Abstract
Network level drainage assessment of the pavement surface plays a crucial role in controlling and decreasing the accident rate. Hydroplaning is one of the major causes of accidents in wet weather conditions and is the consequence of low drainage quality of pavement surfaces. Since no automated system currently exists for the pavement drainage evaluation, this work was conducted to present a new system to assess drainage process quality. For this aim, the saturation situation was simulated for pavement surface and photo acquisition was carried out on the drainage process of pavement surface after saturation. Finally, image processing method was applied to produce an index related to drainage quality. Using a proper method to enhance and prepare these images for the analysis step and find appreciate feature for the drainage quality is also among the necessities of drainage assessment. After a brief overview of multiresolution analysis, we revise the state-of-the-art of multiresolution analysis methods by discussing assessing parameters for asphalt surface image enhancement in nondestructive evaluation, formulated and fused to allow for a general comparison. In this work, different transform methods are used for asphalt surface image enhancement and a comparison is made between wavelet, curvelet, ridgelet, shearlet, and contourlet transforms by assessing parameters including TIME, PSNR, SNR, MSE, MAE, MSE, UQI, and SSIM. The comparison among the obtained results shows the superiority of shearlet transform over other transforms in providing of processed images with higher quality. Furthermore, it was found that ridgelet transform is more suitable for the jobs which time is the main parameter.
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Appendix A: Filter Coefficients
Appendix A: Filter Coefficients
Let \(h\) and \(g\) be the wavelet decomposition (analysis) filters, where \(h~\)is a lowpass filter and \(g\) is a highpass filter. Let the dual filters \({h'}~\)and \(g'\) be the wavelet reconstruction (synthesis) filters. The coefficients of the wavelet filters are shown in the following sections:
Note:Wavelets are indexed by the number of vanishing moments; for example, “daubechies 2” has two vanishing moments and four tap filters.
Haar
h0 = 0.7071067812 | g0 = −0.7071067812 | h′ 0 = 0.7071067812 | g′ 0 = 0.7071067812 |
h1 = 0.7071067812 | g1 = 0.7071067812 | h′ 1 = 0.7071067812 | g′ 1 = −0.7071067812 |
Daubechies
‘db1’
h0 = 0.7071067812 | g0 = −0.7071067812 | h′ 0 = 0.7071067812 | g′ 0 = 0.7071067812 |
h1 = 0.7071067812 | g1 = 0.7071067812 | h′ 1 = 0.7071067812 | g′ 1 = −0.7071067812 |
‘db2’
h0 = −0.1294095226 | g0 = −0.4829629131 | h′ 0 = 0.4829629131 | g′ 0 = −0.1294095226 |
h1 = 0.2241438680 | g1 = 0.8365163037 | h′ 1 = 0.8365163037 | g′ 1 = −0.2241438680 |
h2 = 0.8365163037 | g2 = −0.2241438680 | h′ 2 = 0.2241438680 | g′ 2 = 0.8365163037 |
