Therefore, planar calibration objects are preferred in computer vision applications [8]. Planar calibration objects and projective constraints can be used for calibration of parametric and nonparametric distortions of a camera system [9]. The camera calibration problem for planar robotic manipulators through visual servoing under a fixed-camera configuration has been investigated in [10].Dual images of spheres and the dual image of the absolute conic have been used for solving the problem of camera calibration from spheres in [11]. The mirror-symmetric objects have been used for camera calibration in [12]. An accurate calibration procedure has been introduced for fish-eye lenses in [13]. The calibration of a projector-camera system by estimating the homography has been investigated in [14].

Online calibration methods have been used in virtual reality applications in [15]. A dynamic calibration method for multiple cameras has been investigated in [16]. Due to the noise-influenced image coordinates, most of the existing camera calibration techniques are unsuccessful aspects of robustness and accuracy.The artificial neural networks (ANNs) can mimic the transformation between the image plane and the global coordinate system. By using ANNs, it becomes unnecessary to know both the physical parameters and the geometrical parameters of the imaging systems for 3D perception of objects from their 2D images. ANNs have been intensively used for camera calibration in some recently introduced methods [17, 18, 19]. A planar pattern has been observed at different rotations for setting training and test data sets of the ANN used.

The rotation value of the planar pattern has been acquired by using an Xsens MTi-9 inertial sensor [20, 21]. Dacomitinib With the proposed method, the 3D global coordinates of object points have been predicted from their 2D corresponding image coordinates.The Xsens MTi-9 sensor is a miniaturized, gyro-based Attitude and Heading Reference System whose internal signal processor provides drift-error free 3D acceleration, 3D orientation, and 3D earth-magnetic field data. The drift-error growing nature of inertial systems limits the accuracy of inertial measurement devices. Inertial sensors can supply reliable measurements only for small time intervals. The inertial sensors have been used in some recent research for stabilization and control of digital cameras, calibration patterns and other equipment [22, 23].The Modified Direct Linear Transformation (MDLT) is one of the commonly used camera calibration methods in computational vision applications for 2D and 3D object reconstruction [24]. The success of the proposed method has been evaluated by comparing the test results of the proposed method and MDLT method.