Discrimination of Objects Within Polarimetric Imagery 

Using Principal Component and Cluster Analysis 

by Melvin Felton, Kristan P. Gurton 

Daivd Ligon, and Adrienne Raglin 

ARL-TR-4216 August 2007 

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Army Research Laboratory 

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ARL-TR-4216 August 2007 

Discrimination of Objects Within Polarimetric Imagery 

Using Principal Component and Cluster Analysis 

Melvin Felton, Kristan P. Gurton 

David Ligon, and Adrienne Raglin 

Computational and Information Sciences Directorate, ARL 

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Discrimination of Objects Within Polarimetric Imagery Using Principal 

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14. ABSTRACT 

We apply two multivariate image analysis techniques to several sets of spatially coincident, long-wave infrared (LWIR), 

polarimetric images to improve target contrast and/or aid in the identification of certain object features not present in the 

original image set. Principal component analysis (PCA) was used to obtain new representations of the scene that highlight 

target features based upon the variance of the variables used in the analysis. We show a representation of the scene that 

maintains the same level of target-to-background contrast (when compared to the conventional thermal and degree of linear 

polarization images), as well as additional information content contained in the resultant PCA analysis. Cluster analysis (CA) 

was used to group pixels of the image that have similar values for the variables chosen. We show that this method is an 

effective means for separating objects of interest from complex backgrounds, as well as subdividing different features of an 

object. 

15. SUBJECT TERMS

Principal component analysis, cluster analysis, polarimetric, thermal imagery, image processing 

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Melvin Felton 

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Contents 

List of Figures iv

List of Tables v

Introduction 1

LWIR Polarimetric Imagery 3

Image Processing Method 5

Principle Component Analysis (PCA) 5

Cluster Analysis (CA) 6

Results 7

Discussion 18

References 20

Distribution List 21 

iii
List of Figures 

Figure 1. Image a. and b. show a conventional visible and LWIR thermal image, 

respectively, of a vehicle parked in a tree-line and obscured from view. Image c. shows a 

resultant polarimetric image (commonly termed an S1 image), that is a measure of 

vertically polarized radiation compared to horizontally polarized radiation. Black regions 

within the binary image c. signify regions where the difference between the vertical and 

horizontal sates is zero. The colored region(s) signify some finite difference implying a 

man-made object is present. Image d. shows image b. and c. being fused together 

highlighting the presence of a hidden vehicle............................................................................2 

Figure 2. The LWIR polarimetric imager is designed to produce well calibrated polarimetric 

and/or Stokes imagery................................................................................................................5 

Figure 3. Visible image of scene 1, which is a vehicle in the brush...............................................8 

Figure 4. LWIR DOLP 30x30 pixel image of the vehicle in scene 1.............................................8 

Figure 5a. First derived image which accounts for nearly half of the variance in the data cube 

of scene 1 and is dominated by DOLP and ORT.....................................................................10 

Figure 5b. Second derived image which accounts for nearly 40% of the variance in the data 

cube of scene 1 and is dominated by S0...................................................................................10 

Figure 5c. Third derived image which accounts for approx. 14% of the variance in the data 

cube of scene 1. The magnitudes of the eigenvector components are more evenly 

distributed. ...............................................................................................................................11 

Figure 6a. Cluster analysis plot for 19 clusters. The background is comprised of clusters 1 

through 3 while the features of the vehicle are classified between clusters 4 through 19.......12 

Figure 6b. Cluster analysis plot for 11 clusters. Clusters 1 through 3 are predominantly the 

background but do consist of some portions of the vehicle. Clusters 4 through 11 

correspond to the vehicle. ........................................................................................................12 

Figure 6c. Cluster plot for 2 clusters. Cluster 1 is predominantly the background but does 

contain some of the vehicle. Cluster 2 consists mainly of the side of the vehicle.................13 

Figure 7. Visible image of scene 2 which is a mobile rocket launcher in the brush.....................13 

