Road Navigation by a Passive Millimeter-Wave 

Imager Mounted on an Aircraft 

by Joseph D. Silverstein 

ARL-TR-3017 July 2003 

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Army Research Laboratory 

Adelphi, MD 20783-1197 

ARL-TR-3017 July 2003 

Road Navigation by a Passive Millimeter-Wave 

Imager Mounted on an Aircraft 

Joseph D. Silverstein 

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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Road Navigation by a Passive Millimeter-Wave Imager Mounted on an Aircraft 

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13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

Simulations are carried out of the generation and integration of passive millimeter-wave (PMMW) digital video images of a simple scene 

consisting of a road bordered on either side by vegetation growth. The MMW road and growth brightness temperatures, their standard 

deviations, and the parameters of the simulated PMMW imaging system are based on realistic values. It is assumed that the simulated PMMW 

sensor is mounted on a low-flying aircraft. The processing consists only of straightforward integration of all or parts of consecutive video image 

frames. In the simulations the difference between the vegetation growth and road average brightness temperatures could have values from 1 K 

thru 15 K. The variation in the vegetation growth or road brightness temperature due only to terrain non-uniformities could have values from 0 K 

thru 2 K. Variations due only to system thermal noise could have values from 3 K thru 15 K. The number of consecutive frames integrated could 

be 2 thru 31. These simulations show that road navigation is possible for at least some combinations of the terrain and thermal noise brightness 

temperature variations studied, if the vegetation growth-to-road, average brightness temperature difference is 2 K or larger, and 31 consecutive 

frames or less are integrated. However, in order to accomplish road navigation when that brightness temperature difference is only 1 K, and for 

any of the combinations of terrain and thermal noise brightness temperature variations studied, more than 31 consecutive frames would have to 

be integrated. The simulations also show that, for fixed values of all the brightness temperature parameters, and for a given angular separation 

between consecutive brightness temperature measurements, if the antenna aperture size could be increased over that currently feasible for 

airborne PMMW imaging systems, the number of frames that would need to be integrated to achieve a given degree of vegetation growth-to-road 

brightness temperature contrast would be decreased. 

15. SUBJECT TERMS

Millimeter-wave, video image processing, video frame, frame rate 

16. SECURITY CLASSIFICATION OF: 19a. NAME OF RESPONSIBLE PERSON

Joseph D. Silverstein 

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UNCLASSIFIED 

b. ABSTRACT 

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OF ABSTRACT 

UL 

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OF PAGES 

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(301) 394-3170 

Standard Form 298 (Rev. 8/98) 

Prescribed by ANSI Std. Z39.18 
iii

Contents 

List of Figures iv

List of Tables vi

1. Introduction 1

2. Simulation Parameters and Methodology 1

2a. Scene simulation..............................................................................................................1 

2b. Method of single frame “simulation”..............................................................................4 

2c. Point spread function distortion ......................................................................................4 

2d. Thermal noise addition....................................................................................................4

3. Frame Integration 5

3a. Frame rows and columns.................................................................................................5 

3b. Partially integrated frame formation ...............................................................................5 

3c. dx-column integrated frame formation............................................................................7 

3d. Formation of the fully integrated frame .........................................................................9 

4. Simulation Steps 10

5. Simulation Results 11

5a. Frame images and plots.................................................................................................11 

5b. Contrast figure of merit .................................................................................................13

5c. Road distinguishability..................................................................................................19

6. Generation of Video Frames 23

7. Conclusions 25

References 26
iv

List of Figures 

Figure 1. Schematics of a simulated scene (1a) and a frame (1b). The growth and road 

patches of the scene and frame each have 10 brightness temperature pixels “cross track,” 

for a total of 30, and a sufficient number of brightness temperature pixels “along track” to 

extract the desired number of frames for the simulation. Each frame to be extracted has 

30 “cross track” brightness temperature pixels, and 63 “along track” brightness 

temperature pixels. Each frame is delayed relative to the preceding frame by the time 

needed by the imaging system to measure 2 samples “along track” .........................................3 

Figure 2. Formation of a 25-column, partially integrated frame by integrating portions of 

consecutive, single frame numbers 1–20, where “column” refers to brightness 

temperature pixels at the same “along track” position of the scene. The partially 

integrated frame results from the averaging of the 20 independent brightness temperature 

values, contained in each of the pixels (“cross track,” “along track” location) of columns 

39–63 of the scene. These pixels are in columns 39–63 of single frame 1, columns 37–61 

of single frame 2, columns 35–59 of single frame 3, and so on, down to columns 1–25 of 

single frame 20. These 20, 25-column single frame slices are averaged to form columns 

1–25 of the 63-column, fully integrated from being formed .....................................................6 

Figure 3. Formation of dx(2)column, integrated frame resulting from integrating 20 frames, 

where “column” refers to all pixels at the same “along track” position of the scene. This 

dx-column integrated frame results from the averaging of 20 independent brightness 

temperature measurements, contained in single frames 2–21, in each of the pixels (“cross 

track,” “along track” locations) in columns 64 and 65 of the scene. These pixels are in 

columns 62 and 63 of single frame 2, columns 60 and 61 of single frame 3, columns 58 

and 59 of single frame 4, and so on, down to columns 24 and 25 of single frame 21. 

These 20, 2-column, frame slices are averaged to form columns 26 and 27 of the 63-

column, fully integrated frame being formed. Corresponding procedures are carried out to 

form the fully integrated frame’s columns 28 and 29, 30 and 31, 32 and 33, and so on, 

down to columns 62 and 63 .......................................................................................................8 

Figure 4. Concatenation of one, 25-column slice formed by integrating 25-column portions of 

frames 1–20, where “column” refers to all brightness temperature pixels at the same 

“along track” position of the scene, (see Figure 2), and 19, 2-column slices, each formed 

by integrating 2-column portions of frames 2–21, frames 3–22, frames 4–23, and so on, 

down to frames 20–39 (see Figure 3). The result is a fully integrated, 63-column frame.........9 

Figure 5. Images of a single and processed frame with a road (center patch) average 

brightness temperature of 270 K, a growth (upper and lower patches) average brightness 

temperature and a thermal noise minimum resolvable brightness temperature difference 

of 10 K. The psf is appropriate for a PMMW imaging system at 84.5 GHz oversampling 

the scene by ×2. 5a. A simulated, single frame that has terrain variation noise only. 5b. 

