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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 2 — Jan. 16, 2012
  • pp: 986–1000
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Selection of optimal combinations of band-pass filters for ice detection by hyperspectral imaging

Shigeki Nakauchi, Ken Nishino, and Takuya Yamashita  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 986-1000 (2012)
http://dx.doi.org/10.1364/OE.20.000986


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Abstract

Hyperspectral imaging captures rich information in spatial and spectral domains but involves high costs and complex data processing. The use of a set of optical band-pass filters (BPFs) in the acquisition of spectral images is proposed for reducing dimensionality of spectral data while maintaining target detection and/or categorization performance. A set of BPFs that could distinguish ice from surrounding water on various materials (e.g., asphalt), was designed as an example. Relatively high accuracy (90.28%) was achieved with only two BPFs, showing the potential of this approach for accurate target detection with lesser complexity than conventional methods.

© 2012 OSA

1. Introduction

Although the use of hyperspectral imaging was restricted to the field of remote sensing over most of the past decade, it has recently come to be accepted as one of the most powerful nondestructive imaging technologies in a variety of fields, such as environmental monitoring, quality assessment in food science and agriculture, mineral exploration, and surveillance [1

1. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000). [CrossRef]

3

3. S. S. Shen and P. E. Lewis, eds., Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIII (Proc SPIE), SPIE-International Society for Optical Engine (2007).

]. This technology is called “spectral imagery” because imaging measurements are made in a series of narrow and contiguous wavelength bands, using a particular spectrograph and an imaging sensor. The acquired hyperspectral images contain rich information in both the spectral and spatial domains. Therefore, it is possible to derive a continuous spectrum for each image pixel, making it possible to detect, identify, and quantify imaged objects in more detail than is possible using the ordinary three bands in “color” images (R, G, and B). The main advantage of spectral imaging is the fine resolution in the wavelength domain. However, this can be a disadvantage for image acquisition and processing, in that acquiring and analyzing a hyperspectral image is more time-consuming and expensive than by using the ordinary “three-band” image processing method. Therefore, the efficient processing of spectral data to extract particular information while maintaining a desirable level of accuracy or performance is important in spectral imaging technology. Several relevant methods have been proposed that reduce dimensionality by extracting low-rank structures within the spectral data, e.g., chemometric techniques for chemical imaging, such as principal component analysis (PCA) or partial least-squares (PLS). Although these methods are useful for reducing the number of parameters required to process the acquired spectral data, a spectral acquisition process that costs time and money is still required. In addition, the light is split over many detectors, and therefore, high illumination intensity is required to obtain a sufficient signal-to-noise ratio (SNR) in hyperspectral imaging.

As an alternative, wavelength selection is commonly used in many practical applications to reduce the cost of spectral acquisition [4

4. K. Sasaki, S. Kawata, and S. Minami, “Optimal wavelength selection for quantitative analysis,” Appl. Spectrosc. 40(2), 185–190 (1986). [CrossRef]

7

7. B. Smith, “Wavelength selection and optimization of pattern recognition methods using the genetic algorithm,” Anal. Chim. Acta 423(2), 167–177 (2000). [CrossRef]

] and multi-spectral imaging [8

8. R. L. Ornberg, B. M. Woerner, and D. A. Edwards, “Analysis of stained objects in histological sections by spectral imaging and differential absorption,” J. Histochem. Cytochem. 47(10), 1307–1313 (1999). [CrossRef] [PubMed]

,9

9. P. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61(1), 67–81 (2004). [CrossRef]

]. Images are acquired using a set of specific wavelengths for a given objective, and the acquired gray-level images are used in a calculation process to produce output images in which certain features are highlighted. The measured wavelengths are typically selected by spectral analysis of the target’s absorption wavelengths. To reduce costs, the number of wavelengths used is typically much lower than the number used in an ordinary hyperspectral imaging system. Thus, this kind of multi-spectral imaging system simply consists of an image sensor (i.e., a CCD camera) and a set of optical filters (i.e., interference filters) situated in front of the camera (or light source) or sequential illumination, with different LEDs emitting different wavelength bands. Interference filters transmit (or the LEDs emit) only a specific wavelength, or, to be precise, a very narrow wavelength band. Therefore, the camera used in a multi-spectral imaging system is typically required to be highly sensitive because the energy of the transmitted light tends to be weak. In a hyperspectral imaging system, this light energy problem becomes more serious because of the narrower wavelength bands, as mentioned above.

