小波函数频域旁瓣对三维重建效果影响研究

Impact of Wavelet Function Frequency Sidelobe on the Effect of Three-Dimensional Reconstruction

利用连续小波变换实现三维重建过程中,其重建效果往往取决于小波函数的选择。小波函数在空域和频域的表现,决定着数据处理的效率和效果。不同的小波函数自身具有不同的表现,其频域部分往往有不同的旁瓣产生。讨论了复Gauss系列小波频域旁瓣对三维面形重建的影响,计算得到复Gauss小波随微分阶数增加其旁瓣有变小的趋势,理论分析和实验结果均得到其局部分析能力呈趋好的规律。通过引入复Morlet小波和Mexican hat小波函数,进一步验证了频域旁瓣对重建效果的规律性影响,实验结果与理论分析吻合较好。

Based on continuous wavelet transform（CWT）in three-dimensional surface reconstruction,the result of reconstruction often depends on the choice of wavelet function.The performance of wavelet function′s spatial and frequency domain determines the efficiency and effectiveness of data process.Different wavelet function itself has different performance,which usually exits different sidelobes in frequency domain.This paper discusses the impact of complex Gauss series wavelets′frequency sidelobes in three-dimensional shape reconstruction.The calculation results show that frequency sidelobes have a smaller trend with the increase order of complex Gauss wavelet function differential.Meanwhile,theoretical analysis and experiments give the same results in local analysis abilities.In order to illustrate the frequency sidelobe question,complex Morlet wavelet and Mexican hat wavelet function are used to verify this regularity.The experimental results agree well with the theoretical analysis.