The simulated, single frame that results from convolving the frame in 5a with the psf and 

adding thermal noise. 5c. The fully integrated frame arising from the integration of 20 

consecutive, single frames, such as the one in 5b, in the manner illustrated in 

Figures 1–4...............................................................................................................................12
v

Figure 6. Plots of brightness temperature at “along track” position 32 vs. “cross track” 

position in a frame having only terrain variation, in a frame having both terrain variation 

and thermal noise, as well as distortion from the psf, and the processed frame arising 

from the integration of 20 frames. The road average brightness temperature is 270 K, the 

growth average brightness temperature is 275 K, the terrain variation minimum 

resolvable brightness temperature difference is 1K, the thermal noise minimum 

resolvable brightness temperature difference is 10 K, and the psf is appropriate for a 

PMMW imaging system that oversamples the scene by ×2. The 20-frame integration 

processes illustrated in Figures 1–4 .........................................................................................13

Figure 7. Contrast-to-noise ratio vs. number of frames integrated for the fully integrated 

frame based on the central limit theorem (CLT), and as generated by simulations with 

blurring by a point spread function for an oversampling of ×2, and without blurring. The 

vegetation growth-to-road brightness temperature difference is 5 K, the terrain variation 

minimum resolvable brightness temperature difference is 1 K, and the thermal noise 

minimum resolvable brightness temperature difference is 3 K ...............................................15 

Figure 8. Contrast-to-noise ratio vs. number of frames integrated for the fully integrated 

frame based on the central limit theorem (CLT), and as generated by simulations with 

blurring by a point spread function for an oversampling of ×2, and without blurring. The 

vegetation growth-to-road brightness temperature difference is 5 K, the terrain variation 

minimum resolvable brightness temperature difference is 1 K, and the thermal noise 

minimum resolvable brightness temperature difference is 5 K ...............................................16 

Figure 9. Contrast-to-noise ratio vs. number of frames integrated for the fully integrated 

frame based on the central limit theorem (CLT), and as generated by simulations with 

blurring by a point spread function for an oversampling of ×2, and without blurring. The 

vegetation growth-to-road brightness temperature difference is 5 K, the terrain variation 

minimum resolvable brightness temperature difference is 1 K, and the thermal noise 

minimum resolvable brightness temperature difference is 10 K .............................................17 

Figure 10. Contrast-to-noise ratio vs. number of frames integrated for the fully integrated 

frame based on the central limit theorem (CLT), and as generated by simulations with 

blurring by a point spread function for an oversampling of ×2, and without blurring. The 

vegetation growth-to-road brightness temperature difference is 5 K, the terrain variation 

minimum resolvable brightness temperature difference is 1 K, and the thermal noise 

minimum resolvable brightness temperature difference is 15 K .............................................18 

Figure 11. Brightness temperature contrast-to-noise ratio vs. number of frames integrated for 

the fully integrated frame based on the central limit theorem (CLT), and as generated by 

simulations without blurring as well as with blurring by point spread functions for 

oversamplings of ×1 (aperture diameter = 116 cm), ×2 (aperture diameter = 58 cm), and 

×4 (aperture diameter = 29 cm). The vegetation growth-to-road brightness temperature 

difference is 5 K, the terrain variation minimum resolvable brightness temperature 

difference is 1 K, and the thermal noise minimum resolvable brightness temperature 

difference is 10 K.....................................................................................................................19
vi

Figure 12. Fully integrated frames resulting in brightness temperature contrast-to-noise ratios 

of 0 dB (12a), 1 dB (12b), and 2 dB (12c) for a vegetation growth-to-road brightness 

temperature difference of 5 K, a terrain variation minimum resolvable brightness 

temperature difference of 1 K, and a thermal noise minimum resolvable brightness 

temperature difference of 0 K..................................................................................................20 

List of Tables 

Table 1a. Platform parameters .........................................................................................................2 

Table 1b. Imaging System and Frame Simulation Parameters........................................................2 

Table 2a. Minimum required number of frames that must be integrated to achieve specified 

values of contrast-to-noise ratio (cnr) for vegetation growth-to-road brightness 

temperature differences of 1 K and 2 K...................................................................................21 

Table 2b. Minimum required number of frames that must be integrated to achieve specified 

values of contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness 

temperature difference of 5 K..................................................................................................22 

Table 2c. Minimum required number of frames that must be integrated to achieve specified 

values of contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness 

temperature difference of 10 K................................................................................................22 

Table 2d. Minimum required number of frames that must be integrated to achieve specified 

values of contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness 

temperature difference of 15 K................................................................................................23 

Table 3. Range of the frame numbers of the 39, consecutive single frames involved in 

forming each of the first 10, fully integrated frames. The fully integrated frames are 

formed by integrating portions of 20 consecutive, single frames from among those 39 

consecutive, single frames. For each fully integrated frame number the table also gives 

the range of the column numbers of the scene columns imaged by those fully integrated 

frames. The number of columns in both the single and fully integrated frames is 63, and 

the frame-to-frame delay in “along track” brightness temperature pixels is 2 ........................24 
1

1. Introduction 

It is well known that passive millimeter-wave (PMMW) imaging systems can operate in limited 

visibility conditions during day and night when other sensors have limited performance (1). This 

paper suggests that it may be feasible for an aircraft to navigate along a road, even in limited 

visibility conditions, by means of a PMMW imaging sensor. Moreover, this method is even 

effective when the brightness temperature of the road does not differ significantly from that of its 

surroundings. Such a small difference may occur when the road is made of a material such as 

dirt, asphalt, or concrete, and its surroundings consist of some higher emissivity vegetation. 

PMMW sensors are attractive for road navigation by aircraft flying at a relatively low altitude, 

since in most such road scenarios the spatial resolution that can be achieved by the sensors 

should not be a limiting factor in distinguishing the road from its surroundings. Resolution 

improvement investigations carried out at ARL (2) evaluated the performance of several 

powerful image restoration algorithms that were designed to improve the spatial resolution in 

PMMW images obtained with a stationary sensor. Those investigations showed that the degree 

of resolution improvement is influenced by the inherent temperature contrast and noise in the 

original image. 

The main challenge for processing PMMW video images of navigation scenes is to restore the 

contrast of the road to its surroundings, which is degraded by noise due to spatial variations of 

the terrain and by system thermal noise. This contrast may be improved by decreasing the 

minimum resolvable brightness temperature difference in the processed video image. The latter 

is proportional to the reciprocal of the square root of the sensor integration time, which, in turn, 

is determined by the frame rate of the system. One can effectively increase the sensor integration 

time for a small area of the scene, samples of whose brightness temperatures are measured by the 

sensor, by averaging together, or “integrating,” several consecutive video image frames, each of 

which contains brightness temperature samples of some larger area which contains the smaller 

area. This paper shows that the image contrast may be significantly and efficiently increased 

using consecutive video frame integration. 

2. Simulation Parameters and Methodology 

2a. Scene simulation 

Table 1a gives the airborne platform parameters used in the simulations, and Table 1b gives the 

MMW imaging system and frame parameters used in the simulations. These parameters were 

chosen to approximate those of a PMMW system currently being developed (3), and to be 

appropriate for such a system mounted on a low-flying helicopter. From Table 1b the number of 

brightness temperature measurements in a video frame, henceforth to be referred to as “pixels,” 

is 30 “cross-track” and 63 “along track.” Accordingly, for simplicity, the road scene simulated 

was also assumed to have 30 brightness temperature samples “cross track,” and a number of 
2

brightness temperature samples “along track” that was at least sufficient to allow the 

“simulation” of the desired number of single frames in the manner to be described in subsection 

2b. 

Table 1a. Platform parameters. 

