteroid, (101955) Bennu; confirm acquisition of the asteroid sample; document asteroid sample stowage; and provide supplementary imaging for OSIRIS-REx science investigations. During the almost two-year OSIRIS-REx outbound cruise phase we pursued nine TAGCAMS imaging campaigns to check, calibrate and characterize the camera system’s performance before asteroid arrival and proximity operations began in late 2018. The TAGCAMS in-flight calibration dataset provides the relevant information to enable the three cameras to complete their primary observation goals during asteroid operations. The key performance parameters that we investigated in flight included: linearity, responsivity (both point source and extended body), dark current, hot pixels, pointing, image geometry transformation, image quality and stray light. Analyses of the in-flight performance either confirmed the continued applicability of the TAGCAMS ground test results or substantially improved upon the ground test knowledge. In addition, the TAGCAMS calibration observations identified the source of a spacecraft outgassing feature that guided successful remediation efforts prior to asteroid arrival.

Calculating vertical deformation using a single InSAR pair based on singular value decomposition in mining areas

Vertical deformation estimation can be a significant tool in preventing geological hazards and managing environment impacts of underground mining. Common ground surface vertical deformation calculations are challenged by difficult data collection and dependence on prior knowledge. SVD (singular value decomposition) method was applied to estimate ground surface vertical deformation from single pair SAR (synthetic aperture radar) data in a mining region. During the study, LOS (line of sight) and azimuth displacement was obtained using two pass D-InSAR (differential interferometry synthetic aperture radar) and MAI (multi-aperture radar interferometry) technology, respectively. Two adjustment equations were composed using the imaging geometry of D-InSAR and MAI. The singular value decomposition theorem was used to acquire M-P (Moore-Penrose) generalized inverse of the rank deficiency coefficient matrix. From this, the optimal approximation solution of unknown parameters was calculated using weighted least squares. A working panel in the Datong mining area, Shanxi province, China, was selected to verify the SVD approach using the two ascending Sentinel-1A data. The accuracy of vertical deformation estimated by SVD approach is reliable. The RMSE (root mean square error) of vertical deformation is 2.64 mm (along upright profile) and 4.95 mm (along horizontal profile). These results suggest that the SVD approach will complement widely used vertical ground surface deformation calculations. Further study is needed to validate the method from other deformation scenarios from landslides, groundwater loss, earthquakes, underground mining, and glacier movement.

Ptychographic X-ray speckle tracking.

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X-ray speckle tracking methods, it is robust to low-coherence X-ray sources, making it suitable for laboratory-based X-ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X-ray free-electron laser facilities, where beam-pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.

Deep Learning-Based Single Image Super-Resolution: An Investigation for Dense Scene Reconstruction with UAS Photogrammetry

The deep convolutional neural network (DCNN) has recently been applied to the highly challenging and ill-posed problem of single image super-resolution (SISR), which aims to predict high-resolution (HR) images from their corresponding low-resolution (LR) images. In many remote sensing (RS) applications, spatial resolution of the aerial or satellite imagery has a great impact on the accuracy and reliability of information extracted from the images. In this study, the potential of a DCNN-based SISR model, called enhanced super-resolution generative adversarial network (ESRGAN), to predict the spatial information degraded or lost in a hyper-spatial resolution unmanned aircraft system (UAS) RGB image set is investigated. ESRGAN model is trained over a limited number of original HR (50 out of 450 total images) and virtually-generated LR UAS images by downsampling the original HR images using a bicubic kernel with a factor × 4 . Quantitative and qualitative assessments of super-resolved images using standard image quality measures (IQMs) confirm that the DCNN-based SISR approach can be successfully applied on LR UAS imagery for spatial resolution enhancement. The performance of DCNN-based SISR approach for the UAS image set closely approximates performances reported on standard SISR image sets with mean peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index values of around 28 dB and 0.85 dB, respectively. Furthermore, by exploiting the rigorous Structure-from-Motion (SfM) photogrammetry procedure, an accurate task-based IQM for evaluating the quality of the super-resolved images is carried out. Results verify that the interior and exterior imaging geometry, which are extremely important for extracting highly accurate spatial information from UAS imagery in photogrammetric applications, can be accurately retrieved from a super-resolved image set. The number of corresponding keypoints and dense points generated from the SfM photogrammetry process are about 6 and 17 times more than those extracted from the corresponding LR image set, respectively.

