Precision comparison of different offset-tracking methods at sub-pixel level for glacier velocity study
Optical and/or SAR remote sensing images are frequently used to obtain glacier velocity fields through the use of offset tracking due to its strong decorrelation. Correlation algorithms extract the pixel-level offset,which can then be refined to a sub-pixel level through various interpolation techniques. However,the ac-curacy of these interpolation algorithms incorporated in different offset tracking software has rarely been assessed or compared. The lack of in-situ observations to confirm the sub-pixel precision of derived offset led to the aim of this study,which is to use a digital image processing method to evaluate the precision for various software and algorithms. Furthermore,the study suggests an algorithm to correct the possible offset tracking bias at the sub-pixel level. This study uses six pairs of Sentinel-2 images that observed two of the largest glaciers in Greenland,Petermann Glacier and Kangerlussuaq Glacier. These two glaciers account for roughly 4％ each of the entire ice sheet's glacier mass loss and flow in northwestern and southeastern directions,respectively. The study com-bines the offset tracking results obtained from different algorithms,including COSI-Corr,autoRIFT,and Im-GRAFT (CCF-O and NCC),and treats them as pre-set offset fields. Using the Sinc interpolation,which is an optimal interpolation method according to the sampling theory,simulated offset images are generated using the pre-set offset fields and pre-event images. Performing the mentioned software and algorithms,offset tracking re-sults are obtained based on the pre-event images and simulated offset images. As all the algorithms first establish an offset value at the pixel level and then interpolate to the sub-pixel level,presuming the former being more de-pendable,this research assesses the precision and inspects possible bias at the sub-pixel level only. The displace-ment results obtained and the pre-set offset fields are wrapped to a range of[-0.5,0.5]and designated as y and x. A cubic function,y=ax+4(1-a)x3 (where a is the correction parameter),is chosen for the regression. The precision is exhibited by the fitting's RMSE,while parameter a indicates the presence of bias;if a equals 1,then no bias exists,but if it's not,there is a bias. Tthe inverse function of the fitting can rectify potential system-atic errors at the sub-pixel level. According to the regression results,the sub-pixel systematic error of COSI-Corr is negligible and can be disregarded,whereas autoRIFT and ImGRAFT (CCF-O or NCC) display a certain degree of systematic errors in their offset results. Specifically,the values of a are 1.008,0.778,0.915,and 0.886 for COSI-Corr,autoRIFT,ImGRAFT(CCF-O),and ImGRAFT(NCC),respectively. In COSI-Corr,Sinc function is used to interpolate the correlation coefficient matrix,while ImGRAFT applies bicubic interpola-tion regardless of the correlation algorithm being CCF-O or NCC. autoRIFT utilizes a rapid Gaussian pyramid upsampling algorithm for estimating the sub-pixel displacement with a precision of 1/64 pixel. After systematic error correction,the autoRIFT algorithm's RMSE decreased by an average of 0.0054 pixels in a single direc-tion,resulting in the most significant improvement among all algorithms and an 11％ increase in precision. This demonstrates the significance of performing sub-pixel systematic error correction. On the other hand,the RMSE of ImGRAFT (CCF-O) and ImGRAFT (NCC) reduced slightly by an average of 0.0014 and 0.0012 pixels in a single direction,respectively. Whether to apply this correction to ImGRAFT depends on the desired level of pre-cision,as it results in only a 1.5％ increase. Furthermore,as no noticeable systematic sub-pixel errors were de-tected,it is unnecessary to apply this correction to COSI-Corr. The regression results of all software/algorithms are similar across different study sites and/or deformation directions,indicating that sub-pixel systematic error is solely dependent on interpolation algorithm. After the systematic correction,all algorithms show reliable re-sults. COSI-Corr and autoRIFT show higher precision than ImGRAFT,with RMSEs of 0.04～0.14 pixels at Kangerlussuaq. Conversely,ImGRAFT shows slightly lower precision with RMSEs of 0.08～0.10 pixels at Pe-termann and 0.09～0.13 pixels at Kangerlussuaq. ImGRAFT (CCF-O) shows slightly better precision than Im-GRAFT (NCC). Given the much higher computational requirements of autoRIFT relative to the other algo-rithms,this study recommends combining autoRIFT with a post-correction step for systematic error.
offset trackingCOSI-CorrautoRIFTImGRAFTprecision of interpolationglacier velocity
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