Parameter Value 

Altitude 100 m 

Speed 44.7 m/sec (100 mph) 

Table 1b. Imaging System and Frame Simulation Parameters. 

Parameter Value 

Center Frequency 84.5 GHz 

Antenna circular aperture diameter 58 cm 

Angle between consecutive brightness 

temperature measurement positions at the 

imager: 

“cross track” 

“along track” 

0.38 deg 

0.38 deg 

Number of brightness temperature 

measurements in a frame image: 

“cross track” 

“along track” 

30 

63 

Video frame rate 30 Hz 

Depression angle 90 deg (nadir) 

Figures 1a and 1b show schematics of a typical simulated road scene and frame image, 

respectively. It consists of three long, straight, parallel patches at different brightness 

temperatures. The number of “cross-track” samples for each patch in the scene and frame was 

10, yielding the total number of 30 “cross-track” samples given in Table 1b. In any simulated 

scene the average brightness temperature in the central patch, considered to be the road, was 

fixed at 270 K, while the average brightness temperature in the patches on either side, considered 

to be some type of vegetation growth, was varied and assumed to be 270 K + ∆T, where ∆T was 

assigned the values 1 K, 2 K, 5 K, 10 K, and 15 K (1,4). The statistical variations in the 

brightness temperature of both the road and growth patches can be expressed as the minimum 

resolvable temperature due to terrain variations, mrtte. It was given the values 0 K, 1 K, or 2 K 

(1,4). A Gaussian brightness temperature distribution having an average value of 0 K and a 

standard deviation equal to mrtte was added to the constant brightness temperatures of the scene 

before forming any frames using the simulated scene. 
3

1-10

63 “along track” brightness

temperature samples per “cross 

track” position 

“Along track” direction 

 11-20

1b. Frame 

 Growth brightness temperature = (270 + ∆T) K 

 Road brightness temperature = 270 K 

 Growth brightness temperature = (270 + ∆T) K 

temperature samples  ”cross track” brightness 

 21-30

 Growth brightness temperature = (270 + ∆T) K 

 Road brightness temperature = 270 K 

 Growth brightness temperature = (270 + ∆T) K 

Sufficient number of “along track” brightness

temperature samples per “cross track” position to

simulate the desired number of frames 

1a. Scene 

 1-10 11-20 21-30 

temperature samples  ”cross track” brightness 

Figure 1. Schematics of a simulated scene (1a) and a frame (1b). The growth and road patches of the scene and 

 frame each have 10 brightness temperature pixels “cross track,” for a total of 30, and a sufficient 

 number of brightness temperature pixels “along track” to extract the desired number of frames for the 

 simulation. Each frame to be extracted has 30 “cross track” brightness temperature pixels, and 63 

 “along track” brightness temperature pixels. Each frame is delayed relative to the preceding frame by 

 the time needed by the imaging system to measure 2 samples “along track.” 
4

2b. Method of single frame “simulation” 

It is seen from Table 1b that the angle separating consecutive brightness temperature 

measurements, both “cross track” and “along track,” and henceforth to be referred to as “pixel 

angle,” is 0.38 deg. Thus, the field of view (FOV) of the imager is 11 deg (0.38×30) “cross 

track” and 24 deg (0.38×63) “along track.” Based on that pixel angle and the frame rate of 

30 Hz, given in Table 1b, and on the platform speed of 44.7 m/sec and platform altitude of 100 m 

given in Table 1a, one may infer that the number of “along track” pixels, dx, of the scene by 

which the first pixel of a frame is delayed relative to the first pixel of the preceding frame is 

(1/30)(44.7/100)(180/π)/0.38 = 2.25, which, when rounded down, is 2. This “along-track”, 

2-pixel delay and the number of consecutive single frames that need to be simulated then 

uniquely determine the minimum number of “along track” pixels the simulated scene is required 

to have. Thus, to simulate one single frame, the scene must have 63 columns, to simulate two 

single frames the scene must have 65 columns, to simulate three single frames the scene must 

have 67 columns, and so on. Section 3d discusses the method that was used to determine the 

number of frames that needed to be extracted 

2c. Point spread function distortion 

From Table 1b the central frequency of the imager is 84.5 GHz, and the antenna aperture is a 

circle having a diameter of 58 cm. These two parameters uniquely determine the point spread 

function (psf), which, in turn, determines the shape of the antenna’s footprint on the ground. In 

particular, the null-to-null angle of the central and strongest lobe of the footprint for the psf used 

is 0.856 deg. After a single frame is simulated using the scene, its road and growth brightness 

temperature profiles, which already contained variations due to mrtte, were further distorted by 

convolving them with the psf (2). It can be seen from the simulation results that the extent of the 

blurring increases monotonically with the oversampling, osamp (5). In this paper the latter is 

defined as the ratio of the number of “along track,” brightness temperature measurements that 

are made on the ground in some angular interval and the number of null-to-null angles that are 

on the ground in that interval. Therefore, 

 osamp = floor((null-to-null angle)/(pixel angle)), (1) 

where floor( ) indicates that the quantity in parentheses is rounded to the next lowest integer. 

With the null-to-null angle of 0.86 deg and the pixel angle in Table 1b of 0.38 deg equation 1 

yields an osamp of 2. Some simulations with the same pixel angle of 0.38 deg, and with aperture 

diameters of 29 cm and 116 cm were also carried out, which give a twice-as-large osamp of 4 

and a half-as-large osamp of 1, respectively. 

2d. Thermal noise addition 

The thermal noise of the imaging system can be expressed as the minimum resolvable brightness 

temperature due to thermal noise, mrtth. The minimum, “state-of-the-art” value assigned to this 

parameter was 3 K (3). It was also allowed to have the easily-attainable values 5 K, 10 K, or 

15 K. After the brightness temperature profile of a frame, to which terrain variation noise had 

already been added, was distorted by the psf, a Gaussian brightness temperature distribution 

having an average value of 0 and a standard deviation equal to mrtth was added to that distorted 

profile. This resulted in the final form of a simulated, single frame. 
5

3. Frame Integration 

3a. Frame rows and columns 

It is convenient to consider the collection of brightness temperature measurements in a frame, 

which is determined by the FOV of the imager (see section 2a), to be a matrix of numbers. 

Accordingly, in this report the word “row” is used to denote all the pixels in a frame that are at 

some “cross track” location, and the word “column” is used to denote all the pixels in a frame 

that are at some “along track” location. Thus, from Table 1b, the number, Nrows, of rows in a 

frame is 30 and the number, Ncols, of columns in a frame is 63. 

In the integration process of these simulations portions of consecutive single frames are added to 

form two other types of frames: partially integrated frames and dx-column integrated frames. 

The latter two types of frames are then used to form the processed, fully integrated, Ncolscolumn, integrated frame. The method of forming partially integrated and dx-column frames are 

discussed in subsections 3b and 3c, respectively, and the method of forming the fully integrated 

frame is discussed in subsection 3d. 