h3 = 0.4829629131 | g3 = −0.1294095226 | h′ 3 = −0.1294095226 | g′ 3 = −0.4829629131 |
‘db10’
h0 = −0.0000132642 | g0 = −0.0266700579 | h′ 0 = 0.0266700579 | g′ 0 = −0.0000132642 |
h1 = 0.0000935887 | g1 = 0.1881768001 | h′ 1 = 0.1881768001 | g′ 1 = −0.0000935887 |
h2 = −0.0001164669 | g2 = −0.5272011889 | h′ 2 = 0.5272011889 | g′ 2 = −0.0001164669 |
h3 = −0.0006858567 | g3 = 0.6884590395 | h′ 3 = 0.6884590395 | g′ 3 = 0.0006858567 |
h4 = 0.0019924053 | g4 = −0.2811723437 | h′ 4 = 0.2811723437 | g′ 4 = 0.0019924053 |
h5 = 0.0013953517 | g5 = −0.2498464243 | h′ 5 = −0.2498464243 | g′ 5 = −0.0013953517 |
h6 = −0.0107331755 | g6 = 0.1959462744 | h′ 6 = −0.1959462744 | g′ 6 = −0.0107331755 |
h7 = 0.0036065536 | g7 = 0.1273693403 | h′ 7 = 0.1273693403 | g′ 7 = −0.0036065536 |
h8 = 0.0332126741 | g8 = −0.0930573646 | h′ 8 = 0.0930573646 | g′ 8 = 0.0332126741 |
h9 = −0.0294575368 | g9 = −0.0713941472 | h′ 9 = −0.0713941472 | g′ 9 = 0.0294575368 |
h10 = −0.0713941472 | g10 = 0.0294575368 | h′ 10 = −0.0294575368 | g′ 10 = −0.0713941472 |
h11 = 0.0930573646 | g11 = 0.0332126741 | h′ 11 = 0.0332126741 | g′ 11 = −0.0930573646 |
h12 = 0.1273693403 | g12 = −0.0036065536 | h′ 12 = 0.0036065536 | g′ 12 = 0.1273693403 |
h13 = −0.1959462744 | g13 = −0.0107331755 | h′ 13 = −0.0107331755 | g′ 13 = 0.1959462744 |
h14 = −0.2498464243 | g14 = −0.0013953517 | h′ 14 = 0.0013953517 | g′ 14 = −0.2498464243 |
h15 = 0.2811723437 | g15 = 0.0019924053 | h′ 15 = 0.0019924053 | g′ 15 = −0.2811723437 |
h16 = 0.6884590395 | g16 = 0.0006858567 | h′ 16 = −0.0006858567 | g′ 16 = 0.6884590395 |
h17 = 0.5272011889 | g17 = −0.0001164669 | h′ 17 = −0.0001164669 | g′ 17 = −0.5272011889 |
h18 = 0.1881768001 | g18 = −0.0000935887 | h′ 18 = 0.0000935887 | g′ 18 = 0.1881768001 |
h19 = 0.0266700579 | g19 = −0.0000132642 | h′ 19 = −0.0000132642 | g′ 19 = −0.0266700579 |
‘db15’
h0 = 0.0000000613 | g0 = −0.0045385374 | h′ 0 = 0.0045385374 | g′ 0 = 0.0000000613 |
h1 = −0.0000006317 | g1 = 0.0467433949 | h′ 1 = 0.0467433949 | g′ 1 = 0.0000006317 |
h2 = 0.0000018113 | g2 = −0.2060238640 | h′ 2 = 0.2060238640 | g′ 2 = 0.0000018113 |
h3 = 0.0000033630 | g3 = 0.4926317717 | h′ 3 = 0.4926317717 | g′ 3 = −0.0000033630 |
h4 = −0.0000281333 | g4 = −0.6458131404 | h′ 4 = 0.6458131404 | g′ 4 = −0.0000281333 |
h5 = 0.0000257927 | g5 = 0.3390025355 | h′ 5 = 0.3390025355 | g′ 5 = −0.0000257927 |
h6 = 0.0001558965 | g6 = 0.1932041396 | h′ 6 = −0.1932041396 | g′ 6 = 0.0001558965 |
h7 = −0.0003595652 | g7 = −0.2888825966 | h′ 7 = −0.2888825966 | g′ 7 = 0.0003595652 |
h8 = −0.0003734824 | g8 = −0.0652829528 | h′ 8 = 0.0652829528 | g′ 8 = −0.0003734824 |
h9 = 0.0019433240 | g9 = 0.1901467140 | h′ 9 = 0.1901467140 | g′ 9 = −0.0019433240 |
h10 = −0.0002417565 | g10 = 0.0396661766 | h′ 10 = −0.0396661766 | g′ 10 = −0.0002417565 |
h11 = −0.0064877346 | g11 = −0.1111209360 | h′ 11 = −0.1111209360 | g′ 11 = 0.0064877346 |
