Fringe projection profilometry (FPP) using a digital video projector is widely used for three-dimensional shape measurement. However, the gamma nonlinearity, system vibration, and noise cause the captured fringe patterns to be nonsinusoidal waveforms and have a grayscale deflection from their true value. This leads to an additional phase measurement error for a general phase-shifting algorithm. Based on the theoretical analysis, we propose a method to eliminate the phase error considering two factors. In this method, four-step phase-shifting is done four times with an initial phase offset of 22.5 deg and the average of these four phase maps precisely results in the real phase. As a result, phase error caused by gamma nonlinearity can be effectively suppressed. In addition, every image in phase shifting is replaced by the average of 20 fringe images continuously captured at the same state to avoid the phase error caused by system vibration and noise. Experimental results show that this method is effective in eliminating the phase error in practical phase-shifting FPP. In general, more than 90% of the phase error can be reduced.
Digital image correlation matches the corresponding locations in the reference and deformed images by optimizing
the correlation of the related intensities. Iterative algorithm is regarded as the most effective approach to solving
the optimization, but it requires accurate initial guess of the deformation parameters to converge correctly and
rapidly. This paper presents a fully automated method which provides accurate initialization for all points of
interest in a deformed images and deals with large rotation and heterogeneous deformation. Image features are
extracted and pre-matched in the reference and the deformed images. The deformation parameter of a sample
point is initialized by the mapping function fitted to the matched features in the vicinity. Once the subsequent
iterative optimization achieves a qualified correlation measure, the optimized parameter is used to initiate a
parameter transfer. To account for potential deformation difference between successive points, propagation
functions are used during the transfer, which are analytically derived to accurately relate the parameters of
two points separated by a given distance. The parameter transfer is conducted by the quality of correlation
optimization and continued till all the points have been analyzed. Results on both simulated deformations and
real-world experiments demonstrate that image features can be reliably matched and automatically generate
qualified seed points even in the presence of complex transformation. Parameter transfer using propagation
function enables rapid and correct convergence of the nonlinear iterative optimization, allows more flexible choice
on the interval between adjacent sample points, and meanwhile handles the heterogeneity of the deformation
field.
Three-dimensional (3-D) tracking and trajectory measurement of group translating and rotating particles may greatly help applications in collective behavior study, motion measurement, etc. Binocular stereo methods are commonly used to track and measure 3-D trajectories of drifting particles. Nevertheless, binocular methods usually suffer from severe stereo-matching ambiguity facing these situations even if motion constraint is adopted to disambiguate stereo matching. We try to help the disambiguating by optimizing viewpoint placement. We model the stereo-matching ambiguity and test different viewpoint placements upon our geometrical analysis to show the influence on the disambiguation that utilizes motion constraint. When the targets undergo group translation and rotation which are highly ambiguous, we find the optimal viewpoint placement such that stereo-matching ambiguity decreases as fast as possible over time. The optimal viewpoint placement can greatly improve the performance of existing methods.
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