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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 16 — Aug. 11, 2014
  • pp: 18924–18933
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Investigation of fragment sizes in laser-driven shock-loaded tin with improved watershed segmentation method

Weihua He, Jianting Xin, Genbai Chu, Jing Li, Jianli Shao, Feng Lu, Min Shui, Feng Qian, Leifeng Cao, Pei Wang, and Yuqiu Gu  »View Author Affiliations


Optics Express, Vol. 22, Issue 16, pp. 18924-18933 (2014)
http://dx.doi.org/10.1364/OE.22.018924


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Abstract

Studying dynamic fragmentation in shock-loaded metals and evaluating the geometrical and kinematical properties of the resulting fragments are of significant importance in shock physics, material science as well as microstructural modeling. In this paper, we performed the laser-driven shock-loaded experiment on the Shenguang-Ш (SGШ) prototype laser facility, and employed X-ray micro-tomography technique to give a whole insight into the actual fragmentation process. To investigate the size distribution of the soft recovered fragments from Poly 4-methyl-1-pentene (PMP) foam sample, we further developed an automatic analysis approach based on the improved watershed segmentation. Comparison results of segmenting fragments in slices with different methods demonstrated that our proposed segmentation method can overcome the drawbacks of under-segmentation and over-segmentation, and has the best performance in both segmentation accuracy and robustness. With the proposed automatic analysis approach, other parameters such as the position distribution and penetration depth are also obtained, which are very helpful for understanding the dynamic failure mechanisms.

© 2014 Optical Society of America

1. Introduction

Studying dynamic fragmentation in shock-loaded metals and evaluating the geometrical and kinematical properties of the resulting fragments are issues of significant importance for shock physics, material science as well as microstructural modeling. Extensive experimental investigations have been mainly dedicated to dynamic failure and spallation of solid material process under explosive loading or plate impacts [1–3

1. V. A. Ogorodnikov, A. L. Mikhailov, V. V. Burtsev, S. A. Lobastov, S. V. Erunov, A. V. Romanov, A. V. Rudnev, E. V. Kulakov, Y. B. Bazarov, V. V. Glushikhin, I. A. Kalashnik, V. A. Tsyganov, and B. I. Tkachenko, “Detecting the ejection of particles from the free surface of a shock-loaded sample,” J. Exp. Theor. Phys. 109(3), 530–535 (2009). [CrossRef]

]. During this process, a compressive pulse propagating in a solid sample reflects from a free surface and the interaction of the incident unloading wave with the reflected release wave generates the tensile stresses that may lead to the ejection of one or several layers of materials. In recent ten years, high-power laser [4,5

4. T. de Rességuier, E. Lescoute, L. Signor, D. Loison, A. Dragon, M. Boustie, J. P. Cuq-Lelandais, and L. Berthe, “Laser shock experiments to investigate and to model various aspects of the response of metals to shock loading,” EPJ Web of Conferences 10, 00023 (2010). [CrossRef]

] and ion beams [6

6. K. Baumung, H. Bluhm, G. I. Kanel, G. Müller, S. V. Razorenov, J. Singer, and A. V. Utkin, “Tensile strength of five metals and alloys in the nanosecond load duration range at normal and elevated temperatures,” Int. J. Impact Eng. 25(7), 631–639 (2001). [CrossRef]

] have been used to extend this investigation towards shorter pulsed loads associated with extremely high strain rates. In this case, the interaction of the reflected and incident release waves gives rise to tensile stresses which cannot be sustained by the molten material. This one is consequently fragmented into a cloud of fine droplets ejected at a high velocity. Such fragmentation process has been commonly referred as micro-spalling [3

3. L. Signor, G. Roy, P. Y. Channal, P. L. Héreil, F. Buy, C. Voltz, F. Llorca, T. de Rességuier, and A. Dragon, “Debris cloud ejection from shock-loaded tin melted on release or on compression,” AIP proceedings on Shock Compression of Condensed Matter (2009). [CrossRef]

].