3b. Partially integrated frame formation 

In this report a partially integrated frame is a frame resulting from consecutive frame integration 

that has fewer columns than Ncols. The partially integrated frame is formed by adding the 

common areas of a particular set of Nframes, consecutive, single frames. This process is 

illustrated in Figure 2 for the case in which Nframes = 20. Since there is a column pixel delay, 

dx, between frames, the number of columns, Com_cols, in the partially integrated frame must be 

Com _ cols = Ncols − (Nframes −1)dx . (2) 

As is expected, Com_cols =Ncols when Nframes = 1. For the case illustrated in Figure 2, i.e. 

Nframes = 20 and dx = 2 , equation 2 yields Com_cols = 25. Figure 2 shows how the partially 

integrated frame is formed by adding columns 39-63 of single frame 1, to columns 37-61 of 

single frame 2, to columns 35-59 of single frame 3, and so on, down to columns 1-25 of frame 

20. The fact that the frame-to-frame column pixel delay, d x= 2 guarantees that each of these 

25-column slices of those single frames that is involved in this integration process contains 

brightness temperature measurements of the same 25-column slice of the sensor’s FOV. 
6

 

 

 

 Columns 1-36 

 Columns 37-61 

 

 

 

 

 

 

 

 

 

 Columns 1-38

 Columns 39-63 

Columns 35-59

 Columns 1-25

 Columns 26-63 

25-column

slices common

to frames 1-20

used for

integration 

“Along track” direction 

2-column delay

Frame 3 

Frame 20

Frame 2 

 

 

 

Columns 1-25 of the

63-column integrated

frame 

Frame 1 

 Columns 1-34

*

*

*

Figure 2. Formation of a 25-column, partially integrated frame by integrating portions of consecutive, single 

 frame numbers 1–20, where “column” refers to brightness temperature pixels at the same “along 

 track” position of the scene. The partially integrated frame results from the averaging of the 20 

 independent brightness temperature values, contained in each of the pixels (“cross track,” “along 

 track” location) of columns 39–63 of the scene. These pixels are in columns 39–63 of single frame 1, 

 columns 37–61 of single frame 2, columns 35–59 of single frame 3, and so on, down to columns 1–25 

 of single frame 20. These 20, 25-column single frame slices are averaged to form columns 1–25 of the 

 63-column, fully integrated from being formed. 
7

The maximum number of consecutive frames, Nframes_maxp, for which such a partially 

integrated frame formation process is possible is that value of Nframes in equation 2 that yields 

Com_cols = 1. Thus,

1 1+ − _ = floor( ) dx

Ncols Nframes maxp . (3) 

In our case, in which Ncols = 63 and dx = 2, equation 3 yields Nframes_maxp = 32. 

3c. dx-column integrated frame formation 

As can be seen from equation 2, the number of columns of the Ncols-column, fully integrated 

frame that remain to be formed after forming the partially integrated frame is (Nframes–1)dx. In 

these simulations each set of dx columns beyond the first Com_cols columns of the Ncolscolumn, fully integrated frame is formed by adding the appropriate dx columns of a different set 

of Nframes frames. We call the result of this process a dx-column integrated frame. Figure 3 

illustrates this procedure for the formation of the first dx(=2)-column integrated frame, which 

will contain the processed columns 26 and 27 of the fully integrated frame. Again, the number of 

frames, Nframes, being integrated is 20, just as it was for the partially integrated frame 

formation illustrated in Figure 2. It is seen in Figure 3 that these two columns are formed by 

adding columns 62 and 63 of frame 2, columns 60 and 61 of frame 3, columns 58 and 59 of 

frame 4, and so on, down to columns 24 and 25 of frame 21. Again, the fact that the frame-toframe column pixel delay dx = 2 guarantees that each of these 2-column frame slices contains 

brightness temperature measurements of the same 2-column slice of the scene. Moreover, from 

Figure 2, it is seen that the last column of frame 2 entering into the formation of the partially 

integrated frame is 61. It is also seen from Figure 3, that the first column of frame 2 entering into 

the formation of the first dx-column frame is 62. It is therefore guaranteed that this first dxcolumn frame has brightness temperature measurements of the two columns of the scene that 

immediately follow the 25 columns of the scene that are processed in the partially integrated 

frame. 

In a similar manner the next two columns, 28 and 29, of the fully integrated frame are formed by 

adding appropriate 2-column slices of frames 3 thru 22. This procedure is repeated until all the 

Nframes(=20) −1 = 19, dx(=2)-column integrated frames that are required are formed. 

The maximum number of consecutive frames, Nframes_maxd, which can enter into the 

formation of a dx-column integrated frame is the maximum number of consecutive frames which 

can contain a common, dx-column, slice of the scene. Clearly this number is 

_ floor( ) dx

Ncols Nframes maxd = . (4) 

In our case, in which Ncols = 63 and dx = 2, equation 4 yields Nframes_maxd = 31. 
8

 

2 –column slices

common to frames 2-21

used for integration 

Columns 1-57 

Frame 4 

 

 

 

 

 

 

 

 

Columns 1-61 

Columns 62-63 

Columns 1-59 

Columns 60-61 

 

 

 

Columns 24-25 

Frame 2 

Frame 3 

2-column delay 

Columns 58-59 

Columns 1-23

Frame 21 

Columns 26 and 27 of

the 63-column,

integrated frame 

“Along track” direction 

*

*

*

Figure 3. Formation of dx(2)-column, integrated frame resulting from integrating 20 frames, where “column” refers 

 to all pixels at the same “along track” position of the scene. This dx-column integrated frame results from 

 the averaging of 20 independent brightness temperature measurements, contained in single frames 2–21, in 

 each of the pixels (“cross track,” “along track” locations) in columns 64 and 65 of the scene. These pixels 

 are in columns 62 and 63 of single frame 2, columns 60 and 61 of single frame 3, columns 58 and 59 of 

 single frame 4, and so on, down to columns 24 and 25 of single frame 21. These 20, 2-column, frame 

 slices are averaged to form columns 26 and 27 of the 63-column, fully integrated frame being formed. 

 Corresponding procedures are carried out to form the fully integrated frame’s columns 28 and 29, 30 and 

 31, 32 and 33, and so on, down to columns 62 and 63. 
9

3d. Formation of the fully integrated frame 

Figure 4 shows how the processed, fully-integrated frame is formed. The first dx(=2)-column 

integrated frame, which contains columns 26 and 27 of the fully integrated frame is concatenated 

to the end of the Com_cols (=25)-column partially integrated frame, which contains columns 1-

25 of the fully integrated frame. Then the second dx(=2)-column integrated frame, which 

contains columns 28 and 29 of the fully integrated frame, is concatenated to the end of the frame 

resulting from the previous concatenation. This concatenation procedure is repeated until all 63 

columns of the fully integrated frame are formed. 

· · ·

1-20 2-21 3-22 4-23 · · · 20-39

1-25 26-27 28-29 30-31 · · · 62-63

39-63 64-65 66-67 68-69 · · · 100-101

Contributing frame

numbers 

Fully integrated frame

columns.

Scene columns imaged. 