An open source heterogeneous 3D printed mouse phantom utilising a novel bone representative thermoplastic

The lack of rigorous quality standards in pre-clinical radiation dosimetry has renewed interest in the development of anthropomorphic phantoms. Using 3D printing customisable phantoms can be created to assess all parts of pre-clinical radiation research: planning, image guidance and treatment delivery. We present the full methodology, including material development and printing designs, for the production of a high spatial resolution, anatomically realistic heterogeneous small animal phantom. A methodology for creating and validating tissue equivalent materials is presented. The technique is demonstrated through the development of a bone-equivalent material. This material is used together with a soft-tissue mimicking ABS plastic filament to reproduce the corresponding structure geometries captured from a CT scan of a nude mouse. Air gaps are used to represent the lungs. Phantom validation was performed through comparison of the geometry and x-ray attenuation of CT images of the phantom and animal images. A 6.6% difference in the attenuation of the bone-equivalent material compared to the reference standard in softer beams (0.5 mm Cu HVL) rapidly decreases as the beam is hardened. CT imaging shows accurate (sub-millimetre) reproduction of the skeleton (Distance-To-Agreement 0.5 mm ± 0.4 mm) and body surface (0.7 mm ± 0.5 mm). Histograms of the voxel intensity profile of the phantom demonstrate suitable similarity to those of both the original mouse image and that of a different animal. We present an approach for the efficient production of an anthropomorphic phantom suitable for the quality assurance of pre-clinical radiotherapy. Our design and full methodology are provided as open source to encourage the pre-clinical radiobiology community to adopt a common QA standard. Abbreviations ABS – acrylonitrile butadiene styrene, CBCT – cone beam computed tomography, FDM – fused deposition modelling, HVL – half value layer, HU – Hounsfield units, ICRU - International Commission on Radiation Units and Measurements, NIST – National Institute of Standards and Technology, NPL – National Physical Laboratory, QA – quality assurance, ROI – region of interest, SARRP – small animal radiation research platform, STL – stereolithography.

A Novel Image Representation Method Under a Non-Standard Positional Numeral System

Image representation is an active research area in the field of image processing. This paper proposes a novel image representation method under a non-standard positional numeral system, wherein complex numbers are used as bases in such non-standard positional numeral system. It is different with binary code and decimal code, where the digit 2 is used as the base in the binary system, and the digit 10 is used as the base in the decimal system. In the proposed image representation method, a two-dimensional image is transformed into a one-dimensional 0 $\sim$ 1 sequence, and its Gaussian integer is calculated based on the derived one-dimensional 0 $\sim$ 1 sequence. On the contrary, the original two-dimensional image can be recovered from its Gaussian integer. When images are represented as Gaussian integers, the classical geometrical operations are introduced into image processing. Then, the relationship of different images is established by the methods of plane geometry, i.e., the addition, subtraction, multiplication, division, conjugate, and inverse operations of images are defined. The experimental results show that the selection of complex number as base in the positional numeral system is a very special coding method, a given digital image is effectively converted to a Gaussian integer by using the proposed image representation method, and the image arithmetic is also successfully achieved. In addition, three applications based on the proposed image representation method including image camouflage, image sharing, and image scrambling are selected to demonstrate that the new image representation has good and potential practical applicability in the field of secure encryption of digital images.

Spatiotemporal Coverage of a Moon-Based Synthetic Aperture Radar: Theoretical Analyses and Numerical Simulations

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.

Compression of geometry videos by 3D-SPECK wavelet coder

A geometry video is formed as a sequence of geometry images where each frame is a remeshed form of a frame of an animated mesh sequence. For efficiently coding geometry videos by exploiting temporal as well spatial correlation at multiple scales, this paper proposes the 3D-SPECK algorithm which has been successfully applied to the coding of volumetric medical image data and hyperspectral image data in the past. The paper also puts forward several postprocessing operations on the reconstructed surfaces that compensate for the visual artifacts appearing in the form of undulations due to the loss of high-frequency wavelet coefficients, cracks near geometry image boundaries due to vertex coordinate quantization errors and serrations due to regular or quad splitting triangulation of local regions of large anisotropic geometric stretch. Experimental results on several animated mesh sequences demonstrate the superiority of the subjective and objective coding performances of the newly proposed approach to those of the commonly recognized animated mesh sequence coding approaches at low and medium coding rates.

