结构光测量中快速相位解包裹算法的讨论

Fast Phase-unwrapping Algorithms Used for Structural-light Measurement

对Schofield等提出的快速傅里叶变换(采用4次傅里叶变换和4次逆傅里叶)解包裹算法和Volkov等提出的相位重建算法(仅采用两次傅里叶变换和一次逆傅里叶变换)进行了讨论,提出基于离散余弦变换的快速相位解包裹算法.指出前两种算法在处理一般带噪音的模拟相位图时具有明显的优势,其处理结果非常接近理想值,而在处理相位变化剧烈或不连续区域的实验相位图(采用四步相移法测量雕刻佛像的三维面形)时出现较大误差,甚至无法处理,而基于离散余弦变换算法能很好的解决这个问题,并且拥有比前两种算法更快的运算速度.在实际应用中,针对不同的相位图把Schofield所提出的算法与基于离散余弦变换的算法结合起来,可以解决大部分相位解包裹问题.

Two kinds of fast phase-unwrapping algorithms were studied, namely, Sehofield＇ s 4-FFT algorithm and Volkov＇s deterministic 2-FFT algorithm. Then a DCT-based phase-unwrapping algorithm is proposed. The former two algorithms were proved to enjoy an obvious advantage in processing phase maps with much stochastic noise. Their final unwrapped-phase results are very close to the ideal ones. But, there appear some big errors in unwrapping the experimental phase map with large gradient and some inconsistent regions. It is hard for them to achieve a reasonable solution. In this case, the DCT-based algorithm can make up the above disadvantages and is able to achieve a reliable solution even though the experimental phase map is destroyed by sharp variance or discontinuities, and it boasts a little higher computation speed. Therefore,in application,most problems are expected to be solved smoothly by way of Schofield＇s 4-FFT algorithm integrated with DCT-based one.