Figure 8. LWIR DOLP 30x30 pixel image of mobile rocket launcher in scene 2. ......................14 

Figure 9a. First derived image which accounts for 44% of the variance of the data cube of 

scene 2 and is dominated by DOLP and S0..............................................................................15 

Figure 9b. Second derived image which accounts for 33% of the variance of the data cube in 

scene 2 and is dominated by ORT. ..........................................................................................16 

Figure 9c. Third derived image which accounts for 23% of the variance of the data cube in 

scene 2 and is dominated by DOLP and S0..............................................................................16 

Figure 10a. Cluster plot for 15 clusters. Clusters 1 through 7 corresponds to the background 

while 8 through 15 to the mobile rocket launcher. ..................................................................17 

iv
Figure 10b. Cluster plot for 5 clusters. Clusters 1 and 2 correspond to the background and 3 

through 5 correspond to the mobile rocket launcher. ..............................................................17 

Figure 10c. Cluster plot for 3 clusters. Cluster 1 corresponds to the background and clusters 

2 and 3 correspond to the mobile rocket launcher. ..................................................................18 

Figure 10d. Cluster plot for 2 clusters. Cluster 1 corresponds to the background and rocket 

and cluster 2 to the vehicle and mount of the rocket launcher.................................................18 

List of Tables 

Table 1. Percent variance and cumulative percent variance for the principal components............8 

Table 2. Components of the eigenvectors Vi (i=1,2,3) which serve as basis vectors for the 

projection of the data in the multivariate space of scene 1........................................................9 

Table 3. Percent variance and cumulative percent variance for the principal components..........14 

Table 4. Components of the eigenvectors Vi (i=1,2,3) which serve as basis vectors for the 

projection of the data in the multivariate space of scene 2......................................................14 

v
INTENTIONALLY LEFT BLANK

vi
Introduction 

There is great interest in assessing the usefulness of polarization-based imaging for improved 

targeting and tracking of “man-made” objects that are obscured by complex “natural” 

backgrounds (1). Polarimetric based imaging shows particular promise when applied in the 

thermal infrared (IR) (2). 

Thermal IR polarimetric imaging exploits the fact that man-made objects, such as vehicles, 

roads, buildings, etc., tend to emit radiation that exhibits a greater degree of polarization than 

natural background materials i.e., soil, vegetation, brush, etc. By filtering the image forming 

radiation based solely on polarization state, one can construct a polarimetric image that 

highlights objects that are most polarized and suppress regions of the scene that are least 

polarized. The net result is that thermal polarimetric imagery tends to increase the contrast 

between the man-made targets and complex backgrounds within a scene. In a study by Gurton et 

al., it has been shown that information content is greatly enhanced by fusing polarimetric 

imagery with conventional thermal imagery (1). An example of this can be seen in figures (1a 

through 1d.). 

1
a. b. 

c. d. 

Figure 1. Image a. and b. show a conventional visible and LWIR thermal image, respectively, of a vehicle 

parked in a tree-line and obscured from view. Image c. shows a resultant polarimetric image 

(commonly termed an S1 image), that is a measure of vertically polarized radiation compared to 

horizontally polarized radiation. Black regions within the binary image c. signify regions where 

the difference between the vertical and horizontal sates is zero. The colored region(s) signify some 

finite difference implying a man-made object is present. Image d. shows image b. and c. being fused 

together highlighting the presence of a hidden vehicle. 

However, because polarimetric imaging produces a multivariate set of at least four spatially 

coincident images per frame, i.e., thermal intensity, amount of horizontally and vertically 

polarized light, amount of +45°and –45° polarized light, and the amount of left- and rightcircular polarized light, there are many ways of processing the data to identify objects of interest. 