To reduce the dimensionality of the spectral data it is not necessary to select a set of individual wavelengths by using narrow-band filters. Instead, any type of transmittance function of the filter can be selected to reduce the dimensionality of the data, provided one can find a better low-rank structure within the given data set. Furthermore, it is easier to obtain a sufficient SNR by using filters with broad, rather than narrow, wavelength bands. The present study considers a data-driven optimization problem to formulate a method for selecting the optimal set of band-pass filters that can detect and quantify the target in a multi-spectral image. Herein, we report the theoretical design and realization of an optimal set of real optical band-pass filters for ice detection on roads, by focusing on the spectral difference between ice and water.

The detection of ice is important for a number of purposes. For example, ice formed on road pavements or on car windows causes serious traffic accidents [10

10. A. Troiano, E. Pasero, and L. Mesin, “New system for detecting road ice formation,” IEEE Trans. Instrumentat. Meas. 60(3), 1091–1101 (2011). [CrossRef]

]. In addition, layers of ice on aircraft wings can make flights unsafe [11

11. R. Kind, M. Potapczuk, A. Feo, C. Golia, and A. D. Shah, “Experimental and computational simulation of in-flight icing phenomena,” Prog. Aerosp. Sci. 34(5-6), 257–345 (1998). [CrossRef]

13

13. M. Homola, P. Nicklasson, and P. A. Sundsbø, “Ice sensors for wind turbines,” Cold Reg. Sci. Technol. 46(2), 125–131 (2006). [CrossRef]

], and ice accretion on leaves can cause damage to plants [14

14. R. Pearce, “Plant freezing and damage,” Ann. Bot. (Lond.) 87(4), 417–424 (2001). [CrossRef]

]. At present, the determination of ice presence is performed visually by technicians under most types of circumstances, followed by tactile inspections. However, visual inspection is difficult and time consuming, and can only produce rough results. Tactile inspection determines the presence of ice through changes in the acoustic or electrical properties of the material as detected by a sensor [10

10. A. Troiano, E. Pasero, and L. Mesin, “New system for detecting road ice formation,” IEEE Trans. Instrumentat. Meas. 60(3), 1091–1101 (2011). [CrossRef]

14

14. R. Pearce, “Plant freezing and damage,” Ann. Bot. (Lond.) 87(4), 417–424 (2001). [CrossRef]

]. However, the drawback is that this often requires physical contact between the sensing device and the target, and the reliability of readings is low due to the narrow (usually a point or a line) sensing areas, which offer localized and sparse coverage. Alternatively, there is an automatic and non-tactile method to inspect ice using reflectance spectroscopy [15

15. D. Gregoris, S. Yu, and F. Teti, “Multispectral imaging of ice” in Canadian Conference on Electrical and Computer Engineering (2004), vol. 4, pp. 2051–2056.

]. Ice contamination on aircraft wings and snow layers on road pavements have been successfully inspected in this way, but black ice, a slick, transparent form of roadway ice, cannot be successfully identified using this method because of its low light reflectance. These methods focus on the difference in the absorption wavelength of ice and water, and they use narrow-bands filters for ice detection, which leads to a low SNR. The present study selected the optimum broad wavelength bands to distinguish ice from water based on a measured radiance spectrum, achieving a higher level of accuracy of discrimination than that achieved by the previously discussed methods.

In the following text, we describe the mathematical formulation used for selecting the filter’s properties. We then compare the detection accuracy with the accuracy obtained using the ordinary wavelength selection method for ice detection, as applied to the simple cases of two narrow-band filters (hereafter referred to as “two-wavelength filters”) and two broad wavelength bands. Finally, the design method is extended and generalized for larger numbers of filters and applied to the same data set to evaluate the generalization of the method.

2. Basic idea

Figure 1
Fig. 1 Basic concept used to reduce the dimensionality of a given spectral data set by selecting wavelength bands with band-pass filtering.
outlines the concept we have used to reduce the dimensionality of a given set of spectral data, e.g., measurements of three properties of objects are performed by selecting a limited number of wavelengths and wavelength bands. Two wavelengths are selected by placing two interference filters in front of the detector or image sensor, which allow the wavelengths λ1 and λ2 to pass. The outputs from these devices span a two-dimensional space, which is a subspace of the original spectral data space. The objective of the selection is to find the optimum subspace in which the projected data contains as much of the desired information as possible (i.e., the properties of the measured objects). Conventionally, a certain specific wavelength that depends on the category or condition (λ1 in Fig. 1), and another wavelength, which does not depend on them and is used as a reference (λ2), are selected. To do so, the correlation or another similar index is evaluated for each wavelength as the entire range of wavelengths is scanned, and the best wavelengths are selected.