RGB2AO: Ambient Occlusion Generation from RGB Images

AbstractWe present RGB2AO, a novel task to generate ambient occlusion (AO) from a single RGB image instead of screen space buffers such as depth and normal. RGB2AO produces a new image filter that creates a non‐directional shading effect that darkens enclosed and sheltered areas. RGB2AO aims to enhance two 2D image editing applications: image composition and geometry‐aware contrast enhancement. We first collect a synthetic dataset consisting of pairs of RGB images and AO maps. Subsequently, we propose a model for RGB2AO by supervised learning of a convolutional neural network (CNN), considering 3D geometry of the input image. Experimental results quantitatively and qualitatively demonstrate the effectiveness of our model.

Monte Carlo simulation driven time resolved photon fluence analysis

In this study, time resolved (TR) Monte Carlo (MC) simulation program code was run to generate photon fluencies with increasing time steps. TR MC simulation was performed for ten time series from 4 ps to 52 ps. Generated photon fluencies were transferred to the image analysis programming platform. Imaging device geometry was created for test purpose in image reconstruction programming platform environment. Forward model weight matrix functions were calculated during each time period for 38 sources, and 38 detectors according to the back-reflected imaging geometry. A homogenous phantom, which simulated tissue, was chosen. Depending on the homogeneous tissue optical properties, such as tissue absorption coefficient μa, and tissue scattering coefficient μs, photons emitted from the laser source positions; migrated differently inside the imaging tissue. Photons migrate inside the tissue by some multiplication factor of ps depending on the tissue type for each 100-micrometer vertical distance. Superficial photons come photodetector point fast, depend on the source-detector neighborhood distances and tissue optical properties, respectively. Time resolved diffuse optic tomography (TRDOT) imaging systems are an emerging biomedical optic imaging modality due to progressive electronic technologies are helping to build the systems faster and cheap. As such, emerging microelectronic technology is giving important access to design and implement compact laser sources and photodetector units. Vertical cavity surface emitting light (VCSEL) as laser source and single photon avalanche diode (SPAD) arrays as photodetector units are becoming in common use as important hardware tools for designers and researchers in this field. TR diffuse photon analysis should be done routinely for better understanding of TRDOT devices. Hence, MC simulation driven TR photon fluence analysis was done for such a purpose in this study.

Applied Mathematics of Ray Tracing and Perspective Projection in Fiducial-Based Registration of X-Ray Images.

Ray tracing (RT) and perspective projection (PP) using fiducial-based registration can be used to determine points of interest in biplanar X-ray imaging. We sought to investigate the implementation of these techniques as they pertain to X-ray imaging geometry. The mathematical solutions are presented and then implemented in a phantom and actual case with numerical tables and imaging. The X-ray imaging is treated like a Cartesian system in millimeters (mm) with a standard frame-based stereotactic system. In this space, the point source is the X-ray emitter (focal spot), the plane is the X-ray detector, and fiducials are in between the source and plane. In a phantom case, RT was able to predict locations of fiducials after moving the point source. Also, a scaled PP matrix could be used to determine imaging geometry, which could then be used in RT. Automated identification of spherical fiducials in 3D was possible using a center of mass computation with average Euclidean error relative to manual measurement of 0.23 mm. For PP, RT projection or a combinatorial approach could be used to facilitate matching 3D to 2D points. Despite being used herein for deep brain stimulation (DBS), utilization of this kind of imaging analysis has wide medical and non-medical applications.