Accurately segmenting fragments from X-ray micro-tomography imaging is a crucial step in quantitating fragment-size distribution. However it remains a challenging problem due to their irregular shape, different sizes and intensity inhomogeneity within fragments and over the whole image. So far, very few works have been reported in this field. In 2010, Signor et al. [9,10

9. L. Signor, T. de Rességuier, A. Dragon, G. Roy, A. Fanget, and M. Faessel, “Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-load tin,” Int. J. Impact Eng. 37(8), 887–900 (2010). [CrossRef]

] introduced a semi-automatic threshold approach to segment tin fragments in the scanning electron micrograph of a polycarbonate shield. At its first key step, circles were superimposed manually on the observed fragments to roughly locate each fragment, which can avoid suffering from intensity inhomogeneity within fragments and over a whole image in the subsequent segmentation step of grey level thresholding.

The present paper is organized as follows. Section 2 describes the laser driven shock experiment on tin target. Section 3 demonstrates the reconstruction results of X-ray micro-tomography of PMP foam sample and also gives some interpretation about the collected fragment distribution. In Section 4, an improved watershed segmentation algorithm is proposed to segment the fragments in each slice. In Section 5, to verify the proposed algorithm performance, comparison results with different segmentation methods are reported, and then the calculated sizes of fragments and their position distribution with the proposed method are presented in the same Section. Section 6 concludes with a summary result.

2. Experimental setup

Our experiment was performed on the Shenguang-Ш (SGШ) prototype laser facility at Laser Fusion Research Center in MianYang, China. The setup is schematically represented in Fig. 1(a)
Fig. 1 (a) Schematic of the experimental setup. (b) The soft recovery device PMP foam. (c) Intensity distribution of the irradiated spot.
. Two high-power single-pulsed laser beams of 0.351μm wavelength, 3ns duration, and 85J energy, were focused onto a tin target of 106μm thickness and 2mm diameter. In order to provide a planar shock front to propagate into the target, the beams were smoothed by a continuous phase plate (CPP), and the irradiated spot was quasi circular of ~1mm radius at the target surface, with a homogeneous intensity distribution as in Fig. 1(b). The laser power intensity at the surface of the tin was about 9.0 × 1011 W/cm2. To limit the modifications of the fragments during their impact and penetration, a very low density of PMP foam, 200mg/cm3, was chosen as the fragment soft-recovery device, shown in Fig. 1(c). In order to keep the back surface of the tin target to be a free surface, the foam should not be contact with the tin target. With this premise, the range for the distance between tin back surface and foam is relatively flexible. In our experiment, we set it to be about 1mm, considering the space constraint of the setup. And the PMP foam is a cylinder of about 8mm diameter and 10mm height.

3. X-ray micro-tomography of PMP foam sample and reconstruction

In order to explore the fragments collected within PMP foam, X-ray micro-tomography was employed. We first acquired radiographs under 512 different orientations with the industrial CT scanner of TERARECON Inc.., and then reconstructed these radiographs slice by slice using the traditional Feldkamp (FDK) algorithm and ‘Shepp-Logan’ filter algorithm. The reconstructed voxel size is 6.27μm in both width and length and 9.41μm in height. Figure 2(a)
Fig. 2 (a) 3D reconstruction of tin fragments detected within the PMP foam sample. (b) Three of the reconstructed slices at different penetration depths of 0.11mm(sliceA-A), 2.37mm (slice B-B) and 3.93mm(C-C).
shows the 3D reconstruction of tin fragments detected in PMP foam, and Fig. 2(b) shows three of these slices at different depths. As shown in Fig. 2, due to the huge discrepancy in absorption coefficients of the two materials, the reconstructed results can well depict tin fragments and exclude the background of PMP foam at the same time.

