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Accurate correction of radial lens distortion is a fundamental requirement in computer vision and photogrammetry, as geometric inaccuracies directly affect 3D reconstruction, mapping, and geospatial measurements, particularly in high-precision imaging systems. In this study, we propose a fully analytical, non-iterative method for truncated inverse modeling of radial lens distortion, applicable to general radial distortion polynomials that contain constant terms. Unlike classical truncated Lagrange series reversion, which relies on recursive expansion and combinatorial series construction, the proposed formulation determines inverse distortion coefficients directly through a system of constrained algebraic inverse polynomials. This enables deterministic computation of inverse parameters without iterative refinement, numerical root finding, or combinatorial complexity. The method was evaluated using ultra-wide-angle smartphone camera imagery exhibiting severe barrel distortion modeled by an eighth-degree depressed radial distortion polynomial. Its performance was compared with a commonly used iterative inverse modeling approach. The analytical formulation demonstrated improved numerical stability and substantially reduced reprojection errors when correcting highly nonlinear distortion profiles, achieving sub-pixel accuracy in image rectification. In contrast, the iterative approach exhibited instability and significantly larger reprojection errors under identical conditions. These results demonstrate that the proposed framework provides a general, robust, and repeatable solution for inverse radial distortion modeling, particularly for high-order polynomial models. The method offers clear practical advantages for camera calibration pipelines in photogrammetry, remote sensing, robotics, and other applications requiring high-fidelity imaging.

Estimating the absolute pose of a camera is one of the key steps for computer vision. In some cases, especially when using a wide-angle or zoom lens, the focal length and radial distortion also need to be considered. Therefore, in this paper, an efficient and robust method for a single solution is proposed to estimate the absolute pose for a camera with unknown focal length and radial distortion, using three 2D–3D point correspondences and known camera position. The problem is decomposed into two sub-problems, which makes the estimation simpler and more efficient. The first sub-problem is to estimate the focal length and radial distortion. An important geometric characteristic of radial distortion, that the orientation of the 2D image point with respect to the center of distortion (i.e., principal point in this paper) under radial distortion is unchanged, is used to solve this sub-problem. The focal length and up to four-order radial distortion can be determined with this geometric characteristic, and it can be applied to multiple distortion models. The values with no radial distortion are used as the initial values, which are close to the global optimal solutions. Then, the sub-problem can be efficiently and accurately solved with the initial values. The second sub-problem is to determine the absolute pose with geometric linear constraints. After estimating the focal length and radial distortion, the undistorted image can be obtained, and then the absolute pose can be efficiently determined from the point correspondences and known camera position using the undistorted image. Experimental results indicate this method’s accuracy and numerical stability for pose estimation with unknown focal length and radial distortion in synthetic data and real images.

Camera or lens-based detector calibration is essential for spatial accuracy in applications like dimensional tomography, optical metrology, and computer vision. Many methods and software exist yet there is still a lack of approaches that achieve both high accuracy and robustness while being easy to use and capable of handling a wide range of distortions. Radial lens distortion is common in high-resolution X-ray detector optics used in parallel-beam tomography at synchrotrons. Achieving sub-pixel accuracy requires calibrating with an optical target image. Although methods for characterizing radial distortion are well established, acquired images often also include perspective distortion and optical center offset. Here, we present our approaches to individually characterize and correct both types of distortion using a single calibration image, implemented in the Discorpy software.

This article presents a new approach to calculating the inverse of radial distortions. The method presented here provides a model of reverse radial distortion, currently modeled by a polynomial expression, that proposes another polynomial expression where the new coefficients are a function of the original ones. After describing the state of the art, the proposed method is developed. It is based on a formal calculus involving a power series used to deduce a recursive formula for the new coefficients. We present several implementations of this method and describe the experiments conducted to assess the validity of the new approach. Such an approach, non-iterative, using another polynomial expression, able to be deduced from the first one, can actually be interesting in terms of performance, reuse of existing software, or bridging between different existing software tools that do not consider distortion from the same point of view.

Many computer vision algorithms rely on the assumptions of the pinhole camera model, but lens distortion with off-the-shelf cameras is usually significant enough to violate this assumption. Many methods for radial distortion estimation have been proposed, but they all have limitations. Robust automatic radial distortion estimation from a single natural image would be extremely useful for many applications, particularly those in human-made environments containing abundant lines. For example, it could be used in place of an extensive calibration procedure to get a mobile robot or quadrotor experiment up and running quickly in an indoor environment. We propose a new method for automatic radial distortion estimation based on the plumb-line approach. The method works from a single image and does not require a special calibration pattern. It is based on Fitzgibbon’s division model, robust estimation of circular arcs, and robust estimation of distortion parameters. We perform an extensive empirical study of the method on synthetic images. We include a comparative statistical analysis of how different circle fitting methods contribute to accurate distortion parameter estimation. We finally provide qualitative results on a wide variety of challenging real images. The experiments demonstrate the method’s ability to accurately identify distortion parameters and remove distortion from images.

