Radially-Distorted Conjugate Translations

This paper introduces the first minimal solvers that jointly solve for affine-rectification and radial lens distortion from coplanar repeated patterns. Even with imagery from moderately distorted lenses, plane rectification using the pinhole camera model is inaccurate or invalid. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle imagery, which is now common from consumer cameras. The solvers are derived from constraints induced by the conjugate translations of an imaged scene plane, which are integrated with the division model for radial lens distortion. The hidden-variable trick with ideal saturation is used to reformulate the constraints so that the solvers generated by the Grobner-basis method are stable, small and fast. Rectification and lens distortion are recovered from either one conjugately translated affine-covariant feature or two independently translated similarity-covariant features. The proposed solvers are used in a \RANSAC-based estimator, which gives accurate rectifications after few iterations. The proposed solvers are evaluated against the state-of-the-art and demonstrate significantly better rectifications on noisy measurements. Qualitative results on diverse imagery demonstrate high-accuracy undistortions and rectifications. The source code is publicly available at https://github.com/prittjam/repeats

Rectification from Radially-Distorted Scales

This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from repetitions of rigidly transformed coplanar local features. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle images that contain nearly any type of coplanar repeated content. We demonstrate a principled approach to generating stable minimal solvers by the Grobner basis method, which is accomplished by sampling feasible monomial bases to maximize numerical stability. Synthetic and real-image experiments confirm that the solvers give accurate rectifications from noisy measurements when used in a RANSAC-based estimator. The proposed solvers demonstrate superior robustness to noise compared to the state-of-the-art. The solvers work on scenes without straight lines and, in general, relax the strong assumptions on scene content made by the state-of-the-art. Accurate rectifications on imagery that was taken with narrow focal length to near fish-eye lenses demonstrate the wide applicability of the proposed method. The method is fully automated, and the code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin

Minimal Solvers for Single-View Lens-Distorted Camera Auto-Calibration

This paper proposes minimal solvers that use combinations of imaged translational symmetries and parallel scene lines to jointly estimate lens undistortion with either affine rectification or focal length and absolute orientation. We use constraints provided by orthogonal scene planes to recover the focal length. We show that solvers using feature combinations can recover more accurate calibrations than solvers using only one feature type on scenes that have a balance of lines and texture. We also show that the proposed solvers are complementary and can be used together in a RANSAC-based estimator to improve auto-calibration accuracy. State-of-the-art performance is demonstrated on a standard dataset of lens-distorted urban images. The code is available at https://github.com/ylochman/single-view-autocalib

An Experimental Study of Fan Inflow Distortion Tone Noise

The tone noise generated when a fan ingests circumferentially distorted flow was studied by an experiment conducted with the Advanced Noise Control Fan at the NASA Glenn Research Center. The inflow was distorted by inserting cylindrical rods radially into the duct. The rods were arranged in circumferentially irregular patterns in three of the five configurations tested. Rods were held in place using a mounting ring with 30 equally spaced holes placed at an axial location one rotor chordlength upstream of the fan. Acoustic pressure was measured in the inlet and exhaust duct of the fan using the Rotating Rake fan tone measurement system. Sound power levels, calculated from the measured data, were plotted as a function of circumferential mode. An analytic description of the unsteady pressure distribution at the interaction plane between the stationary rods and the fan rotor is presented in a form suitable for representing the circumferentially irregularly placed rods. Terms in the analytical description for sound power were proven to be useful in determining the dominant circumferential modes measured in the experiment and the differences in mode power level between the configurations tested. Insight gained through this work will be useful in the development of tools to compute fan inflow distortion tone noise

Predicted and Measured Modal Sound Power Levels for a Fan Ingesting Distorted Inflow

Refinements have been made to a method for estimating the modal sound power levels of a ducted fan ingesting distorted inflow. By assuming that each propagating circumferential mode consists only of a single radial mode (the one with the highest cut-off ratio), circumferential mode sound power levels can be computed for a variety of inflow distortion patterns and operating speeds. Predictions from the refined theory have been compared to data from an experiment conducted in the Advanced Noise Control Fan at NASA Glenn Research Center. The inflow to the fan was distorted by inserting cylindrical rods radially into the inlet duct. The rods were placed at an axial location one rotor chord length upstream of the fan and arranged in both regular and irregular circumferential patterns. The fan was operated at 2000, 1800, and 1400 rpm. Acoustic pressure levels were measured in the fan inlet and exhaust ducts using the Rotating Rake fan mode measurement system. Far field sound pressure levels were also measured. It is shown that predicted trends in circumferential mode sound power levels closely match the experimental data for all operating speeds and distortion configurations tested. Insight gained through this work is being used to develop more advanced tools for predicting fan inflow distortion tone noise levels

BabelCalib: A Universal Approach to Calibrating Central Cameras

Existing calibration methods occasionally fail for large field-of-view cameras due to the non-linearity of the underlying problem and the lack of good initial values for all parameters of the used camera model. This might occur because a simpler projection model is assumed in an initial step, or a poor initial guess for the internal parameters is pre-defined. A lot of the difficulties of general camera calibration lie in the use of a forward projection model. We side-step these challenges by first proposing a solver to calibrate the parameters in terms of a back-projection model and then regress the parameters for a target forward model. These steps are incorporated in a robust estimation framework to cope with outlying detections. Extensive experiments demonstrate that our approach is very reliable and returns the most accurate calibration parameters as measured on the downstream task of absolute pose estimation on test sets. The code is released at https://github.com/ylochman/babelcalib

Trust Your IMU: Consequences of Ignoring the IMU Drift

In this paper, we argue that modern pre-integration methods for inertial measurement units (IMUs) are accurate enough to ignore the drift for short time intervals. This allows us to consider a simplified camera model, which in turn admits further intrinsic calibration. We develop the first-ever solver to jointly solve the relative pose problem with unknown and equal focal length and radial distortion profile while utilizing the IMU data. Furthermore, we show significant speed-up compared to state-of-the-art algorithms, with small or negligible loss in accuracy for partially calibrated setups. The proposed algorithms are tested on both synthetic and real data, where the latter is focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the proposed solvers on different commercially available low-cost UAVs, and demonstrate that the novel assumption on IMU drift is feasible in real-life applications. The extended intrinsic auto-calibration enables us to use distorted input images, making tedious calibration processes obsolete, compared to current state-of-the-art methods