From both Fig. 2(a) and 2(b), it can be found that the size and shape of fragments are greatly different at different penetration depths. Our interpretation for this phenomenon could be illustrated schematically in Fig. 3
Fig. 3 Illustration of our interpretation of the experiment.
. In the central region near the laser axis, the micro-jet process is first expected to occur and lead to rapid ejection of fine particles from scratches or microgrooves on sample surface. In such case, the edge effects should be negligible and particles are expected to move quickly towards the foam with a great axial component velocity. The slice C-C at the penetration depth of 3.93mm gives an example of such particles. In the same region, the thin layers are then expected to be generated from the broken surface beneath the free surface, and these layers move towards the foam with a much lower axial component velocity than that of the aforementioned fine particles. The slice B-B at the penetration depth of 2.37mm shows an example of some typical thin layers. These two kinds of fragments are both included within a cylindrical region of the foam, whose diameter is less than that of the irradiated spot. Near the edges of the loaded zone, lateral unloading wave issued from the edges of the irradiated spot, and the pressure in this region would be lower than that in the central loaded zone. The spherical particles observed in this region are expected to be generated from micro-spalling process upon tension loading of molten materials. Therefore, the velocities of ‘micro-spalled’ ones would be lower than that of aforementioned fine particles. And a significant outward radial component appears apparently, which gives rise to an obvious “annular configuration” observed in slice A-A at the penetration depth of 0.11mm and schematicallly depicted in Fig. 3.

4. Fragment segmentation with the improved watershed method

Fragment segmentation is an essential step because the segmentation results directly affect the estimation accuracy of size distribution and other characteristic parameters. To avoid over-segmentation and under-segmentation problems of traditional methods such as gradient watershed and level set, an improved watershed method is proposed for segmenting the fragments by per slice. In the following, we present the details of the improved watershed method.

The first main step is coarse segmentation which aims to identify fragment candidates in a slice. The extended minima transform is applied to complemented image Ĩ of contrast-enhanced slice I. This transform is defined as the region minima of H-minima transform [11

11. P. Soille, “Morphological image analysis: principles and applications,” 2nd Ed, Springer-Verlag, Berlin Heidelberg, Charper 6, 183–216 (2002).

].

H-minima transform suppresses all minima in the intensity image whose depth is less than a given h [12

12. L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991). [CrossRef]

]. This is achieved by performing the reconstruction by erosion of image g from g + h:
HMINh(g)=Rgδ(g+h)
(1)
The region minima M are connected components of pixels with the same intensity value whose external boundary pixels all have a higher value than a given threshold level h:
RMINh[g]={pM,g(p)=hpδ(1)(M)\M,g(p)>h
(2)
Then the extended minima transform can be expressed as
gE=RMIN[HMINh(g)]
(3)
The output slice gE is a binary image in which the white pixels represent the regional minima in the original image. Figure 4(a)
Fig. 4 Illustration of the main steps of detecting fragments. (a) Source slice. (b) Result of extend minimum transform. (c) Result of watershed transform. (d) Result of adaptive region threshold segmentation.
illustrates one of the contrast-enhanced slices. The corresponding result of extended minima transform is given in Fig. 4(b), which has marked the fragments of the slice very well. To locate the outer marks, the watershed method is then imposed on the result of extended minima transform, and the resultant marked regions are illustrated in Fig. 4(c).

Considering the intensity inhomogeneity within fragments and over the whole image, an adaptive region thesholding technique is further imposed on each marked region. The adaptive threshold for each region Ti*can be calculated using Otsu method [13

13. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979). [CrossRef]

], i.e. maximizing the between-class variance σi2(k) of each marked region,
{Ti*=argmaxk{σi2(k)}σi2(k)=ω0i(μ0iμi)2+ω1i(μ1iμi)2
(4)
where µ0i1i)denotes the average grey level of background (foreground) in the region i, ω0i (ω1 i) denotes the probability of background (foreground) and µi denotes the average grey level of the two classes in the region i. Figure 4(d) shows the segmentation result by the adaptive region thesholding technique. Boundaries between fragments and background represented with red curves in this figure find the fragments’ edge reasonably.

5. Results and discussion

We performed segmentation of fragments slice by slice. As shown in Fig. 5
Fig. 5 Comparison results of segmenting fragments with different methods. (a) Gradient Watersheds. (b) Level-Set. (c) Our proposed method.
, most of the large fragments in this slice have a spherical shape and high grey level. However, a portion of small fragments whose sizes range from one to several voxels have irregular shapes, low contrast between targets and background and lacking texture. Therefore, it is difficult to detect these fragments by exiting techniques using size-and-shape based feature [14

14. D. Nam, J. Mantel, D. Bull, P. Verkade, and A. Achim, “Segmentation and analysis insulin granule membranes in beta islet cell electron micrographs,” 20th European Signal Processing conference, 2228–2232 (2012).