This paper presents a distortion compensation algorithm for multi-camera systems that does not require specialized calibration targets. A review of classical distortion models as well as modern calibration approaches (such as OpenCV) is provided. A modification of the distortion compensation algorithm is proposed, and an experimental comparison with the classical Brown–Conrady model is conducted using data from cameras equipped with the Sony IMX462 sensor. The results show that the proposed algorithm achieves projection rectification comparable to target-based calibration while preserving a wide field of view. This opens up opportunities for applying the method in wearable monitoring systems, panoramic image creation, and pipeline inspection, where the use of calibration targets is challenging.

Vision-based pose estimation has been widely applied in unmanned aerial vehicle (UAV) navigation. However, existing visual pose estimation algorithms are highly sensitive to camera imaging distortion, which degrades estimation accuracy, and often suffer from noticeable jitter between frames in dynamic scenarios. To address these issues, this paper proposes an improved visual pose estimation algorithm built upon the Perspective Similar Triangle (PST) geometric model. Using a planar fiducial marker as the observation target, the single-frame pose estimation problem is reformulated as a hierarchical geometric inference framework, including image point distortion correction, depth recovery based on planar similar triangle constraint, and rigid transformation estimation between the camera and world coordinate systems. This formulation improves pose estimation accuracy under distorted imaging conditions. To accommodate distortion variations in practical scenarios, a radial distortion coefficient update method is further designed to adaptively adjust the radial distortion parameters under single-frame observations, ensuring that the distortion model remains consistent with the actual imaging distortion and providing reliable model inputs for distortion correction in pose estimation. In addition, to enhance pose stability in dynamic scenarios, a multi-frame optical center consistency constraint (MOCCC) method is introduced to optimize the pose estimation for more stability. By constraining pose estimation across adjacent frames using the mean optical center over multiple frames as the optimization objective, the proposed method effectively suppresses pose jitter caused by single-frame observation noise. Finally, a three-degree-of-freedom (3-DOF) attitude motion platform is established, and both static and dynamic experimental scenarios are designed to validate the accuracy and stability of the proposed algorithm. Experimental results demonstrate that the proposed algorithm achieves high accuracy and high stability pose estimation under imaging distortion and small perturbations, exhibiting good robustness and suitability for practical UAV visual navigation applications.

Corner detection is important in image analysis and understanding, but most existing corner detectors are sensitive to image quality, lens radial distortion, and illumination. In this paper, we propose a corner detector for robust corner detection in continuous space. We use the open string theory to construct the continuous representation of an image. Defining a corner as the intersection of two or more curve edges or straight line edges, we design a corner response function for corner determination. In detail, for each integer point, we construct multiple grayscale-parallelograms by any two directed line segments of that point, and the corner response function is based on these grayscale-parallelograms. Finally, a point with a high response value is detected as a corner. Experimental results on conventional images, wide-angle images, and fisheye images show that the proposed method obtains state-of-the-art performance on conventional images and achieves superior performance on wide-angle images and fisheye images, even under weak lighting and low-quality conditions.

This paper presents a novel technique for wide-angle fisheye lens calibration which requires neither metric information nor particular reference pattern. First, the fisheye imaging model with the interior Orientation parameters (IOPs)—principal point ( u 0 ,v 0 ), focal length f , aspect ratio λ and radial distortion coefficients ( k 1 , k 2 ), is established. Then, upon the fisheye imaging model and the parameter dependency between f and ( k 1 , k 2 ), the radial distortion projection ellipse constraint (RDPEC) for space lines in fisheye image is mathematically formulated to build a non-linear calibration model for high-precision estimation of the IOPs. In this step, parameter initialization based on the geometry of fisheye image outline ellipse (FIOE) is discussed as well. Finally, initial IOPs are further optimized though least square technique by taking the projection ellipse arcs of space lines in fisheye image as observation. The proposed calibration technique was tested on two kinds of fisheye images: (a) simulated image with a set of ground-truth IOPs, (b) internet images with unknown IOPs. Experimental results show that the calibration parameters in this paper are in the best agreement with the fisheye imaging model, compared with the ground-truth parameters and the parameters estimated by two state-of-the-art literature. Compared to that by a state-of-the-art CNN and the well-known software DXO, the proposed technique can enable a high-quality correction of fisheye images in different regions. This makes it very useful in application scenarios containing space lines, such as urban panorama surveillance, auto-parking and, robot navigation.

There is increasing adoption of cost-effective nonmetric camera-equipped unmanned aerial vehicles due to the perceived benefits of timesaving, ease of use, and the accuracy of the digital elevation models that can be produced using structure from motion software. The introduction of systematic elevation errors, doming and bowing, has been evidenced by several authors, and various methods have been identified to reduce these errors. This paper aims to analyse the impact of flight plans on these systematic errors using the especially challenging case of a corridor survey. Two sites were flown for the survey using a DJI Zenmuse. The first site, a car park, was utilised for on-the-job pre-calibration of the camera and consisted of several orbit flights and a double grip flight. Subsequently, an adjacent road (a corridor survey overall 428 m long) was also surveyed at 60 m and 80 m heights using varying flight configurations. This study confirms that pre-calibrating the camera's IOPs significantly reduces the root mean squared elevation error (from 0.268 m to 0.034 m) compared to self-calibrated IOPs using the corridor flights. The impact of flight design on elevation errors confirms a single flight path's risk and the benefits of two or more flight paths, including a point-of-interest orbit flight.