As a result, polarimetry (as well as multi- or hyper-spectral imaging) generates a significant 

sized data cube that must be processed in real-time (or pseudo-realtime) rates. Therefore, it is 

desirable to work with a reduced data set to increase computational efficiencies. Several image 

processing techniques have been suggested that would produce a reduced data set for analysis 

and provide varying degrees of image enhancement. 

2
Sadjadi, et al., presented a suite of algorithms designed for automatic target recognition (ATR) 

and detection within IR polarimetric imagery (3,4). The algorithms were tested using simulated 

IR polarimetric imagery and required an estimate of the size of the object of interest in terms of 

its pixel area within the scene, as well as an a priori generated library of first and second order 

statistics for the particular object being examined. Zallat, et al., proposed methods based on 

cluster analysis that involves polarization enhancement and an image processing algorithm based 

on a Markovian model (5). 

We propose applying a well-known multivariate image processing technique called principal 

component analysis (PCA) that reduces the overall data set, and then apply a cluster analysis 

(CA) methodology to increase processing efficiency further (6). We applied these techniques to 

various polarimetric image cubes of recorded long-wave infrared (LWIR) polarimetric imagery 

of DoD relevant targets recorded during various field tests during the summer of 2006. 

First, we describe the polarimetric data acquisition methodology and the LWIR polarimetric 

imager used to record the polarimetric images used here. We then describe in detail the 

particular features unique to the PCA and CA methods used in this study and present examples 

of processed imagery. Finally, we end with a discussion highlighting the various strengths and 

weaknesses associated with either PCA or CA and suggest conditions for optimum utility. 

LWIR Polarimetric Imagery 

The polarimetric camera system used is a modified LWIR thermal imager designed to produce 

well calibrated Stokes imagery by deriving the Stokes parameters over the wavelength region 8.5 

to 10.5 μm. The Stokes parameters are then used to calculate the degree of linear polarization 

(DOLP) and an orientation angle (ORT). The definitions of the Stokes images as well as the 

DOLP and ORT images are defined by equations 1 through 6, 

2

3

2

2

2

0 1 ++≥ SSSS , (1) 

( ) (900 ) 1 = − IIS , (2) 

( ) ( ),4545 2 = + − IIS − (3) 

( ) ( ), 3 = − LIRIS (4) 

0

2

2

2

1 += SSSDOLP , (5) 

and 

( ( )) 21 ORT = arctan21 SS (6) 

3
where I(0), I(90), and I(±45) represent the measured radiance values obtained when a polarizer 

placed in front of a detector is rotated through 0°, 90°, and ±45° with respect to the observation 

plane and I(R) and I(L) represent the right- and left-handed circular states. Here we define the 

observation plane as the plane that contains the surface normal at a point on an object and the 

line-of-sight vector from the camera to that point on the object. Notice that S0 is simply the 

incident irradiance and that the equality holds for completely polarized light. S1, S2, and S3

specify the state of polarization. From equation 2, we see that if S1 > 0, there is an abundance of 

horizontal polarization, and if S1 < 0 there is an abundance of vertical polarization. If S1 = 0 there 

is no preferential polarization with respect to the horizontal or the vertical. Similarly, in equation 

3 if S2 > 0 there is an abundance of +45° polarization and if S2 < 0, there is an abundance of 

–45° polarization. The LWIR polarimetric imager consists of two primary components: 1) a 

polarimetric module that houses a spinning achromatic cadmium selenide (CdSe) quarter wave 

plate which is mounted in series with a fixed wire-grid polarizer, and 2) a camera module that 

consists of a liquid nitrogen cooled, 240x360 pixel, mercury cadmium telluride (MCT) focalplane-array (FPA) (see figure 2). 

Sequential LWIR polarimetric images are recorded digitally at a rate as fast as 240 frames/sec 

and synchronized to the rotation of the spinning CdSe wave-plate. The spinning wave-plate and 

fixed wire-grid polarizer combination effectively acts like a variable polarimetric filter. As a 

result, each digital image recorded is generated by polarized emittance of a particular orientation. 