One 25-column slice and 19

2-column slices, resulting

from 20-frame integrations, 

that are to be concatenated. 

Fully integrated, 63-column

frame resulting from the

concatenation. 

Figure 4. Concatenation of one, 25-column slice formed by integrating 25-column 

 portions of frames 1–20, where “column” refers to all brightness temperature 

 pixels at the same “along track” position of the scene, (see Figure 2), and 19, 

2-column slices, each formed by integrating 2-column portions of frames 2–21, 

frames 3–22, frames 4–23, and so on, down to frames 20–39 (see Figure 3). 

The result is a fully integrated, 63-column frame. 

It was seen in subsections 2b that the number of single frames required to form the partially 

integrated frame is Nframes, and it was seen in subsection 2c that the number of additional 

single frames required to form all the required dx-column integrated frames is Nframes-1. Thus, 

the total number of single frames, Nfull, that need to be simulated for the formation of a fully 

integrated frame is 

Nfull = 2(Nframes) – 1. (5) 

For Nframes = 20 equation 5 yields Nfull = 39. 
10

Since there is a frame-to-frame delay of dx column pixels, the simulated scene must have at least 

Ncols_scene columns, where 

Ncols_scene = Ncols + (Nfull−1)dx. (6) 

In our case, for which Ncols = 63, Nframes = 20, and dx = 2, equations 5 and 6 yield 

Ncols_scene = 139. This is the number of “along track” brightness temperature measurements 

that need to be made in the scene for each “cross-track” position to fully integrate all the pixels 

in each of the 63 columns of the sensor’s FOV. 

Clearly the maximum value, Nframes_max, that Nframes may have when the column size of 

the frames is Ncols and the frame-to-frame column pixel delay is dx is 

 Nframes_max = smallest(Nframes_maxp, Nframes_maxd), (7) 

where smallest( ) indicates the smallest of the quantities in the parentheses. In our case, for 

which Ncols = 63 and dx=2, equations 3, 4, and 7 yield Nframes_max = 31. 

4. Simulation Steps 

In summary, the steps of the simulation are as follows: 

 1. Given Nrows, Ncols and dx, compute Nframes_maxp from equation 3 and 

Nframes_maxd from equation 4. 

 2. Choose a value of Nframes satisfying 

 1 < Nframes < Nframes_max, (8) 

 where Nframes_max is computed from equation 7. 

 3. Simulate a scene having Nrows rows and at least Ncols_scene columns, where 

Ncols_scene is computed from equations 5 and 6. 

 4. Apply terrain variation noise to the scene, as discussed in Section 2b. 

 5. Form Nfull single frames based on the simulated scene, where Nfull is computed from 

equation 5. 

 6. Distort the brightness temperature profiles of each of the Nfull frames, as discussed in 

section 2c. 

 7. Add thermal noise to each of the Nfull frames, as discussed in section 2d. 

 8. In the manner discussed in section 3b form the partially integrated frame, having Nrows

rows and Com_cols, where the latter is computed from equation 2. 

 9. Form the Nframes − 1, dx-column, integrated frames, as discussed in section 3c. 

 10. As discussed in subsection 3d, concatenate the partially integrated frame and the 

Nframes − 1, dx-column, integrated frames to form the fully integrated frame. 
11

5. Simulation Results 

5a. Frame images and plots 

Sections 3b and 3c described in detail how one com_cols-column, partially integrated frame and 

several dx-column integrated frames, respectively, may be generated from the simulated, single, 

image frames extracted from the scene by adding appropriate portions of some number of sets of 

Nframes consecutive frames. Figure 5 shows frames at three stages in the integration process. 

The road and vegetation growth average brightness temperatures are 270 K and 275 K, 

respectively (∆T = 5 K), the terrain variation, standard deviation, mrtte, is 1K, the thermal noise, 

standard deviation, mrtth, is 10 K, and the psf is that of a PMMW imaging system at 84.5 GHz 

with a 58-cm diameter antenna, for which osamp = 2. Figure 5a shows a simulated, single, image 

frame, to which only terrain variation noise was added. The vegetation growth-to-road contrast 

in Figure 5a is quite good, since mrtte is small compared to ∆T. Figure 5b shows the same frame 

after convolution with the psf was performed and thermal noise was added. The growth-to-road 

contrast in Figure 5b is poor since mrtth is larger than ∆T, making it virtually impossible to 

discern the road from the vegetation growth. Figure 5c shows the processed, fully integrated 

frame arising from a 20-frame integration. It is seen that the integration has greatly improved the 

vegetation growth-to-road contrast over that of Figure 5b, to the extent that now the road and 

vegetation growth are easily distinguishable. 
12

 5a 

 5b 

 5c 

Figure 5. Images of a single and processed frame with a road (center patch) average brightness 

 temperature of 270 K, a growth (upper and lower patches) average brightness temperature 

 and a thermal noise minimum resolvable brightness temperature difference of 10 K. The 

 psf is appropriate for a PMMW imaging system at 84.5 GHz oversampling the scene by 

×2. 5a. A simulated, single frame that has terrain variation noise only. 5b. The simulated, 

 single frame that results from convolving the frame in 5a with the psf and adding thermal 

 noise. 5c. The fully integrated frame arising from the integration of 20 consecutive, single 

 frames, such as the one in 5b, in the manner illustrated in Figures 1–4. 

Figure 6 shows a plot of the brightness temperatures in column 32 vs. row number of column 32 

for the images in Figures 5a(stars), 5b(circles), and 5c(squares). Note the scatter in both 

vegetation growth and road regions for the pixels of the single frame (circles) whose temperature 

profiles had terrain variation and thermal noise added, and on which convolution with psf was 

performed. That scatter is much greater than that of either the pixels of the same frame prior to 

psf distortion and thermal noise addition (stars), or the pixels of the processed, fully integrated 

frame resulting from a 20-frame integration (squares). The very low value and large deviation 

from the average of the brightness temperatures of the pixels of rows 1 and 30 seen both in 

Figure 5c as well as in the fully integrated frame plot (squares) of Figure 6 are edge effects due 

to the abrupt cutoff of brightness temperature where the vegetation growth strips end. 
13

Figure 6. Plots of brightness temperature at “along track” position 32 vs. “cross 

 track” position in a frame having only terrain variation, in a frame having 

 both terrain variation and thermal noise, as well as distortion from the psf 

 and the processed frame arising from the integration of 20 frames. The 

 road average brightness temperature is 270 K, the growth average brightness 

 temperature is 275 K, the terrain variation minimum resolvable brightness 

 temperature difference is 1K, the thermal noise minimum resolvable brightness 

 temperature difference is 10 K, and the psf is appropriate for a PMMW imaging 

 system that oversamples the scene by ×2. The 20-frame integration processes 

 illustrated in Figures 1–4. 

5b. Contrast figure of merit 

In this work the brightness temperature contrast figure of merit was taken to be the contrast-tonoise ratio, cnr, in dB, defined as 

cnr(dB) ≡ (10)log(∆T/σall), (9) 

where ∆T is the vegetation growth-to-road brightness temperature difference, and σall is 

computed either from the simulated, fully integrated frame or by means of the central limit 

theorem. 