Our proposed method focuses on selecting wavelength bands instead of individual wavelengths. The transmittance properties of an ideal BPF are described by two parameters: the lower cut-off and higher cut-off wavelengths. The problem of finding an optimum set of BPFs can be formulated as the need to find a set of parameters that maximize a pre-defined evaluation function describing the level of target detection or categorization achieved from the low-dimensional data.

3. Theory

Consider a system consisting of a camera and a set of optical filters placed in front of the camera lens. Suppose that the output of the camera with the i-th filter (i=1,,N) is simply described as
Oi=Ti(λ)S(λ)I(λ)dλ,
(1)
where Ti(λ) is the spectral transmittance of the i-th filter, S(λ) is the spectral sensitivity of the camera, and I(λ) is the spectral distribution of the incoming light. Here, the filters are assumed as ideal band-pass filters (BPFs) with a transmittance of 1.0 at transmitting wavelength ranges and 0.0 at blocking wavelength ranges, as mentioned in Section 2. Then, the output of the camera is described as Oi=λLiλHiS(λ)I(λ)dλ, when
Ti(λ)={1forλLiλλHi0forλ<λLi,λ>λHi,
(2)
where λLi and λHi are the lower and higher cut-off wavelengths of the i-th filter, respectively.

The camera output is expressed as a vector in N-dimensional feature space as O = (O1, O2, …, ON)t and is defined by a set of filters. Suppose that the set of camera outputs for certain objects have to be categorized into the known classes A:{OA} and B: {OB}. The optimization problem here is defined as the need “to find an optimal set of the filter parameters {λLi,λHi}, (i=1,,N), to categorize the camera outputs O into class A or B.”

In order to solve this problem, a measure of the separability between the camera outputs categorized into classes A:{OA}and B:{OB}must be defined. We seek to obtain a scalar value by projecting the camera outputs O onto a line defined by a projection matrix w asf(O)=wtO. We here define the separability of a given set of filters as the separability of the scores f(O), which is maximized by selecting the best line from all possible lines. According to Fisher’s linear discriminant [23

23. R. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugen. 7(2), 179–188 (1936). [CrossRef]

], the separability of the scores is explicitly expressed as the ratio of the variance between the classes to the variance within the classes as
J(w)=wtΣBWNwwtΣWTNw,
(3)
where ΣBWN=(O¯AO¯B)(O¯AO¯B)t represents the between-class scatter, O¯A,O¯Bare the mean vectors, and
ΣWTN=ΣA+ΣB,ΣA,B=OA,B(OA,BO¯A,B)(OA,BO¯A,B)tt
(4)
represents the within-class scatter matrix. It is known that the w that maximizesJ(w) is given as

w*=argmaxwJ(w)=ΣWTN1(O¯AO¯B).
(5)

Linear discriminant analysis (LDA) yields an equivalent result. Assume that the conditional probability functions, p(O|class=A) and p(O|class=B) are both normally distributed with means of μA and μB, respectively, with the same covariance matrix for both classes, i.e., ΣA=ΣB=Σ. The discriminant function is then expressed as

f(O)=12{(OμA)tΣ1(OμA)(OμB)tΣ1(OμB)}={Σ1(μAμB)}tO12(μA+μB)tΣ1(μAμB).
(6)

The first term in Eq. (6) corresponds to the projection of the camera outputs, O, onto a line defined by w=Σ1(μAμB), which maximizes the separability of the scores, as mentioned above. The second term is a scalar that is used to determine the category boundary. Whenf(O)>0, then Ois categorized into class A. Whenf(O)<0, then Ois categorized into class B, with the best separability between f(OA) and f(OB) under the given filter parameters{λLi,λHi}.

The filters can be optimized by choosing parameters from all the possible sets of parameters that maximize the separability of the discriminant score f(OA) and f(OB), as determined by the camera outputs, depending on the set of filters. Separability as a function of the filter parameters can be expressed as
J({λLi,λHi})=w*tΣBWNw*w*tΣWTNw*={f(OA)¯-f(OB)¯}2var[f(OA]+var[f(OB],
(7)
where f(OA)¯ and f(OB)¯ in Eq. (7) are the means of the discriminant scores and var[f(OA)] and var[f(OB)] are the variances of the scores. Note that J({λLi,λHi}) is a nonlinear function of the parameters of {λLi,λHi}, and thus, an iterative optimization method is required to find the solution, as described in Section 4.2.