EasyMesh: An efficient method to reconstruct 3D mesh from a single image

How to reconstruct the complete 3D mesh model from a single natural image is now still considered as a challenging problem. Most existing methods describe 3D shapes in the form of voxel or point cloud, and it is not always trivial to convert them into meshes with high quality. In this paper, we present a novel method to effectively address this problem by using a specially-designed GAN model to map a given natural image to a geometry image, from which the corresponding 3D mesh can be reconstructed. Specifically, we disentangle the tasks of viewpoint estimation and 3D reconstruction, ensuring that the reconstruction network focuses on generating vivid 3D meshes with accurate viewpoint information. We also add a differentiable module to create silhouettes from various viewpoints for the synthesized geometry image, aiming to improve the consistency between the generated 3D model and its input 2D image. Furthermore, we design a compact but effective discriminator for geometry images to guarantee a plausible overall contour of the generated object. Experiments conducted on a publicly available database demonstrate that the proposed method can generate 3D meshes with high fidelity and outperforms other state-of-the-art approaches in both qualitative and quantitative results. Our code is publicly available at https://github.com/tasx0823/EasyMesh.

Meshless reconstruction technique for digital tomosynthesis

A novel meshless reconstruction algorithm for digital tomosynthesis (DT) is presented and assessed against experimental data. The algorithm does not require a three-dimensional grid or mesh allocation and performs a slice-by-slice reconstruction where each slice position can be chosen at runtime. The methodology is based on the filtered backprojection algorithm adapted to DT. However, in the traditional approach the backprojection comes first and the filtering follows. Because the backprojection requires ray tracing, in our case it is replaced with an equivalent image mapping procedure. The idea to swap the filtering and backprojection had been introduced earlier for computerized tomography (CT). Here we use this idea but develop it differently. Contrary to CT imaging, where the source and detector are rotated, in DT the subject and the flat panel detector are fixed in space. This imaging geometry allows reconstruction in planes parallel to the flat panel detector, which results in a significant simplification of the filter of backprojection algorithm. Moreover, the algorithm is not memory demanding and can be used with very large datasets. Two versions of the meshless algorithm are presented. One of them is based on convolution type filtering, while another uses filtering in the Fourier domain. Both versions are assessed and compared against the cone beam algorithm.

Взаимные задачи с кониками

The problem for construction of straight lines, which are tangent to conics, is among the dual problems for constructing the common elements of two conics. For example, the problem for construction of a chordal straight line (a common chord for two conics) ~ the problem for construction of an intersection point for two conics’ common tangents. In this paper a new property of polar lines has been presented, constructive connection between polar lines and chordal straight lines has been indicated, and a new way for construction of two conics’ common chords has been given, taking into account the computer graphics possibilities. The construction of imaginary tangent lines to conic, traced from conic’s interior point, as well as the construction of common imaginary tangent lines to two conics, of which one lies inside another partially or thoroughly is considered. As you know, dual problems with two conics can be solved by converting them into two circles, followed by a reverse transition from the circles to the original conics. This method of solution provided some clarity in understanding the solution result. The procedure for transition from two conics to two circles then became itself the subject of research. As and when the methods for solving geometric problems is improved, the problems themselves are become more complex. When assuming the participation of imaginary images in complex geometry, it is necessary to abstract more and more. In this case, the perception of the obtained result’s geometric picture is exposed to difficulties. In this regard, the solution methods’ correctness and imaginary images’ visualization are becoming relevant. The paper’s main results have been illustrated by the example of the same pair of conics: a parabola and a circle. Other pairs of affine different conics (ellipse and hyperbola) have been considered in the paper as well in order to demonstrate the general properties of conics, appearing in investigated operations. Has been used a model of complex figures, incorporating two superimposed planes: the Euclidean plane for real figures, and the pseudo-Euclidean plane for imaginary algebraic figures and their imaginary complements.

The Missing Data Encoder: Cross-Channel Image Completion with Hide-and-Seek Adversarial Network

Image completion is the problem of generating whole images from fragments only. It encompasses inpainting (generating a patch given its surrounding), reverse inpainting/extrapolation (generating the periphery given the central patch) as well as colorization (generating one or several channels given other ones). In this paper, we employ a deep network to perform image completion, with adversarial training as well as perceptual and completion losses, and call it the “missing data encoder” (MDE). We consider several configurations based on how the seed fragments are chosen. We show that training MDE for “random extrapolation and colorization” (MDE-REC), i.e. using random channel-independent fragments, allows a better capture of the image semantics and geometry. MDE training makes use of a novel “hide-and-seek” adversarial loss, where the discriminator seeks the original non-masked regions, while the generator tries to hide them. We validate our models qualitatively and quantitatively on several datasets, showing their interest for image completion, representation learning as well as face occlusion handling.