] or texture-based feature [15,16

15. D. R. Martin, C. C. Fowlkes, and J. Malik, “Learning to detect natural image boundaries using local brightness, color, and texture cues,” IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 530–549 (2004). [CrossRef] [PubMed]

].

Segmentation result with our proposed algorithm is displayed in Fig. 5(c). Meanwhile, to validate the efficiency of the proposed segmentation algorithm, we also compared our method with classical gradient watershed algorithm [17

17. J. M. Gauch, “Image segmentation and analysis via multiscale gradient watershed hierarchies,” IEEE Trans. Image Process. 8(1), 69–79 (1999). [CrossRef] [PubMed]

] and level set algorithm [18

18. L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” Int. J. Comput. Vis. 50(3), 271–293 (2002). [CrossRef]

]. The segmentation results are demonstrated in Fig. 5(a) and 5(b), respectively. The gradient watershed algorithm uses the gradient map as the distance transform input, while the level set algorithm starts with an initial approximate contour and evolves according to the minimization of certain energy function that is defined on both contours and enclosed region. In our implementation, the extended minima transform and watershed are combined to coarsely mark the fragment region, and then an adaptive thesholding technique Otsu is imposed on each marked region for further refining segmentation. The classical gradient watershed algorithm has advantages in speed, simplicity, and can segment fragments in a slice within 0.6s. However, it usually suffers from over-segmentation due to its high sensitivity to edges and noises. As for the level set algorithm, the level set function is stabilized after 1500 iterations and its time cost is about 337s, i.e., it takes much longer time than that of the watershed algorithm. Moreover, it fails to segment many small fragments from the background, which demonstrates its serious drawback of under-segmentation. In contrast, our proposed method can segment fragments more appropriately, and process a slice within 1s. Therefore, the proposed method cannot only achieve good segmentation results, but also maintain low time cost.

To further investigate robustness of the proposed algorithm, we also applied the aforementioned three algorithms to segment spall in slices. Some segmentation results are shown in Figs. 6(a)
Fig. 6 Comparison results of segmenting spall with different methods. (a) Gradient Watersheds. (b) Level-Set. (c) Our proposed method.
-6(c). As we expected, the classical gradient watershed algorithm suffers from severe drawback of over-segmentation, while level set algorithm cannot segment the spall with intensity variations appropriately because the curvature flow is not powerful for weak edge and concave components. In contrast, the method we proposed demonstrates good performance in segmentation accuracy and robustness.

In order to validate the segmentation performance of the proposed method quantitatively, we take the manually segmented image as the ground-truth image and the segmented images with the above three methods as the object images, and adopt the modified Hausdorff distances (MHD) performance criteria [19

19. M. Sezgin, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron. Imaging 13(1), 146–165 (2004). [CrossRef]

] to evaluate them. Table 1

Table 1. Evaluation Results of Segmenting Particles and Spalls According to the MHD Criteria

table-icon
View This Table
lists the evaluation results for segmenting particles or spalls in Fig. 5 and Fig. 6, as well as the total number of the extracted object regions. From this table, we can find that the proposed method has gained the best segmentation performance with the lowest MHD value. Meanwhile, the total number of the extracted object regions with our proposed method is equal to that of the manual segmentation results.

6. Conclusions

In this paper, tin foil laser-driven shock-wave experiment on the SGШ prototype laser facility was reported, and ejected fragments were soft recovered by low-density PMP foam sample. X-ray micro-tomography technique was then employed to give a whole insight into the actual fragmentation process. In order to infer the size-distribution, an automatic analysis approach based on the improved watershed segmentation strategy was proposed to segment the fragments slice by slice. In addition, other important characteristic parameters such as the penetration depth, position distribution can also be obtained with this analysis approach.