Although the maximum acquisition rate is 240 frames/second, the present data were acquired at 

128 frames/second and the 240x360 pixels FPA was windowed down to 152x158 pixels. With 

the speed of the spinning wave plate set at 8 revolutions/second, 16 frames were measured every 

125 ms and averaged over 10 revolutions. The averaged frames were then used with a 

prerecorded calibration file to derive the four Stokes images. The imager was calibrated by 

recording the radiometric response when we observe known linear polarization states produced 

by the transmission of the radiance from an extended blackbody through a wire-grid polarizer, 

allowing us to measure the intensity parameters in equations 2 and 3. Because in practice we 

have seen no evidence of circularly polarized emission in the natural environment, the 

corresponding Stokes image S3 (equation 4) is always taken to be zero in this analysis. 

Therefore, we did not measure I(L) or I(R) in the calibration procedure. 

4
Figure 2. The LWIR polarimetric imager is designed to produce well calibrated 

polarimetric and/or Stokes imagery. 

Image Processing Method 

For static or slowly moving objects the LWIR polarimetric imager generally produces a 

minimum of 4 multivariate Stokes images as described above. This results in a stack of images 

in which the pixel positions match for all of the images in the stack (6). For the analysis 

conducted here, we considered only the most robust Stokes image(s) and polarimetric products, 

i.e., the three values DOLP, ORT, and S0. We then apply PCA and CA to a given stack of three 

images, which serve to characterize the scene. 

The first step is to construct a data matrix, , from a given image stack such that the n row(s) 

represent the pixels of a particular image in the stack, and the p column(s) are taken to be a 

particular variable associated with one of the multivariate images, e.g., p represents one of the 3 

parameters defining our image stack, DOLP, ORT, or S0. This creates a p-dimensional variable 

space in which each pixel is represented by a p-element vector which allows the similarities of 

the pixels to be assessed geometrically (5). If the image stack used is 30x30 = 900 pixels, then 

n = 900. Since our image space is limited to the 3 states DOLP, ORT, and S0, p=3. Therefore the 

dimensions for the data matrix, , produced from a typical image stack is 900 x 3. 

Xnp

Xnp

Principle Component Analysis (PCA) 

PCA was used to obtain a reduced/alternative representation of the image stack which effectively 

performs a linear transformation that projects the data set to a new orthogonal multi-dimension 

coordinate system, thus creating a new set of derived variables. This projection is such that the 

5
greatest variance of the data lies on the first coordinate, the second greatest variance on the 

second coordinate, and so on. By displaying the image of each derived variable, we obtain a 

representation of the original image in terms of the interrelationships between the variables in the 

data set (7). 

We begin by calculating the covariance matrix, , of the standardized data matrix, . The 

data, , was standardized to avoid dominance of one variable over another by dividing each 

element by its corresponding column-wise variance, σp. 

Cnp Snp

X np

np = XS σ pnp (7) 

The eigenvectors and eigenvalues of were calculated and placed in descending order 

according to the eigenvaluesto obtain Vpp and λp, respectively. The projection into variable 

space, Pnp, is obtained by the matrix multiplication in equation 8. 

Cnp

np VCP ppnp = ⋅ (8) 

The matrix Pnp consists of derived variables that are the projection of the original data set onto 

the basis found in the PCA. The image plot of Pnp reflects the correlation of each pixel with the 

principal components. Examination of the elements of Vpp reveals detailed information of the 

contribution of each variable to the principal components. 

Other meaningful parameters include the “percent energy” which is obtained by calculating the 

cumulative sum of the elements of λp. The percent energy represents the amount of the variance 

of the entire data set that is accounted for based upon the number of principal components one 

chooses to include in the analysis. This also allows for the reduction of the dimensions of the 

data by disregarding the principal components that only account for a negligible amount of the 

total variance. 