4. Materials and methods

4.1 Spectral data set

Spectra of ice and water were measured using a spectroradiometer (Field-Spec3, ASD Inc.). A layer of ice approximately 1-cm thick was generated on a small block of asphalt repairing material, as shown in Fig. 2
Fig. 2 Schematic diagram of experiment setup (left) and measured samples (right). The sample in the near side of the image is the water sample and the one behind it is the ice sample. After the ice sample melted, it was used as a water sample.
(height: 6 cm; width: 11 cm; depth: 1.5 cm); this was used as an ice sample for the measurement. Once melted, the ice sample was used as a water sample. Details of the measurement conditions are shown in Table 1

Table 1. Measurement conditions

table-icon
View This Table
. The spectral radiance over the range of 900 - 2500 nm was measured at 10 nm intervals. Each sample was illuminated from both sides by two sets of halogen lamps (500 W), and a spectroradiometer probe was set perpendicular to the light sources. Both of the light sources and the probe were set at an angle of 45° with respect to the sample to exclude specular reflection, as shown in Fig. 2. A total of 54 radiance spectra of ice and water were obtained from 9 points on each of six different samples.

Figure 3
Fig. 3 Radiance spectra of ice (solid red line) and water (dashed blue line) on asphalt. The thin lines show the original spectra and the bold lines show the average spectra for ice and water.
shows each of the 54 individually measured radiance spectra, as well as their averages, for ice and water. The original spectra are quite noisy and overlap one another because of irregularities in the water layer and the black asphalt. There are a number of spectra with a peak around 1700 nm for some water samples (blue lines); these were probably caused by oil floating on water that originated from the asphalt.

4.2 Method for filter selection

First, all parameters of the algorithm are initialized. PF is the set of filter parameters that are already optimized and fixed (to begin with, this is an empty set, i.e., no parameters have been optimized), Cnt(λL,λH) represents the number of times the filter with the set of parameters {λL,λH} is selected (0 to begin with), and Ev(λL,λH) represents the evaluation index value of these parameter sets (which are also 0, to begin with). The evaluation index is the average value of the Fisher criterion that is obtained with the filters of parameters {λL,λH} when the k-1 first filters are fixed and the others filters are randomly chosen. k is the index number of the filter whose parameters are being optimized (set at 1 to begin with). Next, the parameters of the filters that are not fixed (all of the parameters, to begin with) are randomly selected. PV is the set of parameters of the filters that are varied and N is the total number of filters to be optimized.

For these randomly selected filters, the projection matrix w* as defined by Eq. (5) is first determined by the calibration data set, then the evaluation index value and therefore the Fisher criterion J({λL,λH}) is calculated and stored as Ev(λL,λH), using the validation data set (two-fold cross-validation). The number of selections for the parameters {λL,λH} is also stored as Cnt(λL,λH). After repeating this process, the optimal parameters {λL*,λH*}, which maximize the evaluation index, are selected and stored in PF. This process is repeated until all the filter parameters are fixed. Note that in the global optimization process, from k = 1 to k = N - 1, parameters are randomly selected, but when k = N, all possible parameter values for the last Nth filter are sequentially evaluated, because the number of parameters is small sufficient for all of them to be searched sequentially.

After the global optimization process, the local optimization process is performed. First, one filter (with index number k) is selected. Then, by fixing the parameters of the other N-1 filters, the parameters {λLk,λHk} are optimized such that J({λL,λH}) is maximized by searching all possible parameter values. If the optimized parameter{λLk*,λHk*} is different from the one obtained by the global optimization process, then the filter parameter is updated. This process is repeated until no filters are updated by this local optimization procedure.

4.3 Optimization conditions

Filters were selected using spectral data measured in the 900–2500 nm range, as shown in Fig. 3. Here, the spectral sensitivity of the camera, S(λ), was assumed to be S(λ) = 1 over the entire wavelength range, even though there were no such imaging sensors. However, it would not have a great effect upon the wavelength band selection if the sensor were somehow sensitive in the wavelength range to be analyzed. As described in Section 5.4, after the band-pass filters are selected, it is possible to compensate for the discrepancies between reality and theory in the actual camera sensors, as well as in the transmittance of the filters, by using the actual camera outputs with the real filters to re-calibrate the projection matrix defined by Eq. (5) and the discriminant function defined by Eq. (6).