In the simulations σall was computed as the weighted average of the standard deviations, σgrowth

and σroad of the brightness temperatures in the vegetation growth and road areas, respectively, of 

the fully integrated frame. Thus σall was computed as σsim, where 
14

σsim = (2/3)σgrowth + (1/3)σroad, (10) 

since there are twice as many vegetation growth pixels as road pixels in a frame. 

In the absence of distortion due to the psf the value of σall can still be computed from the fully 

integrated frame using Equation 10. However σall can also be predicted using the Central Limit 

Theorem (6) (CLT). That theorem states that if x and y are completely independent variables, 

and have distributions with variances, σx

2

 and σy

2

, then the variance, σ2, of the distribution of x

+ y values is 

σ2 = σx

2

 + σy

2

. (11)

Each integrated frame pixel has a temperature deviation from 270 K or from 270 + ∆T due to 

terrain variation noise, characterized by mrtte, and thermal noise characterized by mrtth. Since 

the terrain variation noise and thermal noise are completely independent, from equation 11 the 

variance, σCLT

2

, of the integrated frame can be written as having two independent contributions, 

one from the terrain noise and one from the thermal noise: 

σ σ (mrtte) σ (mrtth) 2

2

2

1

2

CLT = + , (12) 

where (mrtte) 2 σ1 and (mrtth) 2 σ2 are functions of mrtte and mrtth, respectively. But the 

temperature deviation of any fully integrated frame pixel due to the terrain variation noise arises 

from the addition of Nframes pixels, each of which has the same member of a zero-mean, 

brightness temperature distribution whose variance is (mrtte)

2

. Therefore 

2 2

1 σ (mrtte) = (mrtte) . (13) 

On the other hand, the temperature deviation of an integrated frame pixel due to thermal noise 

arises from the addition of Nframes pixels, each of which has a different member of a zeromean, brightness temperature distribution whose variance is (mrtth)

2

. For that situation it can be 

shown (6)that the CLT gives 

Nframes

mrtth mrtth

2

2

2

( ) σ ( ) = . (14) 

Equations (12) thru (14) therefore yield a CLT-based value for σall of σCLT, where 

1 2 2

2

CLT

/

( ) ( ) 



 



 = +

Nframes

mrtth

σ mrtte . (15) 

Figures 7, 8, 9, and 10 compare plots of cnr vs. Nframes, as computed from equation 9 for 

∆T =5 K, mrtte = 1 K, and mrtth=3 K, 5 K, 10K, and 15 K, respectively. The psf is that of a 

sensor frequency of 84.5 GHz and an antenna diameter of 58 cm, for which osamp = 2 when the 

pixel angle is 0.38 deg. For the solid curve in each figure σall in equation 9 was taken to be σCLT

computed according to equation 15; for the circles curve in each figure σall in equation 9 was 

taken to be σsim computed according to equation 10 without distortion from the psf; and for the 

asterisks curve in each figure σall in equation 9 was taken to be σsim computed according to 
15

equation 10 with distortion from a psf . As expected the agreement between the circles and the 

solid curve is excellent. Figures 7, 8, 9, and 10 show that, whether or not distortion is included in 

the simulation, cnr increases monotonically with Nframes. However, unlike the shape of the cnr

data without blurring, which is always concave looking from lower toward higher dB, the cnr

data with blurring starts out concave, but it transitions to convex at Nframes values between 15 

and 20. They also show that for a given value of Nframes the reduction in cnr with distortion 

from its value without distortion is a decreasing function of mrtth. 

Figure 7. Contrast-to-noise ratio vs. number of frames integrated for the fully integrated 

 frame based on the central limit theorem (CLT), and as generated by 

 simulations with blurring by a point spread function for an oversampling of 

×2, and without blurring. The vegetation growth-to-road brightness temperature 

 difference is 5 K, the terrain variation minimum resolvable brightness 

 temperature difference is 1 K, and the thermal noise minimum resolvable 

 brightness temperature difference is 3 K. 
16

Figure 8. Contrast-to-noise ratio vs. number of frames integrated for the fully 

integrated frame based on the central limit theorem (CLT), and as generated 

by simulations with blurring by a point spread function for an oversampling 

of ×2, and without blurring. The vegetation growth-to-road brightness 

temperature difference is 5 K, the terrain variation minimum resolvable 

brightness temperature difference is 1 K, and the thermal noise 

minimum resolvable brightness temperature difference is 5 K. 
17

Figure 9. Contrast-to-noise ratio vs. number of frames integrated for the fully 

 integrated frame based on the central limit theorem (CLT), and as generated 

by simulations with blurring by a point spread function for an oversampling 

of ×2, and without blurring. The vegetation growth-to-road brightness 

temperature difference is 5 K, the terrain variation minimum resolvable 

brightness temperature difference is 1 K, and the thermal noise minimum 

resolvable brightness temperature difference is 10 K. 
18

Figure 10. Contrast-to-noise ratio vs. number of frames integrated for the fully 

integrated frame based on the central limit theorem (CLT), and as 

generated by simulations with blurring by a point spread function for 

an oversampling of ×2, and without blurring. The vegetation growthto-road brightness temperature difference is 5 K, the terrain variation 

minimum resolvable brightness temperature difference is 1 K, and the 

thermal noise minimum resolvable brightness temperature difference 

is 15 K. 

Figure 11 compares plots of cnr vs. Nframes, as computed from equation 9 for ∆T = 5 K, mrtte 

= 1 K, and mrtth = 5 K. For the solid curve σall in equation 9 was taken to be σCLT computed 

according to equation 15; for the circles curve σall in equation 9 was taken to be σsim computed 

according to equation 10 without distortion from a psf; for the squares curve, the asterisks curve, 

and for the plusses curve σall in equation 9 was taken to be σsim computed according to equation 

10 with distortion from a psf for which the sensor frequency is 84.5 GHz and the antenna 

aperture diameter is 116 cm, 58 cm, and 29 cm, respectively, for which osamp = 1, 2, and 4, 

respectively (see equation 1), when the pixel angle of 0.38 deg. It was already seen in Figures 7, 

8, 9, and 10 that there is excellent agreement between cnr values for no blurring calculated using 

σsim and cnr values based on σCLT. Figure 11, however, shows that, at any given value of 

Nframes the cnr data based on σsim increases with decreasing osamp, and it approaches the 

maximum cnr value, which is the one based on σCLT, as osamp approaches 1. The reason this 

occurs may be seen from the definition of osamp in equation 1. As the null-to-null angle of the 

psf approaches the pixel angle from above, so that osamp approaches 1 from above, the psf, as a 

function of angle, in units of the pixel angle, in both the “cross track” and “along track” 

directions, approaches a delta function in both of those arguments. Therefore, since the 

convolution of any function with a delta function has no effect at all on the shape of the function, 

the image in a frame suffers practically no distortion at all when it is convolved with a psf for 
19

osamp =1. The important conclusion from Figure 11 is that increasing Nframes is not the only 

way to increase cnr. It may also be increased from its value for some Nframes and pixel angle 

by increasing the sensor’s antenna aperture at a given frequency, which results in decreasing the 

null-to-null angle, and, therefore, according to equation 1, in decreasing osamp. That method of 

increasing cnr may be the preferred one since it minimizes the computational effort required to 

perform the frame integration. However, at the present time 58 cm is the practical upper limit on 

the diameter of a PMMW sensor that can be accommodated by a low-flying aircraft that is 

suitable for road navigation. 