h12 = 0.0051010004 | g12 = −0.0338771439 | h′ 12 = 0.0338771439 | g′ 12 = 0.0051010004 |
h13 = 0.0150839180 | g13 = 0.0547805506 | h′ 13 = 0.0547805506 | g′ 13 = −0.0150839180 |
h14 = −0.0208100502 | g14 = 0.0257670073 | h′ 14 = −0.0257670073 | g′ 14 = −0.0208100502 |
h15 = −0.0257670073 | g15 = −0.0208100502 | h′ 15 = −0.0208100502 | g′ 15 = 0.0257670073 |
h16 = 0.0547805506 | g16 = −0.0150839180 | h′ 16 = 0.0150839180 | g′ 16 = 0.0547805506 |
h17 = 0.0338771439 | g17 = 0.0051010004 | h′ 17 = 0.0051010004 | g′ 17 = −0.0338771439 |
h18 = −0.1111209360 | g18 = 0.0064877346 | h′ 18 = −0.0064877346 | g′ 18 = −0.1111209360 |
h19 = −0.0396661766 | g19 = −0.0002417565 | h′ 19 = −0.0002417565 | g′ 19 = 0.0396661766 |
h20 = 0.1901467140 | g20 = −0.0019433240 | h′ 20 = 0.0019433240 | g′ 20 = 0.1901467140 |
h21 = 0.0652829528 | g21 = −0.0003734824 | h′ 21 = −0.0003734824 | g′ 21 = −0.0652829528 |
h22 = −0.2888825966 | g22 = 0.0003595652 | h′ 22 = −0.0003595652 | g′ 22 = −0.2888825966 |
h23 = −0.1932041396 | g23 = 0.0001558965 | h′ 23 = 0.0001558965 | g′ 23 = 0.1932041396 |
h24 = 0.3390025355 | g24 = −0.0000257927 | h′ 24 = 0.0000257927 | g′ 24 = 0.3390025355 |
h25 = 0.6458131404 | g25 = −0.0000281333 | h′ 25 = −0.0000281333 | g′ 25 = −0.6458131404 |
h26 = 0.4926317717 | g26 = −0.0000033630 | h′ 26 = 0.0000033630 | g′ 26 = 0.4926317717 |
h27 = 0.2060238640 | g27 = 0.0000018113 | h′ 27 = 0.0000018113 | g′ 27 = −0.2060238640 |
h28 = 0.0467433949 | g28 = 0.0000006317 | h′ 28 = −0.0000006317 | g′ 28 = 0.0467433949 |
h29 = 0.0045385374 | g29 = 0.0000000613 | h′ 29 = 0.0000000613 | g′ 29 = −0.0045385374 |
coiflets 1
h0 = −0.0156557281 | g0 = 0.0727326195 | h′ 0 = −0.0727326195 | g′ 0 = −0.0156557281 |
h1 = −0.0727326195 | g1 = 0.3378976625 | h′ 1 = 0.3378976625 | g′ 1 = 0.0727326195 |
h2 = 0.3848648469 | g2 = −0.8525720202 | h′ 2 = 0.8525720202 | g′ 2 = 0.3848648469 |
h3 = 0.8525720202 | g3 = 0.3848648469 | h′ 3 = 0.3848648469 | g′ 3 = −0.8525720202 |
h4 = 0.3378976625 | g4 = 0.0727326195 | h′ 4 = −0.0727326195 | g′ 4 = 0.3378976625 |
h5 = −0.0727326195 | g5 = −0.0156557281 | h′ 5 = −0.0156557281 | g′ 5 = 0.0727326195 |
Biorthogonal 1.1
h0 = 0.7071067812 | g0 = = −0.7071067812 | h′ 0 = 0.7071067812 | g′ 0 = 0.7071067812 |
h1 = 0.7071067812 | g1 = 0.7071067812 | h′ 1 = 0.7071067812 | g′ 1 = −0.7071067812 |
Reverse biorthogonal 1.1
h0 = 0.7071067812 | g0 = −0.7071067812 | h′ 0 = 0.7071067812 | g′ 0 = 0.7071067812 |
h1 = 0.7071067812 | g1 = 0.7071067812 | h′ 1 = 0.7071067812 | g′ 1 = −0.7071067812 |
Symlets 2
h0 = −0.1294095226 | g0 = −0.4829629131 | h′ 0 = 0.4829629131 | g′ 0 = −0.1294095226 |
h1 = 0.2241438680 | g1 = 0.8365163037 | h′ 1 = 0.8365163037 | g′ 1 = −0.2241438680 |
h2 = 0.8365163037 | g2 = −0.2241438680 | h′ 2 = 0.2241438680 | g′ 2 = 0.8365163037 |
h3 = 0.4829629131 | g3 = −0.1294095226 | h′ 3 = −0.1294095226 | g′ 3 = −0.4829629131 |
Discrete Meyer
h0 = 0 | g0 = 0.0000000000 | h′ 0 = −0.0000000000 | g′ 0 = 0 |