All possible combinations of filter parameters were searched for the case of selecting two filters. To compare this approach with the conventional method, two optimal wavelengths were also selected using the same procedure by fixing the filter’s bandwidth at 10 nm. The multiple selection method was performed for the case of more than two and as many as eight filters (N = 2, 3, …, 8). The maximum number of iterations in the random selection process (MaxItr in Fig. 4) was set at 100,000. In these experiments, a logarithmic transformation was applied to the camera outputs as it is in the transformation from reflectance to absorbance used in conventional spectral analysis.

5. Results

5.1 Al-possible-combinations search

The Fisher criteria J for both cases, which were computed by leave-one-out cross-validation, were 74.57 for the selected BPFs and 18.08 for the two individual wavelengths, as shown in Fig. 6
Fig. 6 Comparison of the Fisher criteria J as computed by conventional spectral analysis techniques (MCS + PCA + LDA) for various wavelength regions, for two wavelengths (Two WL), and for the proposed two BPFs (Two bands).
. For comparison, the Fisher criterion obtained using conventional spectral analytical techniques in which multiplicative scattering correction (MSC), principal component analysis (PCA) and linear-discriminant analysis (LDA) was applied to the entire wavelength region (900–2500 nm), was 61.74. The number of principal components was chosen to maximize the Fisher criterion J. It should be noted that for the multivariate case, the Fisher criterion varied depending on the wavelength region (17.29 for 900–2000 nm, and 129.55 for 900–2370 nm, which showed the best performance of this method found by searching the wavelength range), as shown in Fig. 6. The proposed two BPFs (two bands) method is superior to the two-wavelength method and even to traditional spectral analysis that uses all the spectral information (900–2500 nm). The reason for this is probably that the data at a wavelength range longer than approximately 2000 nm were noisy, which had a large effect upon the accuracy of the method that uses the entire wavelength range. Further, the BPFs method itself includes the wavelength range selection, and thus, all data longer than approximately 2000 nm were automatically removed from the analyzed wavelength range by maximizing the Fisher criterion.

Based upon Fig. 7
Fig. 7 Distributions of the discriminant score defined by Eq. (6) for the two wavelengths (Two WL), the proposed two BPFs (Two bands) and the multivariate cases (MSC + PCA + LDA) for 900–2500 and 900–2370 nm.
, which shows the distribution of discriminant scores expressed by Eq. (6), it is appropriate to assume that the camera outputs obtained by the BPFs method were normally distributed, whereas there were outliers in the two WL and MSC + PCA + LDA for the 900–2500 nm cases, and hence, this distribution appears non-Gaussian. This implies that LDA of signals obtained by the BPFs method works better than these two cases.

5.2 Filters selected by multiple selection method

5.3 Filter realization

The two selected BPFs were realized as real optical filters, which we then tested for visualization of the detection result by placing them in front of a near-infrared camera. The filters were developed using a multilayer thin film coating technology. The spectral transmittances of the realized optical filters are shown in Fig. 9
Fig. 9 Theoretical and realized spectral transmittances of tested filters. The computed Fisher criterion is displayed at the top of the figure.
alongside the theoretically designed transmittances. Here, filter 1, with cut-off edges at 1260 nm and 1700 nm, was developed as a high pass filter because the image sensor of the near-infrared camera used in this experiment had no sensitivity for wavelengths longer than 1700 nm. The Fisher criterion J calculated for the set of real filters was 67.20. The obtained performance was high, despite the mismatches between the theoretical and the realized transmittance functions.

5.4 Ice detection by real optical filters

Figure 10
Fig. 10 Measurement setup: a near-infrared camera XSVA XS FPA-1.7–320 (Xenics) with installed developed filters was used to take the spectral images. Two sets of halogen lamps (300 W each) illuminated the samples from both sides. The camera was set just above the sample.
shows the experimental setup for ice and water discrimination and visualization on asphalt using a camera with the realized filters. A near-infrared camera XSVA XS FPA-1.7–320 (InGaAs sensors with 320 × 256 pixels; Xenics) was used in this experiment. Filters were placed in front of the camera by a rotating filter wheel (Newport Japan) controlled by a PC through a USB interface. The integration time was approximately 10 ms for all conditions. The samples were the same as those used for the previously described spectral measurements shown in Fig. 2. Two sets of halogen lamps (300 W each) illuminated the samples from both sides. The camera was set just above the samples. A white reference (Spectralon) was used for the camera calibration. Images of the ice and water samples were taken at 1-minute intervals for 14 minutes to monitor the ice melting over time. The background area surrounding the asphalt sample was masked manually for visualization purposes.