Although the present work provides an effective means to detect fragment size distribution of laser shock-loaded tin, more experiments are still needed to explore the complex dynamic fragmentation mechanism. In the past two years, our group has investigated the fragments recovered from laser shock-loaded tin [20

20. J. T. Xin, W. H. He, J. L. Shao, J. Li, P. Wang, and Y. Q. Gu, “Experimental investigation of fragments recovered from laser shock-loaded tin,” J. Phys. D. (Accepted).

]. Under different laser power and different thickness of tin target, the pressure near free surface of the target would be different. The fragments would be some pieces of thin layer in solid state under the pressure of 9Gpa and 12.5Gpa, and turn into a large number of small spherical particles under the pressure of 43Gpa.In the future, studies under different conditions such as various pressures, target thickness, and groove depths and orientations would be planned to gain more insights about the fragment characteristics, including the penetration depth, velocities, size distribution and the total ejected mass.

Acknowledgments

The authors are very grateful to Guanghui Yuan in the Department of Target Science and Facture for fabricating the tin targets we used in experiments and Dr Xuan Luo in the Department of Material Science and Technique for providing the low-density PMP foam. The authors would also like to thank all the staff of the SGШ prototype facility especially Ping Li for operating the laser facility. This work is supported by the Foundation of Laboratory of Science and Technology on Plasma Physics titled with “Study on characteristics of Al spallation under super-high strain rate”.

References and links

1.

V. A. Ogorodnikov, A. L. Mikhailov, V. V. Burtsev, S. A. Lobastov, S. V. Erunov, A. V. Romanov, A. V. Rudnev, E. V. Kulakov, Y. B. Bazarov, V. V. Glushikhin, I. A. Kalashnik, V. A. Tsyganov, and B. I. Tkachenko, “Detecting the ejection of particles from the free surface of a shock-loaded sample,” J. Exp. Theor. Phys. 109(3), 530–535 (2009). [CrossRef]

2.

M. B. Zellner, M. Grover, J. E. Hammerberg, R. S. Hixson, A. J. Iverson, G. S. Macrum, K. B. Morley, A. W. Obst, R. T. Olson, J. R. Payton, P. A. Rigg, N. Routley, G. D. Stevens, W. D. Turley, L. Veeser, and W. T. Buttler, “Effect of shock-breakout pressure on ejection of micron-scale material from shocked tin surface,” J. Appl. Phys. 102(1), 013522 (2007). [CrossRef]

3.

L. Signor, G. Roy, P. Y. Channal, P. L. Héreil, F. Buy, C. Voltz, F. Llorca, T. de Rességuier, and A. Dragon, “Debris cloud ejection from shock-loaded tin melted on release or on compression,” AIP proceedings on Shock Compression of Condensed Matter (2009). [CrossRef]

4.

T. de Rességuier, E. Lescoute, L. Signor, D. Loison, A. Dragon, M. Boustie, J. P. Cuq-Lelandais, and L. Berthe, “Laser shock experiments to investigate and to model various aspects of the response of metals to shock loading,” EPJ Web of Conferences 10, 00023 (2010). [CrossRef]

5.

S. N. Luo, D. C. Swift, T. E. Tierney IV, D. L. Paisley, G. A. Kyrala, R. P. Johnson, A. A. Hauer, O. Tschauner, and P. D. Asimow, “Laser-induced shock waves in condensed matter: some techniques and applications,” High Press. Res. 24(4), 409–422 (2004). [CrossRef]

6.

K. Baumung, H. Bluhm, G. I. Kanel, G. Müller, S. V. Razorenov, J. Singer, and A. V. Utkin, “Tensile strength of five metals and alloys in the nanosecond load duration range at normal and elevated temperatures,” Int. J. Impact Eng. 25(7), 631–639 (2001). [CrossRef]

7.

