Geometric Correction for Line-Scan Imaging: A 1D Projective–Polar Mapping for Highly Reflective Cylindrical Surfaces

This paper proposes a projection correction method which to improve the adaptive perception projection of the projection equipment in different environments. Firstly, in the process of photon signal transmission, projector-camera can cause the loss of photon signal due to the coupling of system channel. Therefore, this paper proposes a system coupling correction scheme, which effectively reduces the system coupling crosstalk. Secondly, in order to establish the feature mapping relationship between the projection image and the deep heterogeneous surface quickly, a projection feature image of color structured light mesh fringe is designed. Finally, due to the feature point of the heterogeneous surface is quite different in topological structure, it will lead to the problem of inconsistent geometric mapping relation. For this reason, a projective geometric correction algorithm for topological analysis is proposed, analyzing the spatial topological distribution of the depth heterogeneous surface and solving the homography matrix of each region in the heterogeneous surface, then the geometric correction of the projected distortion image is solved by using the homography matrix set. From the experimental analysis we can see that, in the deep heterogeneous surface environment, the average error, the maximum error and the root-mean-square error of the correction image respectively are 0.424 pixels, 0.862 pixels and 0.216 pixels. At the same time, the parallelism of the distortion correction image is kept 90° substantially. It can be seen that the geometric distortion correction accuracy of this method has reached the sub-pixel level and the imaging screen consistency level.

Geometric distortion is a very common problem in image capture, remote sensing, image display, and medical imaging. In a complicated imaging system, it can further induce ghosting, blurring, and intensity change. Traditional methods will adapt the approach of pre-calibration. These pre-calibration methods usually require some human intervention, thus their application scope is quite limited. In addition, they are not applicable in variable geometric distortion. The basic geometric distortion correction is to apply appropriate geometric transformations for images. In this thesis, geometric distortion correction means a generalized one that adjusts spatial transformation parameters. By extracting image features and utilizing image quality measures, we propose three novel algorithms for three geometric distortion correction problems, i.e. radial distortion correction, motion compensation in Magnetic Resonance (MR) images, and disparity adjustment. Due to the nonlinearity in radial distortion, it will result in spatially varying distortion for the image. We adapt the framework of utilizing feature transform and image measure to estimate the radial distortion parameters. First, we use edge extraction and transfer features into the feature map; and then assess the quality of feature map to estimate distortion parameters for the image correction. By using this framework, we develop fully automatic calibration and it can be applied in popular fisheye lenses and medical wide-angle endoscopes, which usually require real-time correction. In addition, we also extend the framework to different types of calibration patterns and zoom lenses with varying geometric distortion. Because of the special capturing procedure of MR images in Fourier domain, the motion of subject during the imaging process will result in ghosting and blurring, and thus different motion compensations for different phase encoding lines have to be estimated. Traditional methods use greedy and exhausted search for optimizing an image quality measure, and ignore other important information. We search repeating edge for collecting candidate motion vectors and use graphical models to fuse different information (including symmetry of frequency, smoothness of motion, and an image quality measure) to solve the problem. The disparity adjustment can be regarded as geometric distortion correction. In order to provide better viewing experience of stereoscopic images, we have to adjust the left and right images geometrically. The simplest method is to shift the left and right images to adjust the disparity range within a comfort zone. However, the shifting in stereoscopic images with large disparity range may not work. Hence, we take image feature for image segmentation and utilize a stereoscopic image quality measure to decide different geometric transformations for different segments for the image correction to improve the viewing experience. In this thesis, we focus on a general geometric distortion correction over the domain of spatial parameters. By utilizing image features and image quality measures, we propose novel algorithms to resolve the three image correction problems described above.

The aim of this study was to establish a distortion correction applicable to whole-body imaging of live mice. All magnetic resonance imaging (MRI) scans were acquired on a compact 1-T permanent magnet unit for mouse imaging using a T1-weighted, three-dimensional (3D) fast low-angle shot sequence. We assessed geometric distortion in MR images of a small 3D grid phantom and determined 3D image transformations for distortion correction. The developed distortion correction was applied to MR images of the 3D grid phantom acquired on another day, and the correction was validated. A two-dimensional (2D) grid phantom was imaged with a mouse to investigate the applicability of the distortion correction to whole-body mouse imaging. Obvious geometric distortion was observed in the MR images of the 3D grid phantom. The application of the developed 3D phantom-based distortion correction reduced distortion in the images of the 3D grid phantom acquired on another day. Geometric distortion was observed in the MR images of the 2D grid phantom acquired together with the mouse. The 3D phantom-based correction decreased the distortion substantially, regardless of mouse positioning. The developed distortion correction can reduce distortion in whole-body imaging of live mice and may enhance the capabilities of MRI in small animal experiments.