Cluster Analysis (CA) 

CA was used to exploit the tendency for distinct objects and/or regions of objects to have similar 

values for all p variables in the variable space (7). A geometrical distance in the p-dimensional 

variable space can be used to determine the similarity between pixels. A Euclidean distance 

metric, given by equation 9 was used in this analysis. An n × n matrix was calculated (where n is 

the number of pixels) whose elements are the distances between each pixel in the p-dimensional 

variable space. 

( ) ( ) ( ) 2 2

22

2

ij ji 11 ji jpip xxxxd " −++−+−= xx , i,j≤ n (9) 

6
The cluster algorithm used in this analysis was agglomerative and hierarchical, i.e., each pixel 

begins as an individual cluster, and as the algorithm progresses, the two clusters that are closest 

are fused until the only remaining cluster contains all of the pixels of the image. In addition, 

once a pixel is placed in a cluster, it remains in it through the termination of the algorithm. Each 

time a cluster acquires a new member (pixel), its distance in the p-dimensional variable space 

with respect to the remaining clusters must be recalculated. In this study, the distance between 

two clusters containing more than one pixel is defined as the average distance between all of the 

members of each cluster, known as average-linkage. To limit computation times, we performed 

the analysis on subsections of the original LWIR imagery that we feel contain objects of interest. 

Results 

The results presented here will consist of two scenes that each contains an object of interest. The 

geometry of the objects of interest in the scenes differs greatly from each other, allowing for an 

assessment of the robustness of the algorithm’s ability to distinguish the objects from the 

background as well as distinguish various features of the object. 

For each scene a visible and DOLP image are presented for comparison followed by the PCA 

and CA results. The PCA results consist of the cumulative percent energy, eigenvectors, and 

principal component plots. The CA results consist of cluster plots that exemplify the evolution 

of the clustering processes. The data was grouped into a range of 2 to 20 clusters. The images 

that best exemplify the progression of the cluster output were selected for presentation below. 

Scene 1 

The first scene is shown in figure 3 for reference and consists of a vehicle that is in the brush. A 

corresponding LWIR DOLP image is shown in figure 4 (the highly pixilated nature of the 

polarimetric image is due to the fact that it is a subsection of the original image, i.e. the original 

image is 152x158 pixels, and figure 4 is only a 30x30 pixel subsection of the original). 

7
Figure 3. Visible image of scene 1, which is a 

vehicle in the brush. 

Figure 4. LWIR DOLP 30x30 pixel image of the vehicle 

in scene 1. 

The percent variance and cumulative percent variance for the three principal components are 

shown in table 1. The first component accounts for the largest amount of the variance, 

approximately 48%. The next component accounts for 38% and the last for 14%. The 

components of the eigenvectors listed in table 2 indicate each variable’s contribution to the 

principal components. 

Table 1. Percent variance and cumulative percent variance for the principal components. 

Principal Component Percent Variance Cum. Percent Variance 

1 48 48 

2 38 86 

3 14 100 

8
Table 2. Components of the eigenvectors Vi (i=1,2,3) which serve 

as basis vectors for the projection of the data in the multivariate 

space of scene 1. 

V1 V2 V3

DOLP 0.67202 –0.40393 0.62067 

ORT 0.72953 0.21718 –0.64855 

S0 0.12717 0.88864 0.44063 

The variables that contribute most to the first principal component are DOLP and ORT. Recall 

that, from table 1, the first principal component accounts for nearly half of the variance within 

the data set. This suggests that thermal intensity, S0, does not contain the important information 

within the scene, i.e., there is low thermal contrast. In addition, note that each variable is directly 

correlated to each other in the first component. On the other hand, the second principal 

component is dominated by S0 and DOLP is now inversely correlated with ORT and S0. The 

contribution to the third principal component is distributed more evenly among the variables in 

the data set than for the first two principal components and ORT is inversely correlated to DOLP 

and S0. 