The visualization result at 0 minutes is shown in Fig. 11
Fig. 11 Visualization results: the left image shows the RGB color image taken with a digital camera, and the right image shows the detection result computed from the images taken with the NIR camera with the installed optimized filters. The top sample had a 1-cm-thick ice layer and the bottom one had a water layer. The pixels classified as ice were colored red and the areas classified as water were colored blue.
. The left image shows an image taken with an ordinary digital camera and the right image shows the detection result. The top sample has an ice layer and the bottom sample has only a water layer. The classification accuracy, which is defined by the pixel count of the ice and water regions, was found to be 90.28%. The accuracy of ice detection obtained using the proposed method is sufficiently high for real applications, and with two BPFs, the cost for implementation is relatively low. This high accuracy and low cost allowed us to use the proposed method to monitor ice over a period of time. The results, which are shown in Fig. 12
Fig. 12 Visualization results over time, which clearly show the area classified as ice (the sample in the top row) decreasing with time.
, clearly show the detected ice region decreasing with time due to the ice melting. We also confirmed that the same filter worked well for other backgrounds, for example, for detection of ice on leaves (frost detection: 93.56%) and on glass (ice on car window: 98.99%), as shown in Fig. 13
Fig. 13 Visualization results for other materials: ice on leaf (93.56%) and glass (98.99%). Colors are shown in the same manner as in Figs. 11 and 12.
. The detection of ice on asphalt was more difficult than it was on these backgrounds because of the low reflectance of asphalt.

6. Discussion

It is also worth noting that the two selected BPFs shown in Fig. 5, and the BPFs selected by the multiple selection method are ‘nested’. Furthermore, when the proposed method was applied to spectral data sets for purposes other than ice detection, nested filters were also obtained in most cases. In the following, we discuss why nested filters provide a good result.

A graphical image of the evaluation index, Ev, as calculated using the multiple selections method (N = 2), and the obtained transmittance function of the filters, is shown in Fig. 14
Fig. 14 Evaluation index calculated using the multiple selection method and the transmittance functions of the selected filters (N = 2). (a), (b) when the first filter is selected (k = 2); and (c), (d) when the second filter is selected (k = 2). The horizontal axis shows the bandwidth and the vertical axis shows the center wavelength of BPFs. The gray level corresponds to the average Fisher criterion J of the given filter parameters. The white arrow in (a) points to the wavelength selected using the two-wavelength method, and the arrow in (c) points to the parameter of the second filter selected using the multiple selection method.
. The horizontal axis shows the bandwidth and the vertical axis shows the center wavelength of the searching BPFs (originally represented byλL,λH, as shown in Fig. 4, but shown here as the bandwidth and center wavelength, for purposes of explanation). The gray level shows the average Fisher criterion J. The left and right panels respectively show the evaluation index obtained when the first and the second filters were being optimized.

When k = 1 and the first filter (Filter 1) is selected in the “Filter selection” process, the parameter set of Filter 1 at center wavelength = 1395 nm and bandwidth = 10 shows the highest value, as shown and highlighted in Fig. 14(a). On this map, the wavelength of 1400 nm with a narrow bandwidth that was selected using the two-wavelength method also shows a high value. In addition, 1260 nm with a narrow bandwidth, which was selected using the two-wavelength method as another “reference” wavelength, as mentioned in Section 5.1, also shows a high value (indicated by a white arrow). However, when the second filter (Filter 2) is selected after fixing the parameters of Filter 1, the 1260 nm region is no longer high, as shown in Fig. 14(c). Instead, the parameter region that forms the “nested” filter, which is indicated by an arrow, shows higher values. The two-wavelength method is restricted to select only the parameters around the bottom edge of Figs. 14(a) and (c), whereas the proposed method can exhibit significantly improved performance than the fixed narrow-band filter (two wavelength), when the second broadband filter is selected such that the first filter is nested in the second one. This implies that a nested filter is more effective for baseline correction than the reference wavelength, as used in the two-wavelength method.

7. Conclusions

In this paper, we proposed a method for reducing the dimensionality of a spectral data set by using optimal band-pass filters, which facilitates hyperspectral imaging. This method was then applied to ice-region detection on asphalt for roads. The general idea governing this method is the selection of an optimum set of wavelength bands, instead of the individual wavelengths that are conventionally used. The selected BPFs can be easily implemented as real optical interference filters that are mounted in front of a conventional camera. Furthermore, it is easier to obtain sufficient SNR by using filters that have broader wavelength bands than narrow-band filters. The set of band-pass filters can be formulated as the projection function from the spectral domain to the low-dimensional feature space. The filter can be optimized by finding the parameters that maximize the separability, as defined by the discriminant score (Fisher criterion J) among the possible sets of filter parameters.

