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Enhanced material classification using turbulence-degraded polarimetric imagery Milo W. Hyde, IV,* Jason D. Schmidt, Michael J. Havrilla, and Stephen C. Cain Department of Electrical and Computer Engineering, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson Air Force Base, Ohio, 45433, USA *Corresponding author:
[email protected] Received June 15, 2010; revised September 27, 2010; accepted October 2, 2010; posted October 5, 2010 (Doc. ID 130118); published October 21, 2010 An enhanced material-classification algorithm using turbulence-degraded polarimetric imagery is presented. The proposed technique improves upon an existing dielectric/metal material-classification algorithm by providing a more detailed object classification. This is accomplished by redesigning the degree-of-linear-polarization priors in the blind-deconvolution algorithm to include two subclasses of metals—an aluminum group classification (includes aluminum, copper, gold, and silver) and an iron group classification (includes iron, titanium, nickel, and chromium). This new classification provides functional information about the object that is not provided by existing dielectric/metal material classifiers. A discussion of the design of these new degree-of-linear-polarization priors is provided. Experimental results of two painted metal samples are also provided to verify the algorithm’s accuracy. © 2010 Optical Society of America OCIS codes: 280.4991, 110.5405, 100.1455, 010.1330.
Polarization-based material-classification techniques can generally be divided into two types—active polarimetric [1] and, most relevant to the work presented here, passive [2–4] polarimetric techniques. Recently, a passive polarimetric material-classification technique was published that determines whether an object is composed of dielectric or metallic materials using turbulencedegraded polarimetric imagery [4]. The technique uses a variant of the polarimetric maximum-likelihood blinddeconvolution algorithm (shot noise assumed dominant) developed by LeMaster and Cain [5] to recover the first Stokes parameter S 0 , the degree of linear polarization P (DOLP), the angle of polarization α (AOP), and the polarimetric-image point spread functions hn (PSFs). The dielectric/metal classification decision is based on the DOLP maximum-likelihood estimates provided by two DOLP priors (one representative of dielectric materials, the other representative of metallic materials). The DOLP estimate that maximizes the log-likelihood function determines the image pixel’s classification. In this Letter, the existing algorithm in [4] is enhanced to provide a more detailed object classification. This is accomplished by redesigning the DOLP priors to include subclasses of materials. For the research presented here, the metal classification is divided into an aluminum (Al) group (includes aluminum, copper, gold, and silver) classification and an iron (Fe) group (includes iron, titanium, nickel, and chromium) classification. This new classification provides functional information about the object that is not provided by existing dielectric/metal classifiers. A discussion of these new DOLP priors, particularly, the physical motivation behind their mathematical forms, is provided. Experimental results of the enhanced classification technique are also presented and discussed. Note that the enhanced classification algorithm presented here utilizes the same framework as that presented in [4]; therefore, all assumptions (i.e., spatially incoherent and unpolarized illumination, circular polarization can be ignored, and materials must be diattenuators) and limitations (namely, incident θi and 0146-9592/10/213601-03$15.00/0
observation θr angles must be off normal) discussed in [4] apply here as well. Before the Al group, Fe group, and dielectric DOLP priors can be formed, one must understand how these materials polarize light. To gain the necessary understanding, a polarimetric bidirectional distribution function [6] (pBRDF) is used to predict the DOLP’s (P ¼ ðS 21 þ S 22 Þ1=2 =S 0 [7]) of the metals making up the Al and Fe groups as well as a representative sample of dielectric materials. A similar analysis, considering surface roughness and out-of-plane observation, is performed in [6]. Figure 1(a) shows the DOLPs predicted using the pBRDF [see Eq. (17) in [6]]. Note the similarities in DOLP among the materials within each of the three classifications. More importantly, note the differences in DOLP between the different classification groups. As is evident in Fig. 1(a), dielectric materials tend to strongly polarize scattered light with DOLP values encompassing the entire possible range, i.e., 0 ≤ P ≤ 1. Metals, such as those in the Al group, tend to polarize scattered light very weakly with P ≪ 0:1. Other metals, such as those in the Fe group, polarize light more strongly than Al group metals, however, not as strongly as dielectric materials. Metals in the Fe group have DOLP values of 0 ≤ P ≤ 0:3. From the DOLP traces depicted in Fig. 1(a), priors in the shape of uniform probability densities extending from 0 to 0.07, from 0.07 to 0.3, and from 0.3 to 1 would capture a large majority of the DOLP values shown in Fig. 1(a) for the Al group metals, Fe group metals, and dielectric materials, respectively. Unfortunately, the uniform probability density is not differentiable and, therefore, cannot serve as a prior in the deconvolution algorithm [4]. A differentiable approximation to a uniform distribution is a super-Gaussian distribution, namely, ΠðPÞ ¼ c1 expf−½c2 ðP − c3 Þm g;
ð1Þ
where c1 is a constant that ensures the above expression integrates to unity, c2 is a constant that controls the width of the distribution, c3 is a constant that controls where © 2010 Optical Society of America
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Fig. 1. (Color online) (a) DOLP plots of the Al group, Fe group, and dielectrics versus θr ðθi ¼ 45°Þ predicted using a pBRDF (b) Al group, Fe group, and dielectric DOLP priors.