Figure 11. Brightness temperature contrast-to-noise ratio vs. number of frames 

integrated for the fully integrated frame based on the central limit 

theorem (CLT), and as generated by simulations without blurring 

as well as with blurring by point spread functions for oversamplings 

of ×1 (aperture diameter = 116 cm), ×2 (aperture diameter = 58 cm), 

and ×4 (aperture diameter = 29 cm). The vegetation growth-to-road 

brightness temperature difference is 5 K, the terrain variation minimum 

resolvable brightness temperature difference is 1 K, and the thermal 

noise minimum resolvable brightness temperature difference is 10 K. 

5c. Road distinguishability 

All three images in Figures 12a, 12b, and 12c are for ∆T = 5 K, mrtte =1 K, mrtth =10 K. Just as 

for the data in Figures 5–10, the psf for the data in Figures 12a, 12b, and 12c is that of a sensor 

frequency of 84.5 GHz and a sensor antenna aperture of 58 cm, which gives rise to osamp = 2 

when the pixel angle is 0.86 deg. The values of Nframes in Figures 12a, 12b, and 12c are 8, 20, 

and 29, respectively, which, as is seen in Figure 9, give rise to cnr values of 0 dB, 1 dB, and 

2 dB, respectively. Visually distinguishing the road in Figure 12a would be difficult. Visually

distinguishing it in Figure 12b would be feasible almost over the entire length of the road, and 
20

visually distinguishing it in Figure 12c is definitely feasible along the entire length of the road. 

For a given frequency, antenna diameter, and pixel angle, i.e., a given osamp, the degree of 

visual distinguish ability of the road as a function of the cnr resulting from frame integration was 

the same for all combinations of values of ∆T, mrtte, and mrtth for which simulations were 

carried out. 

Figure 12. Fully integrated frames resulting in brightness temperature contrast-to-noise 

ratios of 0 dB (12a), 1 dB (12b), and 2 dB (12c) for a vegetation growth-to-road 

brightness temperature difference of 5 K, a terrain variation minimum resolvable 

brightness temperature difference of 1 K, and a thermal noise minimum resolvable 

brightness temperature difference of 0 K. 

12a 

12b 

12c 
21

Tables 2a, 2b, 2c, and 2d give, for each set of the values of ∆T, mrtte, and mrtth that were 

studied, the smallest value of Nframes for which cn r≥ 0 dB, the smallest value of Nframes for 

which cnr ≥ 1 dB, and the smallest value of Nframes for which cnr ≥ 2 dB. Table 2a shows that 

for ∆T =1 K, even for values of mrtte and mrtth as small as 0 K and 3 K, respectively, and for 

∆T =2 K, even for those values as small as 0 K and 5 K, respectively, that even after integrating 

31 frames the resulting cnr was less than 0 dB. Noted that 31 is the largest possible number of 

frames, Nframes_max (see equation 7), that can be integrated for a fully integrated frame in this 

case. Only for ∆T =2 K, mrtte = 0 K, and mrtth = 3 K and only after integrating 31 frames is 

cnr ≥ 0 dB. Table 2b shows that, for ∆T=5 K, a cnr ≥ 2 dB can be achieved for all 

combinations of the values of mrtte and mrtth studied, except 1 K and 15 K, respectively, 2 K 

and 10 K, respectively, and 2 K and 15 K, respectively, for which the maximum attainable cnr

was between 1 dB and 2 dB. Tables 2c and 2d show that for ∆T = 10 K and 15 K, respectively, 

cnr ≥ 2 dB is attainable for all values of combinations of the values of mrtte and mrtth studied. 

Table 2a. Minimum required number of frames that must be integrated to achieve specified values of 

 contrast-to-noise ratio (cnr) for vegetation growth-to-road brightness temperature differences of 

 1 K and 2 K.

Vegetation 

growth-toroad 

brightness 

temperature 

difference (K) 

Terrain 

mean 

resolvable 

brightness 

temperature 

(K) 

Thermal 

mean 

resolvable 

brightness 

temperature 

(K) 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 0 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 1 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 2 dB 

1 0,1,2 3,5,10,15 >31 >31 >31 

2 0 3 31 >31 >31 

2 0 5,10,15 >31 >31 >31 

2 1,2 3,5,10,15 >31 >31 >31 
22

Table 2b. Minimum required number of frames that must be integrated to achieve specified values of 

 contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness temperature difference of 5 K.

Vegetation 

growth-toroad 

brightness 

temperature 

difference (K) 

Terrain mean 

resolvable 

brightness 

temperature 

(K) 

Thermal 

mean 

resolvable 

brightness 

temperature 

(K) 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 0 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 1 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 2 dB 

5 0 3 2 3 5 

5 0 5 3 6 21 

5 0 10 8 19 27 

5 0 15 17 26 >31 

5 1 3 2 3 20 

5 1 5 3 7 23 

5 1 10 8 20 29 

5 1 15 17 27 >31 

5 2 3 2 6 27 

5 2 5 3 15 30 

5 2 10 10 25 >31 

5 2 15 21 31 >31 

Table 2c. Minimum required number of frames that must be integrated to achieve specified values of 

 contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness temperature difference of 10 K. 

Vegetation 

growth-toroad 

brightness 

temperature 

difference (K) 

Terrain mean 

resolvable 

brightness 

temperature 

(K) 

Thermal 

mean 

resolvable 

brightness 

temperature 

(K) 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 0 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 1 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 2 dB 

10 0 3 1 1 1 

10 0 5 1 1 2 

10 0 10 2 3 4 

10 0 15 3 5 9 

10 1 3 1 1 1 

10 1 5 1 1 2 

10 1 10 2 3 4 

10 1 15 3 5 9 

10 2 3 1 1 1 

10 2 5 1 1 2 

10 2 10 2 3 5 

10 2 15 3 5 9 
23

Table 2d. Minimum required number of frames that must be integrated to achieve specified values of 

 contrast-to-noise ratio (cnr) for a vegetation growth-to-road brightness temperature difference of 15 K. 

