Abstract— Motion sensors as inertial measurement units (IMU) are widely used in robotics, for instance in the navigation and mapping tasks. Nowadays, many low cost micro electro mechanical systems (MEMS) based IMU are available off the shelf, while smartphones and similar devices are almost always equipped with low-cost embedded IMU sensors. Nevertheless, low cost IMUs are affected by systematic error given by imprecise scaling factors and axes misalignments that decrease accuracy in the position and attitudes estimation. In this paper, we propose a robust and easy to implement method to calibrate an IMU without any external equipment. The procedure is based on a multi-position scheme, providing scale and misalignments factors for both the accelerometers and gyroscopes triads, while estimating the sensor biases. Our method only requires the sensor to be moved by hand and placed in a set of different, static positions (attitudes). We describe a robust and quick calibration protocol that exploits an effective parameterless static filter to reliably detect the static intervals in the sensor measurements, where we assume local stability of the gravity’s magnitude and stable temperature. We first calibrate the accelerometers triad taking measurement samples in the static intervals. We then exploit these results to calibrate the gyroscopes, employing a robust numerical integration technique. The performances of the proposed calibration technique has been successfully evaluated via extensive simulations and real experiments with a commercial IMU provided with a calibra- tion certificate as reference data.

Chromatic aberration (also known as colour fringing) is a phenom- ena where different wavelengths of light refract through different parts of a lens system. Thus, the colour channels may not align as they reach the sensor/film. This is most notable in cheaper lenses, it is also noticeable at higher resolutions. We desire an image free of chromatic aberrations is simple, so all the planes are in focus. For a simple lens system this amounts to misaligned colour channels (red, green and blue). The misalignment is due to a uniform scaling and translation. There are many types of other chromatic aberrations. Complex lens assemblies introduce new distortions. We propose a method to deal with the simple, more common scenario. We later discuss possible ways to deal with more complex ones

his paper reports an experiment conducted to evaluate correction methods of chromatic aberrations in images acquired by a non- metric digital camera. The chromatic aberration correction methods evaluated in the experiment are classified into two kinds. One is the method to correct image coordinates by using camera calibration results of color-separated images. The other is the method based on the assumption that the magnitude of chromatic aberrations can be expressed by a function of a radial distance from the center of an image frame. The former is classified further into five types according to the difference of orientation parameters common to all colors. The latter is classified further into three types according to the order of the correction function. We adopt a linear function, a quadratic function and a cubic function of the radial distance as a correction function. We utilize a set of 16 convergent images shooting a white sheet with 10 by 10 black filled circles to carry out camera calibration and estimate unknown coefficients in the correction function by means of least squares adjustment. We evaluate the chromatic aberration correction methods by using a normal image shooting a white sheet with 14 by 10 black filled circles. From the experiment results, we conclude that the method based on the assumption that the magnitude of chromatic aberrations can be expressed by a cubic function of the radial distance is the best method of the evaluated methods, and would be able to correct chromatic aberrations satisfactorily enough in many cases

Instead of more expensive and complex optics, recent years, many researches are focused on high-quality photography using light- weight cameras, such as single-ball lens, with computational image pro- cessing. Traditional methods for image enhancement do not comprehen- sively address the blurring artifacts caused by strong chromatic aber- rations in images produced by a simple optical system. In this paper, we propose a new method to correct both lateral and axial chromatic aberrations based on their different characteristics. To eliminate lateral chromatic aberration, cross-channel prior in shearlet domain is proposed to align texture information of red and blue channels to green channel. We also propose a new PSF estimation method to better correct axial chromatic aberration using wave propagation model, where F-number of the optical system is needed. Simulation results demonstrate our method can provide aberration-free images while there are still some artifacts in the results of the state-of-art methods. PSNRs of simulation results in- crease at least 2 dB and SSIM is on average 6.29% to 41.26% better than other methods. Real-captured image results prove that the pro- posed prior can effectively remove lateral chromatic aberration while the proposed PSF model can further correct the axial chromatic aberration.