h1 = −0.0000000000 | g1 = 0.0000000085 | h′ 1 = 0.0000000085 | g′ 1 = 0.0000000000 |
h2 = 0.0000000085 | g2 = 0.0000000111 | h′ 2 = −0.0000000111 | g′ 2 = 0.0000000085 |
h3 = −0.0000000111 | g3 = −0.0000000108 | h′ 3 = −0.0000000108 | g′ 3 = 0.0000000111 |
h4 = −0.0000000108 | g4 = −0.0000000607 | h′ 4 = 0.0000000607 | g′ 4 = −0.0000000108 |
h5 = 0.0000000607 | g5 = −0.0000001087 | h′ 5 = −0.0000001087 | g′ 5 = −0.0000000607 |
h6 = −0.0000001087 | g6 = −0.0000000820 | h′ 6 = 0.0000000820 | g′ 6 = −0.0000001087 |
h7 = 0.0000000820 | g7 = 0.0000001178 | h′ 7 = 0.0000001178 | g′ 7 = −0.0000000820 |
h8 = 0.0000001178 | g8 = 0.0000005506 | h′ 8 = −0.0000005506 | g′ 8 = 0.0000001178 |
h9 = −0.0000005506 | g9 = 0.0000011308 | h′ 9 = 0.0000011308 | g′ 9 = 0.0000005506 |
h10 = 0.0000011308 | g10 = 0.0000014895 | h′ 10 = −0.0000014895 | g′ 10 = 0.0000011308 |
h11 = −0.0000014895 | g11 = 0.0000007368 | h′ 11 = 0.0000007368 | g′ 11 = 0.0000014895 |
h12 = 0.0000007368 | g12 =−0.0000032054 | h′ 12 = 0.0000032054 | g′ 12 = 0.0000007368 |
h13 = 0.0000032054 | g13 = −0.0000163127 | h′ 13 = −0.0000163127 | g′ 13 = −0.0000032054 |
h14 = −0.0000163127 | g14 = −0.0000655431 | h′ 14 = 0.0000655431 | g′ 14 = −0.0000163127 |
h15 = 0.0000655431 | g15 = −0.0006011502 | h′ 15 = −0.0006011502 | g′ 15 = −0.0000655431 |
h16 = −0.0006011502 | g16 = 0.0027046721 | h′ 16 = −0.0027046721 | g′ 16 = −0.0006011502 |
h17 = −0.0027046721 | g17 = 0.0022025341 | h′ 17 = 0.0022025341 | g′ 17 = 0.0027046721 |
h18 = 0.0022025341 | g18 = −0.0060458141 | h′ 18 = 0.0060458141 | g′ 18 = 0.0022025341 |
h19 = 0.0060458141 | g19 = −0.0063877183 | h′ 19 = −0.0063877183 | g′ 19 = −0.0060458141 |
h20 = −0.0063877183 | g20 = 0.0110614964 | h′ 20 = −0.0110614964 | g′ 20 = −0.0063877183 |
h21 = −0.0110614964 | g21 = 0.0152700151 | h′ 21 = 0.0152700151 | g′ 21 = 0.0110614964 |
h22 = 0.0152700151 | g22 = −0.0174234341 | h′ 22 = 0.0174234341 | g′ 22 = 0.0152700151 |
h23 = 0.0174234341 | g23 = −0.0321307940 | h′ 23 = −0.0321307940 | g′ 23 = −0.0174234341 |
h24 = −0.0321307940 | g24 = 0.0243487459 | h′ 24 = −0.0243487459 | g′ 24 = −0.0321307940 |
h25 = −0.0243487459 | g25 = 0.0637390243 | h′ 25 = 0.0637390243 | g′ 25 = 0.0243487459 |
h26 = 0.0637390243 | g26 = −0.0306550920 | h′ 26 = 0.0306550920 | g′ 26 = 0.0637390243 |
h27 = 0.0306550920 | g27 = −0.1328452004 | h′ 27 = −0.1328452004 | g′ 27 = −0.0306550920 |
h28 = −0.1328452004 | g28 = 0.0350875557 | h′ 28 = −0.0350875557 | g′ 28 = −0.1328452004 |
h29 = −0.0350875557 | g29 = 0.4445930028 | h′ 29 = 0.4445930028 | g′ 29 = 0.0350875557 |
h30 = 0.4445930028 | g30 = −0.7445855923 | h′ 30 = 0.7445855923 | g′ 30 = 0.4445930028 |
h31 = 0.7445855923 | g31 = 0.4445930028 | h′ 31 = 0.4445930028 | g′ 31 = −0.7445855923 |
h32 = 0.4445930028 | g32 = 0.0350875557 | h′ 32 = −0.0350875557 | g′ 32 = 0.4445930028 |
h33 = −0.0350875557 | g33 = −0.1328452004 | h′ 33 = −0.1328452004 | g′ 33 = 0.0350875557 |