Vegetation 

growth-toroad 

brightness 

temperature 

difference (K) 

Terrain mean 

resolvable 

brightness 

temperature 

(K) 

Thermal 

mean 

resolvable 

brightness 

temperature 

(K) 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 0 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 1 dB 

Minimum 

number of 

frames to 

integrate for 

cnr ≥ 2 dB 

15 0 3 1 1 1 

15 0 5 1 1 1 

15 0 10 1 1 2 

15 0 15 2 2 3 

15 1 3 1 1 1 

15 1 5 1 1 1 

15 1 10 1 1 2 

15 1 15 2 2 3 

15 2 3 2 5 27 

15 2 5 1 1 1 

15 2 10 1 1 2 

15 2 15 2 2 4 

6. Generation of Video Frames 

As discussed in subsections 3b, 3c, and 3d, and as noted in Figure 4, adding the brightness 

temperature values in the pixels of appropriate columns of frame Nos. 1 thru 2(Nframes)–1 

yields a processed image of scene columns Nos. (Nframes−1)dx+1 thru Ncols + 

(Nframes−1)dx. An analysis of the relationship between the portion of the scene from which 

some succeeding group of 2(Nframes)−1 unprocessed frames comes and the portion of the scene 

that is imaged by integrations involving that group of frames yields the following result: Let a 

fully, integrated frame be constructed, in the manner described in sections 3b, 3c, and 3d, from 

the 2(Nframes)−1 consecutive, unprocessed frames Nos. 

(k −1)N +1 thru (k −1)N + 2(Nframes) −1, (16a) 

where k, the fully integrated frame number, can have the values 

 k = 2,3,4..., (16b) 

and,

 ) N = floor(Ncols/dx . (16c) 

Then the scene columns imaged will be Nos. 

(k −1)Ncols + (Nframes −1)dx +1− R thru (k)Ncols + (Nframes −1)dx − R , (17a) 

where R is the integer remainder 
24

 ) R ≡ (Ncols)mod(dx . (17b) 

Equations 16 and 17 show that for consecutives values of k for k ≥ 2 there is always overlap in 

the range of single frame Nos. of the (Nframes)–1 single frames, but there is no overlap in the 

scene columns imaged by integrations of those frames. Table 3 shows that to be the case for our 

example of Ncols=63, Nframes=20, and dx=2 for fully integrated frame numbers 2 or greater. 

It is to be noted that Table 3 lists the scene columns imaged by the first fully integrated frame as 

39 thru 101, consistent with Figure 4, for the values of Ncols, Nframes, and dx being considered. 

Thus, in this case there is a one-column overlap between the columns imaged by fully integrated 

frames 1 and 2. However, if a k of 1 and the values of the other parameters being considered 

here are substituted into equation 17a it gives the range of scene columns imaged by integrated 

frame No. 1 as 38 thru 100, which is incorrect. That is why equation 17a is only correct for k ≥ 

2. It turns out, however, that if Ncols is an integral multiple of dx, then, equation 17a does give 

the correct range of scene columns imaged by the fully integrated frame for all k. In particular, 

the non-overlapping and consecutive ranges yielded by equation 17a for the scene columns 

imaged by the first (k =1) and second (k=2) fully integrated frames are correct. 

Table 3. Range of the frame numbers of the 39, consecutive single frames involved in forming each 

of the first 10, fully integrated frames. The fully integrated frames are formed by integrating portions 

of 20 consecutive, single frames from among those 39 consecutive, single frames. For each 

fully integrated frame number the table also gives the range of the column numbers of the scene 

columns imaged by those fully integrated frames. The number of columns in both the single and 

fully integrated frames is 63, and the frame-to-frame delay in “along track” brightness temperature 

pixels is 2. 

Processed, 

fully 

integrated 

frame No. 

First single 

frame No. 

39th single 

frame No. 

First scene 

column No. 

imaged 

63rd scene column 

No. imaged 

1 1 39 39 101 

2 32 70 101 163 

3 63 101 164 226 

4 94 132 227 289 

5 125 163 290 352 

6 156 194 353 415 

7 187 225 416 478 

8 218 256 479 541 

9 247 287 542 604 

10 280 318 605 667 

As was stated in Section 2b, the unprocessed frame rate upon which the value 2 for the frame-toframe delay in “along track” pixels, dx, is based is 30 Hz. It is important that the actual 

navigating video processing system maintain that rate as closely as possible. Therefore, the 

simulations performed in this work, besides yielding the processed frames themselves, also timed 

the frame integration process. Those timing results imply very high rates, on the order of 150 Hz. 

Thus, maintaining a desired, smaller video rate, such as 30 Hz, with this type of processing 

should be quite feasible. 
25

7. Conclusions 

Simulations were carried out of the generation of passive millimeter-wave (PMMW) digital 

video images of a simple road scene by a PMMW imaging system mounted on a moving aircraft. 

The simulations employed documented measurements of mean millimeter-wave (MMW) 

brightness temperatures and minimum resolvable temperatures for various terrains. The 

resolution spot size, frame rate, and sampling frequency assumed for the simulations are those 

for an 84.5-GHz imaging system under development. Measurements with PMMW imaging 

systems have shown that road and vegetation growth mean brightness temperatures can differ by 

an amount so small as to make it comparable to the minimum resolvable temperature (1,4). A 

single image frame resulting from simulating such a scene was found to have insufficient 

contrast for visually distinguishing the road from the growth. However, processed frames formed 

by integrating some number of consecutive video frames had sufficient contrast to enable one to 

visually distinguish the road from its surroundings and allow for reliable navigation. It was found 

that a cnr value of only 2 dB was necessary to enable completely reliable visual vegetationgrowth-to-road distinction. 

For average vegetation-growth-to-road temperatures differences ∆T = 1 K or 2 K it was not 

possible to attain cnr ≥ 1 dB needed for reliable visual distinction of the vegetation growth and 

the road for any combination of the values of the minimum resolvable temperatures due to 

terrain variations, mrtte, of 0 K, 1 K, or 2 K, and the values of minimum resolvable 

temperatures due to thermal noise, mrtth, 3 K, 5 K, 10 K, or 15 K. However, for an average 

vegetation-growth-to-road temperatures differences ∆T = 5 K, 10 K, or 15 K it was possible to 

attain the cnr ≥ 1 dB for all of the combinations of mttte and mrtth, and cnr ≥ 2 dB for most of 

the combinations of mrtte and mrtth. 

The cnr of processed frames arising from the simulations was found to increase monotonically, 

although not linearly, as a function of the number of frames integrated. The diameter of the 

PMMW imaging system assumed in most of the simulations performed is 58 cm. This is the 

current state-of-the-art maximum diameter for such a system mounted on a low-flying aircraft. It 

was found that if this antenna aperture size could be doubled to 116 cm, the resulting contrast-tonoise ratio for any given number of frames integrated could attain the maximum cnr that is 

predicted by the central limit theorem. In this manner one can reduce the number of frames that 

need to be integrated to attain the cnr required for reliable road navigation, while minimizing the 

computational effort needed for the integration process. 

A number of important effects, such as the dependence of measured terrain brightness 

temperature on depression angle from nadir to zenith, and frame-to-frame registration have not 

been included in these simulations. Nevertheless, the results of these simulations imply that a 

state-of-the-art, PMMW, imaging system employing simple, video frame integration holds out 

the promise of enabling road navigation at modest altitudes and non-ideal atmospheric 

conditions. In addition, results of timing the frame integration steps indicate that desired video 

frame rates can be easily maintained for the processed frames. 
26

References 

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