the distribution is centered, and m is an even integer [4]. Figure 1(b) shows plots of the newly designed Al group, Fe group, and dielectric DOLP priors. To produce the Al group, Fe group, and dielectric DOLP prior traces, c1 ¼ ð1; 1; 1Þ, c2 ¼ ð35; 10:5; 3:4Þ, c3 ¼ ð0:035; 0:185; 0:65Þ, and m ¼ ð10; 10; 10Þ, respectively. It should be noted that the DOLP relationships between Al group metals and Fe group metals are applicable to visual and near-infrared optical bands only. Dispersion may cause these relationships to break down for other wavelengths. In addition to the wavelength requirement, the DOLP priors, as just defined, are applicable to θi , θr > 30° [4]. Utilizing these priors for collection geometries that do not satisfy this requirement will result in poor performance. In most situations, the observation geometry can, at the very least, be estimated, and applicable DOLP priors can be formed in the manner outlined above. Note that this technique, as a whole, will perform poorly for near-normal incident angles regardless of
wavelength or θr . This is because natural materials weakly polarize scattered light at θi ≈ 0°. For more information on this requirement, the reader is referred to [4]. Having discussed the formulation of the Al group, Fe group, and dielectric DOLP priors, attention can now be turned to experimental verification of the enhanced classification algorithm. The instrument used to collect the Stokes imagery presented here is a Stokes polarimeter in the Optical Turbulence Estimation, Compensation, and Simulation (OPTECS) laboratory at the Air Force Institute of Technology. A detailed description of the instrument and experimental procedure can be found in [4]. The objects imaged in this experiment are a 25:8 cm2 Al sample and a 25:8 cm2 steel sample (the source is a 1550 nm light emitting diode). A coat of white primer followed lastly by a coat of green paint is applied to half of each sample to produce an object consisting of both dielectric and metallic parts.
Fig. 2. (Color online) S 0 results (collected at θi ¼ θr ¼ 55°) of the enhanced material-classification algorithm: (a) no-turbulence, (b) turbulence-degraded, and (c) corrected S 0 images for the painted Al sample. (d)–(f) show those same S 0 results for the painted steel sample, respectively. The dimensions annotated on the figures are object coordinates in millimeters.
November 1, 2010 / Vol. 35, No. 21 / OPTICS LETTERS
Fig. 3. (Color online) Classification results of the enhanced material-classification algorithm: (a) painted Al and (b) painted steel samples. The dimensions annotated on the figures are object coordinates in millimeters.
Experimental results of the enhanced materialclassification algorithm are shown in Figs. 2 and 3. In Fig. 2, Fig. 2(a) shows the no-turbulence S 0 , Fig. 2(b) shows the turbulence-degraded S 0 (D=r 0 ≈ 7:9, where D is the diameter of the pupil and r 0 is Fried’s parameter [8]), and Fig. 2(c) shows the corrected S 0 (after 250 deconvolution iterations) for the painted Al sample. Likewise, Fig. 2(d) shows the no-turbulence S 0 , Fig. 2(e) shows the turbulence-degraded S 0 (D=r 0 ≈ 12:9), and Fig. 2(f) shows the corrected S 0 (after 250 deconvolution iterations) for the painted steel sample. Note that object features lost in the turbulence-degraded S 0 images are successfully recovered in the corrected S 0 images, particularly small features, e.g., scratches and metal/paint boundary details. Figure 3 shows the classification results for the painted Al Fig. 3(a) and painted steel Fig. 3(b) samples. Note the excellent classification results for the painted steel sample. Also, note that the classification errors for the painted Al sample occur at scratches in the metal’s surface and at the metal/paint boundary. The classification errors at the scratches occur because more light is scattered in the polarization state parallel to the scratches than the polarization state perpendicular to the scratches. Thus, scattered light from the scratches is polarized more strongly than the surrounding Al explaining the incorrect Fe classification. This scattering phenomenon is the same exploited to create wire-grid polarizers. The classification errors at the metal/paint boundary are caused by the manner in which the primer and paint are applied to the metal samples. Masking tape
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is used to ensure that half of the sample remains bare metal. This unfortunately creates a discontinuity at the metal/tape boundary causing the primer and paint to be applied unevenly in this region. Removing the tape, after the paint has dried, disbonds the primer/paint layers from the metal substrate. This is the dark region clearly seen in Fig. 2(a). The same metal/paint boundary effect occurs for the steel sample results [see Fig. 2(d)]; however, since the algorithm classifies that region as Fe, no errors are evident in Fig. 3(b). Note that a quantitative analysis was performed on the classification results shown above. The conclusions of that analysis were very similar to those reported in [4]. This was expected since the classifier described here uses the same basic algorithm as that in [4]. It is for these reasons and for brevity that these quantitative results are not reported here. In this Letter, the dielectric/metal classifier presented in [4] is enhanced to provide a more detailed metal classification. This is accomplished by redesigning the DOLP priors to include Al group (Al, Cu, Au, and Ag) and Fe group (Fe, Ti, Ni, and Cr) metal classifications. It is experimentally demonstrated that the algorithm is able to determine whether an object is composed of Al, Fe, or dielectric materials. This new classification provides functional information about the object that is not provided by existing dielectric/metal classifiers. The views expressed in this paper are those of the authors and do not reflect the official policy or position of the U.S. Air Force, the Department of Defense, or the U.S. Government. References 1. P. Terrier, V. Devlaminck, and J. M. Charbois, J. Opt. Soc. Am. A 25, 423 (2008). 2. L. B. Wolff, IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059 (1990). 3. S. Tominaga and A. Kimachi, Opt. Eng. 47, 123201 (2008). 4. M. W. Hyde, S. C. Cain, J. D. Schmidt, and M. J. Havrilla, IEEE Trans. Geosci. Remote Sens. (to be published) [PP (99), (2010)]. 5. D. A. LeMaster and S. C. Cain, J. Opt. Soc. Am. A 25, 2170 (2008). 6. M. W. Hyde, J. D. Schmidt, and M. J. Havrilla, Opt. Express 17, 22138 (2009). 7. J. R. Schott, Fundamentals of Polarimetric Remote Sensing (SPIE, 2009). 8. J. W. Goodman, Statistical Optics (Wiley, 2000).