A highly compact hyperspectral imager with an automatic geometric rectification function is developed in this study, which can be mounted on a UAV for ultra-wide range hyperspectral imaging. For better application, the system can provide visible light image transmission and hyperspectral imaging in the real-time mode. A specific design is proposed to allow the visible light camera and hyperspectral camera to share the same telescope optical path, making the system have a high integration level with a total mass of 1.9 kilograms. Thanks to the sharing-optical-path design, the field of view (FOV), frame rate, and spatial resolution are modified the same between the visible light camera and hyperspectral camera. As a result, the geometric rectification is easily performed, and repeated rectifications are eliminated to improve the imaging efficiency. A FOV of 40 degrees in the frame direction and 26 degrees in the flight direction are realized with a focal length of 13mm, providing a large spectral range from 400 nm to 1000 nm and an excellent spectral resolution of 2.5 nm. An automatic geometric rectification workflow is presented and verified in experiments, which can improve the geometric rectification of hyperspectral images in the presence of low-quality UAV navigation data through the incorporation of frame images. Experimental results show that the relative accuracy of geometric rectification is less than 2 pixels when applying the algorithm to our system dataset.

Automated geometric correction of multispectral images from High Resolution CCD Camera (HRCC) on-board CBERS-2 and CBERS-2B

To derive and implement a method for correcting spatial distortion caused by in vivo inhomogeneous static magnetic fields in echo-planar imaging (EPI). The reversed gradient method, which was initially devised to correct distortion in images generated by spin-warp MRI, was adapted to correct distortion in EP images. This method provides point-by-point correction of distortion throughout the image. EP images, acquired with a 3 T MRI system, of a phantom and a volunteer's head were used to test the correction method. Good correction was observed in all cases. Spatial distortion in the uncorrected images ranged up to 4 pixels (12 mm) and was corrected successfully. The correction was improved by the application of a nonlinear interpolation scheme. The correction requires that two EP images be acquired at each slice position. This increases the acquisition time, but an improved signal-to-noise ratio (SNR) is seen in the corrected image. The local SNR gain decreases with increasing distortion. In many EPI acquisition schemes, multiple images are averaged at each slice position to increase the SNR; in such cases the reversed gradient correction method can be applied with no increase in acquisition duration.

Geometric accuracy of MRI is one of the main concerns for its use as a sole image modality in precision radiation therapy (RT) planning. In a state-of-the-art scanner, system level geometric distortions are within acceptable levels for precision RT. However, subject-induced B0 inhomogeneity may vary substantially, especially in air-tissue interfaces. Recent studies have shown distortion levels of more than 2 mm near the sinus and ear canal are possible due to subject-induced field inhomogeneity. These distortions can be corrected with the use of accurate B0 inhomogeneity field maps. Most existing methods estimate these field maps from dual gradient-echo (GRE) images acquired at two different echo-times under the assumption that the GRE images are practically undistorted. However distortion that may exist in the GRE images can result in estimated field maps that are distorted in both geometry and intensity, leading to inaccurate correction of clinical images. This work proposes a method for estimating undistorted field maps from GRE acquisitions using an iterative joint estimation technique. The proposed method yields geometrically corrected GRE images and undistorted field maps that can also be used for the correction of images acquired by other sequences. The proposed method is validated through simulation, phantom experiments and applied to patient data. Our simulation results show that our method reduces the root-mean-squared error of the estimated field map from the ground truth by ten-fold compared to the distorted field map. Both the geometric distortion and the intensity corruption (artifact) in the images caused by the B0 field inhomogeneity are corrected almost completely. Our phantom experiment showed improvement in the geometric correction of approximately 1 mm at an air-water interface using the undistorted field map compared to using a distorted field map. The proposed method for undistorted field map estimation can lead to improved geometric distortion correction at air-tissue interfaces, especially in low readout-bandwidth acquisitions, thus making them suitable for clinical use in precision RT without increasing the treatment planning margin.