D. B. Holtkamp, D. A. Clark, E. N. Ferm, R. A. Gallegos, D. Hammon, W. F. Hemsing, G. E. Hogan, V. H. Holmes, N. S. P. King, R. Liljestrand, R. P. Lopez, F. E. Merrill, C. L. Morris, K. B. Morley, M. M. Murray, P. D. Pazuchanics, K. P. Prestridge, J. P. Quintana, A. Saunders, T. Schafer, M. A. Shinas, and H. L. Stacy, “A survey of high explosive-induced damage and spall in selected metals using proton radiography,” AIP proceedings on Shock Compression of Condensed Matter 706,477–482 (2004). [CrossRef]

8.

T. de Rességuier, L. Signor, A. Dragon, M. Boustie, G. Roy, and F. Llorca, “Experimental investigation of liquid spall in laser shock-loaded tin,” J. Appl. Phys. 101(1), 013506 (2007). [CrossRef]

9.

L. Signor, T. de Rességuier, A. Dragon, G. Roy, A. Fanget, and M. Faessel, “Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-load tin,” Int. J. Impact Eng. 37(8), 887–900 (2010). [CrossRef]

10.

L. Signor, T. de Rességuier, G. Roy, A. Dragon, and F. Liorca, “Fragment-size prediction during dynamic fragmentation of shock-melted tin: recovery experiments and modeling issues,” AIP proceedings on Shock Compression of Condensed Matter 706,593–596 (2008). [CrossRef]

11.

P. Soille, “Morphological image analysis: principles and applications,” 2nd Ed, Springer-Verlag, Berlin Heidelberg, Charper 6, 183–216 (2002).

12.

L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991). [CrossRef]

13.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern. 9(1), 62–66 (1979). [CrossRef]

14.

D. Nam, J. Mantel, D. Bull, P. Verkade, and A. Achim, “Segmentation and analysis insulin granule membranes in beta islet cell electron micrographs,” 20th European Signal Processing conference, 2228–2232 (2012).

15.

D. R. Martin, C. C. Fowlkes, and J. Malik, “Learning to detect natural image boundaries using local brightness, color, and texture cues,” IEEE Trans. Pattern Anal. Mach. Intell. 26(5), 530–549 (2004). [CrossRef] [PubMed]

16.

S. Kumar, S. H. Ong, S. Ranganath, and F. T. Chew, “Invariant texture classification for biomedical cell specimens via non-linear polar map filtering,” Comput. Vis. Image Underst. 114(1), 44–53 (2010). [CrossRef]

17.

J. M. Gauch, “Image segmentation and analysis via multiscale gradient watershed hierarchies,” IEEE Trans. Image Process. 8(1), 69–79 (1999). [CrossRef] [PubMed]

18.

L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” Int. J. Comput. Vis. 50(3), 271–293 (2002). [CrossRef]

19.

M. Sezgin, “Survey over image thresholding techniques and quantitative performance evaluation,” J. Electron. Imaging 13(1), 146–165 (2004). [CrossRef]

20.

J. T. Xin, W. H. He, J. L. Shao, J. Li, P. Wang, and Y. Q. Gu, “Experimental investigation of fragments recovered from laser shock-loaded tin,” J. Phys. D. (Accepted).

OCIS Codes
(000.2190) General : Experimental physics
(100.3010) Image processing : Image reconstruction techniques
(100.6950) Image processing : Tomographic image processing
(110.7440) Imaging systems : X-ray imaging

ToC Category:
Image Processing

History
Original Manuscript: April 30, 2014
Revised Manuscript: July 3, 2014
Manuscript Accepted: July 9, 2014
Published: July 29, 2014

Citation
Weihua He, Jianting Xin, Genbai Chu, Jing Li, Jianli Shao, Feng Lu, Min Shui, Feng Qian, Leifeng Cao, Pei Wang, and Yuqiu Gu, "Investigation of fragment sizes in laser-driven shock-loaded tin with improved watershed segmentation method," Opt. Express 22, 18924-18933 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-16-18924


