【4.1 Controlled Evaluation of Decomposed Motion Fields】

Setup A Sony DSC-QX100 camera is mounted on a motorized linear slider (GVM 1.5D-120) supported by a tripod, with a \(13 \times 12\) checkerboard calibration board containing \(18\,\mathrm{mm}\) squares serving as the reference target. Camera calibration is performed using the MATLAB R2025b Camera Calibration Toolbox. Linear slider is performed at a constant speed of \(2.81\,\mathrm{cm/s}\), while the checkerboard is mounted on a motorized turntable rotating clockwise at a constant angular velocity of \(0.197\,\mathrm{rad/s}\). Camera calibration and optical alignment are summarized in the paper, which reports the calibrated intrinsic parameters, lens distortion coefficients, reprojection error, and center-alignment statistics. Optical alignment is quantified by the horizontal and vertical offsets \((dx,dy)\) between the checkerboard center and the optical axis, together with the radial deviation \(r=\sqrt{dx^2+dy^2}\), reported as the mean \(\pm\) standard deviation over ten repeated trials. Four controlled scenarios are evaluated. In Geometric Divergence, the camera moves along its optical axis toward or away from the checkerboard, producing zoom-in and zoom-out effects over a camera-checkerboard distance ranging from \(58.7\) to \(82.8\,\mathrm{cm}\). In Pure Rotation, the camera remains fixed while the checkerboard rotates at a camera-checkerboard distance of \(72.3\,\mathrm{cm}\). In Horizontal Translation, the camera moves leftward along the slide rail while the checkerboard remains stationary, with the camera-checkerboard distance varying from \(88.7\) to \(93.2\,\mathrm{cm}\) at a vertical separation of \(85.5\,\mathrm{cm}\). In Varying Illumination, the camera-checkerboard distance remains fixed at \(57.4\,\mathrm{cm}\), while a light source follows a semicircular trajectory above the camera with a light-checkerboard distance ranging from \(59.0\) to \(69.3\,\mathrm{cm}\). Preview