In this article we investigate the effect of geometrical distortion correction in MR images on the accuracy of the registration of X-ray CT and MR head images for both a fiducial marker (extrinsic point) method and a surface-matching technique. We use CT and T2-weighted MR image volumes acquired from seven patients who underwent craniotomies in a stereotactic neurosurgical clinical trial. Each patient had four external markers attached to transcutaneous posts screwed into the outer table of the skull. The MR images are corrected for static field inhomogeneity by using an image rectification technique and corrected for scale distortion (gradient magnitude uncertainty) by using an attached stereotactic frame as an object of known shape and size. We define target registration error (TRE) as the distance between corresponding marker positions after registration and transformation. The accuracy of the fiducial marker method is determined by using each combination of three markers to estimate the transformation and the remaining marker to calculate registration error. Surface-based registration is accomplished by fitting MR contours corresponding to the CSF-dura interface to CT contours derived from the inner surface of the skull. The mean point-based TRE using three noncollinear fiducials improved 34%-from 1.15 to 0.76 mm-after correcting for both static field inhomogeneity and scale distortion. The mean surface-based TRE improved 46%-from 2.20 to 1.19 mm. Correction of geometrical distortion in MR images can significantly improve the accuracy of point-based and surface-based registration of CT and MR head images. Distortion correction can be important in clinical situations such as stereotactic and functional neurosurgery where 1 to 2 mm accuracy is required.

Geometric distortions in brain MRI images arising from susceptibility artifacts at air-tissue interfaces pose a significant challenge for high-precision radiation therapy modalities like stereotactic radiosurgery, necessitating sub-millimeter accuracy. To achieve this goal, we developed AutoCorNN, an unsupervised physics-aware deep-learning model for correcting geometric distortions. Two publicly available datasets, the MPI-Leipzig Mind-Brain-Body with 318 subjects, and the Vestibular Schwannoma-SEG dataset, encompassing 242 patients were utilized. AutoCorNN integrates two 2D convolutional encoder-decoder neural networks with the forward physical model of MRI signal generation to predict undistorted MR and field map images from distorted MR input. The network is trained in an unsupervised manner by minimizing the mean absolute error between the measured and estimated k-space data, without requiring ground truth images during training or deployment. The model was evaluated on vestibular schwannoma cases. AutoCorNN achieved a peak signal-to-noise ratio (PSNR) of 41.35 ± 0.02dB, a root mean square error (RMSE) of 0.02 ± 0.003, and a structural similarity index (SSIM) of 0.99 ± 0.02 outperforming uncorrected and B0-mapping correction methods. Geometric distortions of about 1.6mm were observed at the air-tissue interfaces at the air canal and nasal cavity borders. Geometrically, distortion correction increased the target volume from 3.12 ± 0.52cc to 3.84 ± 0.54cc. Dosimetrically, AutoCorNN improved target coverage (0.96 ± 0.01 to 0.97 ± 0.02), conformity index (0.92 ± 0.03 to 0.94 ± 0.03), and reduced dose gradients outside the target. AutoCorNN achieves accurate geometric distortion correction comparable to conventional iterative methods while offering substantial computational acceleration, enabling precise target delineation and conformal dose delivery for improved radiation therapy outcomes.

Purpose:Gamma Knife (GK) planning is mostly based upon MRI. Due to the high accuracy required for SRS treatments, geometric distortions in these images should be minimal. MRI Manufacturer provided first order geometric distortions correction algorithms may not reduce distortions to a level that may not be acceptable for treatments requiring high positional accuracy. The purpose of this work is to evaluate the residual, radiosurgery‐relevant geometric distortions on VIBE, MPRAGE, GRE and CISS sequences.Methods:The 3D rectilinear phantom, GRID3D, was scanned in the Leksell Frame‐G with different MRI axial sequences: MPRAGE, VIBE, GRE and CISS, on a Siemens SKYRA 3T MR unit. Siemens 3D distortion correction was applied to all sequences. The residual distortion map of the phantom's 2002 vertices was evaluated by comparing the expected positions of the vertices, with the actual measured locations using Modus’ image distortion analysis software (QUASARTM). Distortions were specified as X, Y, Z, and radial deviations. As an independent verification, the MRI sequences were co‐registered with CT images of the phantom in GammaPlan.Results:All sequences showed mean radial residual distortions greater than 1 mm. Maximum radial distortion ranged between 3 and 8 mm. Z axis distortions were the highest for GRE and CISS sequences, and lowest for VIBE. Y distortions were lowest for the VIBE and MPRAGE sequences. X distortion was lowest for GRE and CISS sequences. Almost equal X and Y distortions were measured for CISS. Larger distortions were mainly observed in peripheral regions of the phantom for all sequences. CT‐MR co‐registration in GammaPlan confirmed these results. The residual distortions were deemed unacceptable for MR based GK treatments.Conclusion:The in‐phantom analysis of MR sequences using the Modus phantom allows for effective quantitative evaluation of residual distortion in MR images. MR‐CT co‐registration facilitates qualitative assessment of MRI distortions.