Figures 5a-c show the principle component images listed in descending order. These images 

contain the information about the correlations of each variable with respect to each principal 

component. One can see in figure 5a the lighter colored pixels are directly correlated to the first 

principal component which, as we saw in table 2, is dominated by both DOLP and ORT whose 

eigenvector component magnitudes are 0.67202 and 0.72953, respectively. The darker pixels are 

inversely correlated to the first principal component. Also, note that there is good contrast 

between the vehicle and the background. Because the contribution by S0 to the first derived 

variable is so low, this also suggests that there is low thermal contrast within this scene. 

However, figure 5b shows that the same region of pixels is directly correlated to the second 

principal component which is dominated by the total radiance image, S0 (see table 2). Note that 

this corresponds to a decrease in the amount of contrast between the vehicle and the background 

in figure 5b. The interpretation of figure 5c is more difficult because, as can be seen in table 2, 

the magnitudes of the components of the eigenvectors are much closer and less distinct, and as a 

result the third principal component accounts for the smallest percent of the total variance seen in 

the image. 

9
Figure 5a. First derived image which accounts for nearly 

half of the variance in the data cube of scene 1 

and is dominated by DOLP and ORT. 

Figure 5b. Second derived image which accounts for nearly 

40% of the variance in the data cube of scene 1 

and is dominated by S0. 

10
Figure 5c. Third derived image which accounts for approx. 

14% of the variance in the data cube of scene 1. 

The magnitudes of the eigenvector components 

are more evenly distributed. 

Figures 6a-c are cluster plots that exemplify the progression of the clustering output. The color 

bar corresponds to the cluster number. Figure 6a shows the scene classified into 19 clusters. 

The background is comprised of clusters 1 through 3 while the features of the vehicle are 

classified between clusters 4 through 19. Clusters 16 through 19 represent the front of the 

vehicle, while the rest of the vehicle is generated via clusters 4 through 15. In figure 6b, the 

scene is split into 11 clusters. Most of the original background has now been fused into one 

cluster. Also fused into this “background” cluster are some pixels that correspond to the vehicle, 

mainly its wheels. Other clusters that represented portions of the vehicle in the previous 

calculation have been fused together as well. In figure 6c, the scene is now split into only two 

clusters. All of the background has become one homogeneous cluster. Also included in this 

cluster are portions of the vehicle which mainly include the front and wheels. Therefore, the two 

distinct clusters that remain are the background and the side of the vehicle. 

11
Figure 6a. Cluster analysis plot for 19 clusters. The background 

is comprised of clusters 1 through 3 while the features 

of the vehicle are classified between clusters 4 through 19. 

Figure 6b. Cluster analysis plot for 11 clusters. Clusters 1 

through 3 are predominantly the background 

but do consist of some portions of the vehicle. 

Clusters 4 through 11 correspond to the vehicle. 

12
Figure 6c. Cluster plot for 2 clusters. Cluster 1 is predominantly 

the background but does contain some of the 

vehicle. Cluster 2 consists mainly of the side 

of the vehicle. 

Scene 2 

The second scene, shown in figure 7, is of a mobile rocket launcher located in the brush. The 

DOLP image is shown in figure 8. Notice that the geometry of this vehicle is very different from 

the vehicle in scene 1 (figure 3). 

Figure 7. Visible image of scene 2 which is a mobile 

rocket launcher in the brush. 

13
Figure 8. LWIR DOLP 30x30 pixel image of mobile rocket 

launcher in scene 2. 

The percent variance and cumulative percent variance for the three principal components is 

shown in table 3. Of the three principal components, the first accounts for the largest amount of 

the variance, approximately 44%. The last two principal components account for 33% and 23% 

of the variance, respectively. The 3 components of the eigenvectors are listed in table 4. The 

variables that contribute most to the first principal component are DOLP and S0 images and 

DOLP and ORT are inversely correlated to S0. As opposed to scene 1, S0 is important in scene 2 

because the shadowed (i.e., cool) regions are very prominent. The second principal component 

is dominated by ORT and DOLP is now inversely correlated to ORT and S0. The contribution to 

the third principal component is dominated by DOLP and S0, respectively, and all of the 

variables are directly correlated. 