Obviously, the proposed method is not restricted to the problem of ice detection. It can be used for many other purposes such as quality assessment of food, mineral exploration, and medical imaging. In addition, our method can be extended from detection to quantification by replacing the target function (separability) with other indexes that are commonly used for the evaluation of quantification accuracy (e.g., the standard error of prediction or the determination coefficient).

Acknowledgments

This study was supported in part by the Regional Innovation Cluster Program (Global Type, 2nd stage) “Hamamatsu Optronics Cluster” of the Ministry of Education. This work was also supported in part by the Global COE Program. “Frontiers of Intelligent Sensing,” of the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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A. Troiano, E. Pasero, and L. Mesin, “New system for detecting road ice formation,” IEEE Trans. Instrumentat. Meas. 60(3), 1091–1101 (2011). [CrossRef]

11.

R. Kind, M. Potapczuk, A. Feo, C. Golia, and A. D. Shah, “Experimental and computational simulation of in-flight icing phenomena,” Prog. Aerosp. Sci. 34(5-6), 257–345 (1998). [CrossRef]

12.

C. E. Bassey and G. R. Simpson, “Aircraft ice detection using time domain reflectometry with coplanar sensors,” in 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–6.

13.

M. Homola, P. Nicklasson, and P. A. Sundsbø, “Ice sensors for wind turbines,” Cold Reg. Sci. Technol. 46(2), 125–131 (2006). [CrossRef]

14.

R. Pearce, “Plant freezing and damage,” Ann. Bot. (Lond.) 87(4), 417–424 (2001). [CrossRef]

15.

D. Gregoris, S. Yu, and F. Teti, “Multispectral imaging of ice” in Canadian Conference on Electrical and Computer Engineering (2004), vol. 4, pp. 2051–2056.

16.

E. Angelopoulou, R. Molana, and K. Danilidis, “Multispectral skin color modelling,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001. CVPR 2001 (IEEE/COMSOC, 2001), vol. 2, pp. II-635–II-642.

17.

S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 913–922 (2004). [CrossRef] [PubMed]

18.

J. Karlholm and I. Renhorn, “Wavelength band selection method for multispectral target detection,” Appl. Opt. 41(32), 6786–6795 (2002). [CrossRef] [PubMed]

19.

O. Kleynen, V. Leemans, and M.-F. Destain, “Selection of the most efficient wavelength bands for ‘Jonagold’ apple sorting,” Postharvest Biol. Technol. 30(3), 221–232 (2003). [CrossRef]

20.

J. Minet, J. Taboury, F. Goudail, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Influence of band selection and target estimation error on the performance of the matched filter in hyperspectral imaging,” Appl. Opt. 50(22), 4276–4285 (2011). [CrossRef] [PubMed]

21.

K. Nishino, M. Nakamura, M. Matsumoto, O. Tanno, and S. Nakauchi, “Optical filter highlighting spectral features part II: quantitative measurements of cosmetic foundation and assessment of their spatial distributions under realistic facial conditions,” Opt. Express 19(7), 6031–6041 (2011). [CrossRef] [PubMed]

22.

K. Nishino, M. Nakamura, M. Matsumoto, O. Tanno, and S. Nakauchi, “Optical filter for highlighting spectral features part I: design and development of the filter for discrimination of human skin with and without an application of cosmetic foundation,” Opt. Express 19(7), 6020–6030 (2011). [CrossRef] [PubMed]

23.

R. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugen. 7(2), 179–188 (1936). [CrossRef]

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(110.3080) Imaging systems : Infrared imaging
(120.2440) Instrumentation, measurement, and metrology : Filters
(110.4234) Imaging systems : Multispectral and hyperspectral imaging

ToC Category:
Imaging Systems

History
Original Manuscript: September 16, 2011
Revised Manuscript: November 24, 2011
Manuscript Accepted: November 28, 2011
Published: January 4, 2012

Citation
Shigeki Nakauchi, Ken Nishino, and Takuya Yamashita, "Selection of optimal combinations of band-pass filters for ice detection by hyperspectral imaging," Opt. Express 20, 986-1000 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-2-986