The reverse ray-tracing method has become a well-known technique to correct the dynamic imaging distortion caused by the Risley-prism imaging system due to its precision and computational efficiency. However, the reverse ray-tracing method is sensitive to equipment error, which seriously degrades the quality of distortion correction when using a prism with a large wedge angle or a camera with a large field of view. We optimize the distortion correction method utilizing reverse ray tracing. In addition, we propose a distortion correction model with error parameters to investigate the influence of prism orientation error, prism tilt error, prism parameter error, and model simplification errors on the correction accuracy. The work on the optimized model clearly indicates the obvious image distortion introduced by different kinds of errors, including model error and systematic error. Furthermore, we propose an error parameter identification method to eliminate the negative results of error on the image correction. The simulation results show that the boresight pointing error and distortion correction error are reduced to about 1% of the initial value after 10 iterations, thus achieving high-precision imaging distortion correction and providing better data support for other subsequent applications.

This paper focuses on the calibration problem using stereo camera images. Currently, advanced vehicle systems such as smart cars and mobile robots require accurate and reliable vision in order to detect obstacles and special marks around. Such modern vehicles can be equipped with sensors and cameras together or separately. In this study, we propose new methodologies of stereo camera calibration based on the correction of distortion and image rectification. Once the calibration is complete, the validation of the corrections is presented followed by an evaluation of the calibration process. Usually, the validation section is not jointly considered with the calibration in other studies. However, the mass production of cameras widely uses the validation techniques in calibrations owned by manufacturing businesses. Here, we aim to present a single process for the calibration and validation of stereo cameras. The experiment results showed the disparity maps in comparison with another study and proved that the proposed calibration methods can be efficient.

Bistatic inverse synthetic aperture radar (ISAR) can help image the high-speed target for its advantage in tracking and more observation angle to provide more information than monostatic ISAR. However, the complex image geometry makes it difficult to achieve a clear image of the target with geometry distortion correction and calibration. Furthermore, high-speed motion will make the image blurred or defocussed. To address these problems, a bistatic ISAR (B-ISAR) imaging method for high-speed motion target with geometric distortion correction and calibration is proposed. According to the motion decomposition idea, we established the B-ISAR echo model of the high-speed motion target. Then, based on the range Doppler algorithm, we deduce the analytic formula of the geometric distortion factor and calibration factor, and transform the imaging problem into a parameter estimation problem. With the sparsity of the scattering points, the required parameters are solved using the expectation maximization algorithm based on the maximum a posteriori probability criterion. With the estimated parameters, a clear B-ISAR image of a high-speed motion target with geometric correction and calibration is obtained. The simulations show that the proposed method has better resolution and simultaneously attains geometric distortion correction and calibration of the image.

Since the spatial field non-linearity of gradient coils translates into image geometric distortion in MRI, in many applications, such as cardiac function analysis and interventional MR-based device tracking/guidance, where the precise geometric information is needed, the presence of geometric image distortion can not be simply ignored. To address the concern for geometric image distortion, we have developed and validated a general and efficient numerical technique for parameterizing the global image distortion for a bi-planar gradient coil as well as accomplishing image restoration as a post-imaging processing. This image correction methodology is based on a global distortion coordinate mapping function which can be systematically defined directly from the gradient field non-linearity in 3-dimension (3D) of a given gradient coil. The image correction was carried out in two steps: (1) map each pixel of the corrected image representation onto its distorted image according to the distortion mapping; (2) interpolate the pixel intensity in the distorted image using its neighboring points via a bi-linear interpolation procedure. The results showed clearly that the distortion correction method was robust in term of the capability of reducing image geometric distortion dramatically. Also it is shown that the magnetic field non-linearity or the image distortion of a typical bi-planar gradient coil can be adequately parameterized using a finite Taylor series expansion based on its design parameters. Furthermore, this image distortion correction method is very efficient in practice for performing 3D correction for any image orientation since a compact parameterized field expression contains non-zero terms.

Effects of geometric distortion in 0.2 T MRI on radiotherapy treatment planning of prostate cancer