Table 3. Percent variance and cumulative percent variance for the principal components. 

Principal Component Percent Variance Cum. Percent Variance 

1 44 44 

2 33 77 

3 23 100 

Table 4. Components of the eigenvectors Vi (i=1,2,3) which serve 

as basis vectors for the projection of the data in the 

multivariate space of scene 2. 

V1 V2 V3

DOLP -0.69008 0.20562 0.69391 

ORT -0.16492 -0.97824 0.12586 

S0 0.70469 -0.02758 0.70898 

14
Figures 9a-c are the 1st, 2nd, and 3rd derived images for the scene shown in figure 8. The dark and 

light pixels are negatively and positively correlated, respectively, to the first principal component 

shown in figure 9a. Recall that the first principal component is dominated by DOLP and S0, 

whose eigenvector component magnitudes are 0.69008 and 0.70469, respectively (see table 4). 

It is apparent that the dark pixels in figure 9a correspond to the rocket, while the light pixels 

correspond to the side of the vehicle transporting the rocket. In figure 9b, the pixels that are 

positively correlated to the second principal component, which is dominated by ORT (see table 

4), seem to correspond to the side of the vehicle as well as the rocket mount. Note that in the 

portion of figure 9b that corresponds to the vehicle, a portion of the back of the vehicle is 

inversely correlated to the second principal component, while the side of the vehicle is positively 

correlated. This is consistent with the fact that the second principal component is dominated by 

ORT. However, figure 9c shows that the pixels corresponding to the rocket are positively 

correlated to the third principal component (which, as seen in table 4, is dominated by DOLP and 

S0). 

Figure 9a. First derived image which accounts for 44% 

of the variance of the data cube of scene 2 and 

is dominated by DOLP and S0. 

15
Figure 9b. Second derived image which accounts for 33% 

of the variance of the data cube in scene 2 and 

is dominated by ORT. 

Figure 9c. Third derived image which accounts for 23% 

of the variance of the data cube in scene 2 and 

is dominated by DOLP and S0. 

Figures 10a-d are the cluster plots for scene 2. Figure 10a shows the scene classified into 15 

clusters. Clusters 1 through 7 corresponds to the background while 8 through 15 to the mobile 

rocket launcher. In figure 10b, many of clusters have been combined so that there are only five 

clusters. The first two clusters correspond to the background, while the rest correspond to the 

mobile rocket launcher. 

16
Specifically, cluster 3 is the side of the vehicle and the rocket mount, and cluster 4 the rocket, 

and cluster 5 is a solitary pixel that corresponds to the side of the vehicle. Figure 10c shows that 

the number of clusters have been reduced further, to three. Here the background is represented 

homogeneously by cluster 1, the rocket by cluster 2, and the side of the vehicle and rocket mount 

by cluster 3. Finally, shown in figure 10d one can see that the rocket has been combined with 

the background so that the only remaining clusters are the background and the side of the vehicle 

along with the rocket mount. 

Figure 10a. Cluster plot for 15 clusters. Clusters 1 through 

7 corresponds to the background while 8 

through 15 to the mobile rocket launcher. 

Figure 10b. Cluster plot for 5 clusters. Clusters 1 and 2 

correspond to the background and 3 through 

5 correspond to the mobile rocket launcher. 

17
Figure 10c. Cluster plot for 3 clusters. Cluster 1 corresponds 

to the background and clusters 2 and 3 

correspond to the mobile rocket launcher. 

Figure 10d. Cluster plot for 2 clusters. Cluster 1 corresponds 

to the background and rocket and cluster 2 to 

the vehicle and mount of the rocket launcher. 