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References

  1. V. A. Ogorodnikov, A. L. Mikhailov, V. V. Burtsev, S. A. Lobastov, S. V. Erunov, A. V. Romanov, A. V. Rudnev, E. V. Kulakov, Y. B. Bazarov, V. V. Glushikhin, I. A. Kalashnik, V. A. Tsyganov, and B. I. Tkachenko, “Detecting the ejection of particles from the free surface of a shock-loaded sample,” J. Exp. Theor. Phys.109(3), 530–535 (2009). [CrossRef]
  2. M. B. Zellner, M. Grover, J. E. Hammerberg, R. S. Hixson, A. J. Iverson, G. S. Macrum, K. B. Morley, A. W. Obst, R. T. Olson, J. R. Payton, P. A. Rigg, N. Routley, G. D. Stevens, W. D. Turley, L. Veeser, and W. T. Buttler, “Effect of shock-breakout pressure on ejection of micron-scale material from shocked tin surface,” J. Appl. Phys.102(1), 013522 (2007). [CrossRef]
  3. L. Signor, G. Roy, P. Y. Channal, P. L. Héreil, F. Buy, C. Voltz, F. Llorca, T. de Rességuier, and A. Dragon, “Debris cloud ejection from shock-loaded tin melted on release or on compression,” AIP proceedings on Shock Compression of Condensed Matter (2009). [CrossRef]
  4. T. de Rességuier, E. Lescoute, L. Signor, D. Loison, A. Dragon, M. Boustie, J. P. Cuq-Lelandais, and L. Berthe, “Laser shock experiments to investigate and to model various aspects of the response of metals to shock loading,” EPJ Web of Conferences 10, 00023 (2010). [CrossRef]
  5. S. N. Luo, D. C. Swift, T. E. Tierney, D. L. Paisley, G. A. Kyrala, R. P. Johnson, A. A. Hauer, O. Tschauner, and P. D. Asimow, “Laser-induced shock waves in condensed matter: some techniques and applications,” High Press. Res.24(4), 409–422 (2004). [CrossRef]
  6. K. Baumung, H. Bluhm, G. I. Kanel, G. Müller, S. V. Razorenov, J. Singer, and A. V. Utkin, “Tensile strength of five metals and alloys in the nanosecond load duration range at normal and elevated temperatures,” Int. J. Impact Eng.25(7), 631–639 (2001). [CrossRef]
  7. D. B. Holtkamp, D. A. Clark, E. N. Ferm, R. A. Gallegos, D. Hammon, W. F. Hemsing, G. E. Hogan, V. H. Holmes, N. S. P. King, R. Liljestrand, R. P. Lopez, F. E. Merrill, C. L. Morris, K. B. Morley, M. M. Murray, P. D. Pazuchanics, K. P. Prestridge, J. P. Quintana, A. Saunders, T. Schafer, M. A. Shinas, and H. L. Stacy, “A survey of high explosive-induced damage and spall in selected metals using proton radiography,” AIP proceedings on Shock Compression of Condensed Matter 706,477–482 (2004). [CrossRef]
  8. T. de Rességuier, L. Signor, A. Dragon, M. Boustie, G. Roy, and F. Llorca, “Experimental investigation of liquid spall in laser shock-loaded tin,” J. Appl. Phys.101(1), 013506 (2007). [CrossRef]
  9. L. Signor, T. de Rességuier, A. Dragon, G. Roy, A. Fanget, and M. Faessel, “Investigation of fragments size resulting from dynamic fragmentation in melted state of laser shock-load tin,” Int. J. Impact Eng.37(8), 887–900 (2010). [CrossRef]
  10. L. Signor, T. de Rességuier, G. Roy, A. Dragon, and F. Liorca, “Fragment-size prediction during dynamic fragmentation of shock-melted tin: recovery experiments and modeling issues,” AIP proceedings on Shock Compression of Condensed Matter 706,593–596 (2008). [CrossRef]
  11. P. Soille, “Morphological image analysis: principles and applications,” 2nd Ed, Springer-Verlag, Berlin Heidelberg, Charper 6, 183–216 (2002).
  12. L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell.13(6), 583–598 (1991). [CrossRef]
  13. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man Cybern.9(1), 62–66 (1979). [CrossRef]
  14. D. Nam, J. Mantel, D. Bull, P. Verkade, and A. Achim, “Segmentation and analysis insulin granule membranes in beta islet cell electron micrographs,” 20th European Signal Processing conference, 2228–2232 (2012).
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