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References

  1. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE4056, 50–64 (2000). [CrossRef]
  2. Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A69A(8), 735–747 (2006). [CrossRef] [PubMed]
  3. S. S. Shen and P. E. Lewis, eds., Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIII (Proc SPIE), SPIE-International Society for Optical Engine (2007).
  4. K. Sasaki, S. Kawata, and S. Minami, “Optimal wavelength selection for quantitative analysis,” Appl. Spectrosc.40(2), 185–190 (1986). [CrossRef]
  5. J. M. Brenchley, U. Horchner, and J. H. Kalivas, “Wavelength selection characterization for NIR spectra,” Appl. Spectrosc.51(5), 689–699 (1997). [CrossRef]
  6. S. D. Osborne, R. Künnemeyer, S. D. Osborne, and R. B. Jordan, “Method of wavelength selection for Partial Least Squares,” Analyst (Lond.)122(12), 1531–1537 (1997). [CrossRef]
  7. B. Smith, “Wavelength selection and optimization of pattern recognition methods using the genetic algorithm,” Anal. Chim. Acta423(2), 167–177 (2000). [CrossRef]
  8. R. L. Ornberg, B. M. Woerner, and D. A. Edwards, “Analysis of stained objects in histological sections by spectral imaging and differential absorption,” J. Histochem. Cytochem.47(10), 1307–1313 (1999). [CrossRef] [PubMed]
  9. P. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng.61(1), 67–81 (2004). [CrossRef]
  10. A. Troiano, E. Pasero, and L. Mesin, “New system for detecting road ice formation,” IEEE Trans. Instrumentat. Meas.60(3), 1091–1101 (2011). [CrossRef]
  11. R. Kind, M. Potapczuk, A. Feo, C. Golia, and A. D. Shah, “Experimental and computational simulation of in-flight icing phenomena,” Prog. Aerosp. Sci.34(5-6), 257–345 (1998). [CrossRef]
  12. C. E. Bassey and G. R. Simpson, “Aircraft ice detection using time domain reflectometry with coplanar sensors,” in 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–6.
  13. M. Homola, P. Nicklasson, and P. A. Sundsbø, “Ice sensors for wind turbines,” Cold Reg. Sci. Technol.46(2), 125–131 (2006). [CrossRef]
  14. R. Pearce, “Plant freezing and damage,” Ann. Bot. (Lond.)87(4), 417–424 (2001). [CrossRef]
  15. D. Gregoris, S. Yu, and F. Teti, “Multispectral imaging of ice” in Canadian Conference on Electrical and Computer Engineering (2004), vol. 4, pp. 2051–2056.
  16. E. Angelopoulou, R. Molana, and K. Danilidis, “Multispectral skin color modelling,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2001. CVPR 2001 (IEEE/COMSOC, 2001), vol. 2, pp. II-635–II-642.
  17. S. J. Preece and E. Claridge, “Spectral filter optimization for the recovery of parameters which describe human skin,” IEEE Trans. Pattern Anal. Mach. Intell.26(7), 913–922 (2004). [CrossRef] [PubMed]
  18. J. Karlholm and I. Renhorn, “Wavelength band selection method for multispectral target detection,” Appl. Opt.41(32), 6786–6795 (2002). [CrossRef] [PubMed]
  19. O. Kleynen, V. Leemans, and M.-F. Destain, “Selection of the most efficient wavelength bands for ‘Jonagold’ apple sorting,” Postharvest Biol. Technol.30(3), 221–232 (2003). [CrossRef]
  20. J. Minet, J. Taboury, F. Goudail, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Influence of band selection and target estimation error on the performance of the matched filter in hyperspectral imaging,” Appl. Opt.50(22), 4276–4285 (2011). [CrossRef] [PubMed]
  21. K. Nishino, M. Nakamura, M. Matsumoto, O. Tanno, and S. Nakauchi, “Optical filter highlighting spectral features part II: quantitative measurements of cosmetic foundation and assessment of their spatial distributions under realistic facial conditions,” Opt. Express19(7), 6031–6041 (2011). [CrossRef] [PubMed]
  22. K. Nishino, M. Nakamura, M. Matsumoto, O. Tanno, and S. Nakauchi, “Optical filter for highlighting spectral features part I: design and development of the filter for discrimination of human skin with and without an application of cosmetic foundation,” Opt. Express19(7), 6020–6030 (2011). [CrossRef] [PubMed]
  23. R. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugen.7(2), 179–188 (1936). [CrossRef]

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