Discussion 

The utility for applying PCA to multivariate polarimetric images is demonstrated by processing 

subsections of two polarimetric images that each contains an object of interest. The original 

DOLP image regions seen in figures 4 and 8 were intentionally chosen to test how effective the 

18
PCA methodology is for enhancing original imagery when applied to a simple three channel 

polarimetric image cube. As seen in the resultant first component images (or “derived” image) 

shown in 5a and 9a, information concerning all of the variables used in the analysis has been 

incorporated into an image that maintains the same level of contrast and target features as the 

original DOLP images. Thus, the PCA methodology provides a more efficient means for 

analyzing the relationships of the variables in the data set. 

We have used the fact that principle components contain the information of the data set in 

descending order to isolate the useful information for further analysis. In general, the first 

component images have the least amount of “noise” because they contain small contributions of 

the channels with the smallest amount of contrast. The later components get noisier since they 

contain less of the total sum of the squares when compared to the first component image, i.e., 

they contain more of the channels with the smallest amount of contrast. As mentioned earlier, 

the first score images seen in either figures 5a or 9a represents a weighted average of the most 

intense raw image of the polarimetric image cube (sometimes termed a “stack”). These images 

can be considered as a noise-reduced “mean” image. In many other applications, the first 

component score image plays an analogous role as a noise-reduced mean. The score images seen 

in figures 5 and 9 shows additional detail of the sample and may be of use depending on the 

application. 

Because the principal components are orthogonal, the corresponding score images show optimal 

visual contrast between two consecutive scores, i.e., most noticeable between the first and 

second score images. The net effect of this is to enhance target features not visible in any single 

image of the original multivariate image set. This additional information may be useful in 

identifying objects not readily distinguishable from complex backgrounds. 

In addition, we also apply cluster analysis that takes into account the similarity (or dissimilarity) 

of all the variables for each data point to provide a representation of the objects within a scene. 

When the number of clusters that a scene is split into is large, the algorithm attempts to 

distinguish between different features of the same object, i.e., one object may be split into more 

than one cluster. A limitation of the technique is that the ability of the algorithm to provide 

information about the features of a particular object depends upon the size of the object within 

the field-of-view of the camera. If the object is large within the field of view, then the clusters 

may reveal information about the geometrical shape and orientation of the object. If the object is 

small within the field of view, the algorithm will most likely have trouble accurately representing 

the different features of the object. A detailed study of the mean polarimetric values for each 

cluster will have to be performed to understand its ability to represent various features of objects. 

Another limitation of this technique is that it is computationally extensive. The array sizes 

involved can become very large, thus slowing the run-time of the algorithm. To improve upon 

the technique, it is recommended that the multivariate image analysis be made more efficient to 

improve the run-time for large subsections of polarimetric images. In addition, this algorithm 

should be combined with another algorithm that quickly identifies locations, or subsections, 

within the entire image that the multivariate image analysis can then be applied to. 

19
References 

1. Gurton, Kristan P.; Dahmani, R.; Videen G. Effect of surface roughness and complex 

indices of refraction on polarized thermal emission. Appl. Opt. 2005, 44, 36. 

2. Gurton, Kristan P. Advancement in Polarimetric Sensor Design, Military Sensing 

Symposium (MSS) Polarimetric Workshop, Atlanta, GA, 4–6 December 2006. 

3. Sadjadi, F.; Chun, C. Improved Feature Classification by means of a Polarimetric IR 

Imaging Sensor. IEEE 1996, 396–398. 

4. Sadjadi, F. Polarimetric IR Automatic Target Detection and Recognition. IEEE 1996, 

2140–2143. 

5. Zallat, J. Clustering of polarization-encoded images. Appl. Opt. 2004, 43 (2), 283–292. 

6. Geladi P.; Grahn, H. Multivariate Image Analysis. John Wiley & Sons Inc., 1996. 

7. Dillon, W.; Goldstein, M. Multivariate Analysis: Methods and Applications. John Wiley & 

Sons Inc., 1984. 

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