h34 = −0.1328452004 | g34 = −0.0306550920 | h′ 34 = 0.0306550920 | g′ 34 = −0.1328452004 |
h35 = 0.0306550920 | g35 = 0.0637390243 | h′ 35 = 0.0637390243 | g′ 35 = −0.0306550920 |
h36 = 0.0637390243 | g36 = 0.0243487459 | h′ 36 = −0.0243487459 | g′ 36 = 0.0637390243 |
h37 = −0.0243487459 | g37 = −0.0321307940 | h′ 37 = −0.0321307940 | g′ 37 = 0.0243487459 |
h38 = −0.0321307940 | g38 = −0.0174234341 | h′ 38 = 0.0174234341 | g′ 38 = −0.0321307940 |
h39 = 0.0174234341 | g39 = 0.0152700151 | h′ 39 = 0.0152700151 | g′ 39 = −0.0174234341 |
h40 = 0.0152700151 | g40 = 0.0110614964 | h′ 40 = −0.0110614964 | g′ 40 = 0.0152700151 |
h41 = −0.0110614964 | g41 = −0.0063877183 | h′ 41 = −0.0063877183 | g′ 41 = 0.0110614964 |
h42 = −0.0063877183 | g42 = −0.0060458141 | h′ 42 = 0.0060458141 | g′ 42 = −0.0063877183 |
h43 = 0.0060458141 | g43 = 0.0022025341 | h′ 43 = 0.0022025341 | g′ 43 = −0.0060458141 |
h44 = 0.0022025341 | g44 = 0.0027046721 | h′ 44 = −0.0027046721 | g′ 44 = 0.0022025341 |
h45 = −0.0027046721 | g45 = −0.0006011502 | h′ 45 = −0.0006011502 | g′ 45 = 0.0027046721 |
h46 = −0.0006011502 | g46 = −0.0000655431 | h′ 46 = −0.0000655431 | g′ 46 = −0.0006011502 |
h47 = 0.0000655431 | g47 = −0.0000163127 | h′ 47 = −0.0000163127 | g′ 47 = −0.0000655431 |
h48 = −0.0000163127 | g48 = −0.0000032054 | h′ 48 = 0.0000032054 | g′ 48 = −0.0000163127 |
h49 = 0.0000032054 | g49 = 0.0000007368 | h′ 49 = 0.0000007368 | g′ 49 = −0.0000032054 |
h50 = 0.0000007368 | g50 = 0.0000014895 | h′ 50 = −0.0000014895 | g′ 50 = 0.0000007368 |
h51 = −0.0000014895 | g51 = 0.0000011308 | h′ 51 = 0.0000011308 | g′ 51 = 0.0000014895 |
h52 = 0.0000011308 | g52 = 0.0000005506 | h′ 52 = −0.0000005506 | g′ 52 = 0.0000011308 |
h53 = −0.0000005506 | g53 = 0.0000001178 | h′ 53 = 0.0000001178 | g′ 53 = −0.0000005506 |
h54 = 0.0000001178 | g54 = −0.0000000820 | h′ 54 = 0.0000000820 | g′ 54 = 0.0000001178 |
h55 = 0.0000000820 | g55 = −0.0000001087 | h′ 55 = −0.0000001087 | g′ 55 = −0.0000000820 |
h56 = −0.0000001087 | g56 = −0.0000000607 | h′ 56 = 0.0000000607 | g′ 56 = −0.0000001087 |
h57 = 0.0000000607 | g57 = −0.0000000108 | h′ 57 = −0.0000000108 | g′ 57 = −0.0000000607 |
h58 = −0.0000000108 | g58 = 0.0000000111 | h′ 58 = −0.0000000111 | g′ 58 = −0.0000000108 |
h59 = −0.0000000111 | g59 = 0.0000000085 | h′ 59 = 0.0000000085 | g′ 59 = 0.0000000111 |
h60 = 0.0000000085 | g60 = 0.0000000000 | h′ 60 = −0.0000000000 | g′ 60 = 0.0000000085 |
h61 = −0.0000000000 | g61 = 0 | h′ 61 = 0 | g′ 61 = 0.0000000000 |
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Mataei, B., Zakeri, H. & Nejad, F.M. An Overview of Multiresolution Analysis for Nondestructive Evaluation of Pavement Surface Drainage. Arch Computat Methods Eng 26, 143–161 (2019). https://doi.org/10.1007/s11831-017-9230-7
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DOI: https://doi.org/10.1007/s11831-017-9230-7