Specific surface area computed with X-ray micro-tomography:
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1 2nd April 2013 Specific surface area computed with X-ray micro-tomography: Impact of the segmentation technique and the effective resolution Pascal Hagenmuller (1), Guillaume Chambon (1), Bernard Lesaffre (2), Frédéric Flin (2), Neige Calonne (2), Mohamed Naaim (1) (1) UR ETGR Erosion torrentielle, neige et avalanches, Irstea, Grenoble (2) Centre d études de la neige (CEN), Météo France/CNRS
2 Binary segmentation Binary segmentation Output of tomograph: grayscale image (X-ray attenuation coefficient) Input of models: binary B/W (ice/air) image Questions: - How can we extract the maximum information out of the grayscale image? - How structural parameters derived from the binary image are sensitive to segmentation?
3 Outline Why is segmentation not straightforward? Segmentation techniques Threshold-based approach Energy-based approach Results
4 Why is segmentation not straightforward?
5 Why is segmentation not straightforward? Images artifacts: - Noise (electronic, small variations inside material, etc.) - Blur (discretization artifact, reconstruction affected by noise, etc.) Segmentation with our eyes seems simple but our brain uses complex criterions (common shapes, continuity, grayscale gradient,...), that are difficult to implement in a computer.
6 Segmentation techniques
7 Threshold-based segmentation Commonly used, simple and fast method Initial image with threshold
8 Threshold-based segmentation Commonly used, simple and fast method Smoothed image with threshold
9 Threshold-based segmentation Commonly used, simple and fast method Difficulties: - size of smoothing (does not define the effective resolution of the image) Smoothed image with threshold
10 Threshold-based segmentation Commonly used, simple and fast method Difficulties: - size of smoothing (does not define the effective resolution of the image) Example of unimodal histogram
11 Threshold-based segmentation Commonly used, simple and fast method Difficulties: - size of smoothing (does not define the effective resolution of the image) - large impact of the threshold that is difficult to chose Example of unimodal histogram
12 Definition of a segmentation energy E. Energy-based method = Imperative method (Boykov and Funka-Lea, 2006)
13 Definition of a segmentation energy E. Energy-based method = Imperative method E(L) =E v (L)+r S(L) (Boykov and Funka-Lea, 2006)
14 Definition of a segmentation energy E. Energy-based method = Imperative method E(L) =E v (L)+r S(L) Data fidelity term (Boykov and Funka-Lea, 2006)
15 Definition of a segmentation energy E. Energy-based method = Imperative method E(L) =E v (L)+r S(L) Data fidelity term Regularization term (Boykov and Funka-Lea, 2006)
16 Definition of a segmentation energy E. Energy-based method = Imperative method E(L) =E v (L)+r S(L) Data fidelity term Regularization term Segmentation scale (Boykov and Funka-Lea, 2006)
17 Definition of a segmentation energy E. Energy-based method = Imperative method E(L) =E v (L)+r S(L) Data fidelity term Regularization term Segmentation scale Minimization of the energy via graph cut approach (Boykov and Funka-Lea, 2006)
18 Data fidelity term E(L) =E v (L)+r S(L) Quantifies the penalty assigning a voxel to ice or to background according to its gray value
19 Data fidelity term E(L) =E v (L)+r S(L) Quantifies the penalty assigning a voxel to ice or to background according to its gray value Equivalent of «thresholding» but also provides the «uncertainty» of the segmentation (value of Ev)
20 Regularization term (minimization of surface area) E(L) =E v (L)+r S(L) Metamorphosed snow scanned with electron microscopy (Erbe et al., 2003)
21 Regularization term (minimization of surface area) E(L) =E v (L)+r S(L) Metamorphism tends to reduce the surface energy of snow. Comparisons between SSA measured via tomography or methane adsorption (Kerbrat et al., 2008) have shown that the snow surface (except fresh snow) is essentially smooth up to a scale of 30 microns. Metamorphosed snow scanned with electron microscopy (Erbe et al., 2003)
22 Regularization term (minimization of surface area) E(L) =E v (L)+r S(L) Metamorphism tends to reduce the surface energy of snow. Comparisons between SSA measured via tomography or methane adsorption (Kerbrat et al., 2008) have shown that the snow surface (except fresh snow) is essentially smooth up to a scale of 30 microns. For air/ice samples, one can weight the surface area by the local grayscale gradient Metamorphosed snow scanned with electron microscopy (Erbe et al., 2003)
23 Regularization term (minimization of surface area) E(L) =E v (L)+r S(L) Metamorphism tends to reduce the surface energy of snow. Comparisons between SSA measured via tomography or methane adsorption (Kerbrat et al., 2008) have shown that the snow surface (except fresh snow) is essentially smooth up to a scale of 30 microns. For air/ice samples, one can weight the surface area by the local grayscale gradient Adding a surface energy criterion that is meant to be physically-based Metamorphosed snow scanned with electron microscopy (Erbe et al., 2003)
24 Segmentation scale E(L) =E v (L)+r S(L)