Esophageal epithelium modeling based on globally coupled map: an approach toward precancerous lesion diagnosis.

Esophageal squamous cell carcinoma is the most predominant malignancy of the esophagus. Its histological precursors (dysplasia) emerge in the esophageal epithelium that their progression into the underlying layers leads to cancer. The epithelium is the origin of many solid cancers and, accordingly, the focus of numerous computational models. In this work, we proposed a framework to establish a two-dimensional, globally coupled map to model the epithelium dynamics. The model aims at diagnosing the early stage of dysplasia based on microscopic images of endoscopic biopsies. We used the logistic map as a black-box model for the epithelial cells. By relating between the structure and dynamic of the epithelium, we defined the coupling function and proposed a case-dependent model in which the parameters were adjusted based on fractal geometry of each pathological image. Thus, by assigning different attractors to the cells' behavior, the lattice dynamic was investigated by the Lyapunov exponent. The decreasing pattern of Lyapunov exponent variations across the epithelium thickness had reasonable performance in diagnosing the normal specimens from the low-grade dysplasia ones. The results showed that there could be a direct relationship between the structural complexity of this system and its uncertainty of dynamics. Graphical abstract The modeling process of the esophageal epithelium to classify the experimental data at normal and LGD stages.

Mechanical Degradation Model of Porous Fe Scaffold: Simulation Approach

This paper proposes a simple degradation model that estimates morphological changes in pure iron scaffolding due to surface erosion. The main contribution of this work is to estimate the degradation of porous pure iron scaffolding and analyze the impact of morphological changes on mechanical properties. In this study, the pure iron scaffolding model was designed in CAD software with 3 different porosity such as 30%, 41%, and 55% respectively. The geometry images of CAD models with a resolution of 3316 x 5530 pixels are captured layer by layer with a thickness of 0.02 mm. The purpose of this method is to replace the function of the u-CT scanning technique. Two-dimensional morphological erosion is applied to reduce the number of pixels of the image model. This erosion process is adjusted iteratively with increasing number of pixels to erode the image model until the volume of the scaffold after reconstruction matches the volume of the model undergoing mathematical calculations. Their changes in the volume of scaffold geometry and degradation of mechanical properties were evaluated using finite element analysis. This study found that mechanical properties such as elastic modulus and yield strength decreased systematically during the 19 week degradation period. In addition, deformation analysis is performed on models based on finite element analysis.

A Finite Element Analysis Study from 3D CT to Predict Transcatheter Heart Valve Thrombosis.

Background: Transcatheter aortic valve replacement has proved its safety and effectiveness in intermediate- to high-risk and inoperable patients with severe aortic stenosis. However, despite current guideline recommendations, the use of transcatheter aortic valve replacement (TAVR) to treat severe aortic valve stenosis caused by degenerative leaflet thickening and calcification has not been widely adopted in low-risk patients. This reluctance among both cardiac surgeons and cardiologists could be due to concerns regarding clinical and subclinical valve thrombosis. Stent performance alongside increased aortic root and leaflet stresses in surgical bioprostheses has been correlated with complications such as thrombosis, migration and structural valve degeneration. Materials and Methods: Self-expandable catheter-based aortic valve replacement (Medtronic, Minneapolis, MN, USA), which was received by patients who developed transcatheter heart valve thrombosis, was investigated using high-resolution biomodelling from computed tomography scanning. Calcific blocks were extracted from a 250 CT multi-slice image for precise three-dimensional geometry image reconstruction of the root and leaflets. Results: Distortion of the stent was observed with incomplete cranial and caudal expansion of the device. The incomplete deployment of the stent was evident in the presence of uncrushed refractory bulky calcifications. This resulted in incomplete alignment of the device within the aortic root and potential dislodgment. Conclusion: A Finite Element Analysis (FEA) investigation can anticipate the presence of calcified refractory blocks, the deformation of the prosthetic stent and the development of paravalvular orifice, and it may prevent subclinical and clinical TAVR thrombosis. Here we clearly demonstrate that using exact geometry from high-resolution CT scans in association with FEA allows detection of persistent bulky calcifications that may contribute to thrombus formation after TAVR procedure.

Robust Mosaicking of Lightweight UAV Images Using Hybrid Image Transformation Modeling

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.