25 Segmentation scale E(L) =E v (L)+r S(L) Simple case of ice protuberances on the surface of smooth snow: The protuberance is segmented as ice if: V P V P V P S P 2S c r
26 Segmentation scale E(L) =E v (L)+r S(L) Simple case of ice protuberances on the surface of smooth snow: The protuberance is segmented as ice if: V P V P V P S P 2S c r r defines an effective resolution of the image (size of the smallest detail in the segmented image)
27 Convex Concave 3.6 mm 4.8 mm Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
28 Convex Concave 3.6 mm 4.8 mm r = 0.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
29 Convex Concave 3.6 mm 4.8 mm r = 0.25 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
30 Convex Concave 3.6 mm 4.8 mm r = 0.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
31 Convex Concave 3.6 mm 4.8 mm r = 0.75 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
32 Convex Concave 3.6 mm 4.8 mm r = 1.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
33 Convex Concave 3.6 mm 4.8 mm r = 1.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
34 Convex Concave 3.6 mm 4.8 mm r = 2.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
35 Convex Concave 3.6 mm 4.8 mm r = 2.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
36 Convex Concave 3.6 mm 4.8 mm r = 3.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
37 Convex Concave 3.6 mm 4.8 mm r = 3.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
38 Convex Concave 3.6 mm 4.8 mm r = 4.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
39 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
40 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 0.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
41 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 0.25 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
42 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 0.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
43 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 0.75 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
44 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 1.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
45 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 1.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
46 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 2.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
47 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 2.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
48 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 3.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
49 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 3.5 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
50 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 4.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
51 Convex Concave 3.6 mm 4.8 mm r = 5.0 vox r = 5.0 vox Sample A: Melt-freeze crust, density 300 kg/m3, SSA 8 m2/kg resolution 9.6 µm Sample D7m: Depth hoar, faceted crystals, density 125 kg/m3, SSA 25 m2/kg resolution 7.2 µm
52 Results
53 Results Name A B B7m D D7m Type MFcr FCso FCso DH/FC DH/FC Voxel size (µm) Samples Snow grain size workshop SHF - Pascal Hagenmuller
54 Results Name A B B7m D D7m Type MFcr FCso FCso DH/FC DH/FC Voxel size (µm) Samples Snow grain size workshop SHF - Pascal Hagenmuller
55 Results Name A B B7m D D7m Type MFcr FCso FCso DH/FC DH/FC Voxel size (µm) Samples Choice of r - if tomograph is well set up, r on the order of the resolution provides the best segmentation - r can be artificially high depending on the use of the binary image (downscaling without grid artifact) Snow grain size workshop SHF - Pascal Hagenmuller
56 Results Comparison with threshold-based Snow grain size workshop SHF - Pascal Hagenmuller
57 Results Comparison with threshold-based Uncertainty on density intrinsic to the discretization and digitization (uncertainty of half voxel on the interface) Snow grain size workshop SHF - Pascal Hagenmuller
58 Results Comparison with threshold-based Uncertainty on density intrinsic to the discretization and digitization (uncertainty of half voxel on the interface) Uncertainty on SSA - uncertainty on density - uncertainty on surface area link to the size distribution of structure details Snow grain size workshop SHF - Pascal Hagenmuller
59 Conclusion
60 Conclusion Conclusion about the energy-based segmentation technique: - Explicit segmentation criterions, explicit effective resolution - Regularization term interesting for snow (metamorphism) - Global optimization (robust) but larger computing time (about 10 h for 1000*1000*1000 voxel image) Conclusion about «tomography» SSA : - noise induced protuberances can significantly contribute to the overall SSA, which will then be overestimated, - for snow with structure details on the order of the voxel size, as fresh snow, the SSA value cannot be measured independently of the used resolution.
61 Thank you for your attention
62 Why is segmentation not straightforward? Quantitative analysis of blur and noise µ Material proportions Material absorptions Noise standard deviation Automatic determination of pure material absorption gray level Quantification of the noise standard deviation and size of the blur zone
63 Results Snow grain size workshop SHF - Pascal Hagenmuller
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