# IR Composite Image Generation by Wavelength Band Based on Temperature Synthesis Estimated from IR Target Signature and Background Scene

Authors: Tae Wuk Bae; Young Choon Kim; Sang Ho Ahn
Journal: Journal of Sensors
 (2019)

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## Abstract

Infrared (IR) target signatures and background scenes are mainly used for military research purposes such as reconnaissance and detection of enemy targets in modern IR imaging systems like IR search and track (IRST) system. For understanding and analyzing IR signatures and backgrounds in the IR imaging systems, an IR wavelength band (WB) conversion which transforms an arbitrary WB image to another WB is very important in the absence of equipment by WB. In addition, IR image synthesis of targets and backgrounds can provide a great deal of information in the IR target detection field. However, the WB conversion is actually a very challenging research due to lack of information on the absorptivity and transmittance of enormous components of an object or atmosphere. In addition, the radiation and reflectance characteristics of short-wave IR (SWIR)-WB are very different from those of long-wave IR (LWIR)-WB and middle-wave IR (MWIR)-WB. Therefore, the WB conversion in this paper is limited only to IR target signatures and monotonous backgrounds, which is commonly used for military purposes, at a long distance. This paper proposes an IR synthesis method for generating a synthesized IR image of three IR-WBs by synthesizing an IR target signature and a real background scene for an arbitrary IR-WB. In the proposed method, each temperature information is first estimated from an IR target signature and IR background image for an arbitrary IR-WB, and then a synthesized temperature image is generated by combining the respective temperature information estimated from the IR target signature and background scene. Finally, the synthesized temperature image is transformed into an IR radiance image of three IR-WBs. Through the proposed method, various IR synthesis experiments are performed for various IR target signature and background scenes.


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## Body

## 1. Introduction

Due to easy investigation and cost reduction in principle establishment and performance evaluation for functionality of an IR system, the demand for IR simulators is quickly increasing for military purpose research. Recent military IR simulators such as IR countermeasures (IRCM), directed IRCM (DIRCM), and IR reticle seeker are broadly used for evaluation, efficiency, and modification for actual military IR sensor systems [1–8]. The basic materials for analyzing arbitrary IR system are IR target and background images which are transformed as IR signatures with an intensity (gray-level) distribution corresponding to the temperature range of the IR target and background scene. Based on various theories such as heat transfer theory, atmospheric transfer characteristics, and radiation principle under material properties and atmospheric environment, various IR signature modeling methods have been studied [9–13]. And commercial IR signature modeling tools such as OKTAL-SE [14], Vega Prime Sensor [15], and MuSES [14] were developed for predicting IR signatures and simulating virtual reality by IR-WBs. However, those IR signature modeling tools require a number of settings for different substances and atmospheric environments under certain circumstances. And those have many security limitations with high cost. In the researches for the IR signature modeling, Pan et al. [9] and Lu and Wang [10] analyzed the IR radiance and surface temperature for helicopters and airplanes, respectively. And Dulski et al. [11] modeled virtual backgrounds as IR signatures for atmospheric environments such as the sky and the clouds. However, the IR signature modeling for IR targets and backgrounds is very challenging, because backgrounds are generally composed of various substances and have complex absorption, reflection, and scattering characteristics.A typical example among IR simulators for military purposes is the DIRCM system for protecting friendly forces from an IR-guided (or heat-seeking) missiles as shown in Figure1(a). In order to actively cope with detected IR-guided missiles, various IRCMs, based on flare or jammer to protect friendly forces against an attack of enemy missiles, have been developed up to now [17–19]. The flare countermeasure is vulnerable to approach attacks and limited in its amount of loading and continuative launch. The jammer countermeasure is categorized as an omnidirectional and directed method [19]. Since the omnidirectional jammer emits IR source in all directions, it requires big power use and very high accuracy for directly shooting strong jamming signals to a missile seeker. In order to improve the vulnerability of the omnidirectional jammer, the DIRCMs have been researched [20]. Because the directed jammer utilizes high luminance lamps (or laser) for converging the jamming energy upon the missile seeker, it can emit the jamming energy continuatively without wasting. Hence, it can immediately counteract the missile seekers for tracking and attacking flying targets such as aircrafts or helicopters. In order to use the jammer efficiently in the DIRCM, it is necessary to have an IR detection system capable of recognizing missiles or threats. The IR detection system also requires the ability to recognize objects and backgrounds under various IR-WBs. For that reason, the synthesis of an IR target and background by IR-WBs can be used for enhancing the performance of the IR detection system.Figure 1
(a) Synthesis example of laser jamming image and (b) example of missile seeker simulation (A: spin-scan seeker, B: cone-scan seeker, C: rosette seeker, and D: imaging seeker).
(a)
(b)In the case of surface-to-air IR-guided missiles, an airplane and the sky become the target and background scene, respectively, in the missile standpoint. In order to detect a target, the reticle seeker or IR-guided missile [17–19] with a single detector utilizes SWIR- or MWIR-WB while an imaging seeker mainly exploits LWIR-WB [7, 21, 22]. Therefore, the military IR simulations require IR images of the same scene by three IR-WBs and the synthesis technique of an IR target and background scene as shown in Figure 1(b). However, it is not easy to produce IR images of three WBs for the same scene due to lack of equipment. Furthermore, synthesizing IR targets and backgrounds is very challenging because of the differences in their original WB characteristics. Some related studies are as follows. The basic step for those simulations is IR signature modeling for IR target and background. Kim et al. [7] constituted IR models for targets with an internal heat source and generated thermal images produced by the optical system of the reticle seeker and atmospheric turbulence. And Cox et al. [23] modeled an aircraft, a cloud, a background, and a sensor for generating an IR scene. Bae et al. [24] studied an IR-WB conversion technique for military IR sensor simulation. In this study, real targets as well as modeled targets by RadThermIR [25] were used and the mentioned IR-WB conversion technique [24] was applied for the synthesis of IR targets and backgrounds.This paper proposes an IR synthesis method for generating an IR image of three WBs by synthesizing a modeled (or actual) IR target and real IR background image for arbitrary (original) IR-WB. First, the size of an IR target is adjusted to a desired target distance using the distance information between the background image and an image detector. Then, each temperature information is estimated from an IR target and a real IR background for an original IR-WB, and then a synthesized temperature image is generated by combining, respectively, estimated temperature information. The synthesized temperature image is transformed into a radiance image of desired IR-WB. Finally, the IR image of the desired IR-WB is produced from the radiance image.


## 2. Related Works and Assumption

### 2.1. Radiance Estimation from WB and Temperature

For an object with temperatureT and spectral emissivity ε, the radiance for an WB width (λ1~λ2) is given by
(1)LT=∫λ1λ2ελC1λ5expC2/λT−1dλ,where C1=1.191×104Wμm4/cm2sr and C2=1.428×104μmK are the radiation constants [1, 20, 26]. ελ<1 and ελ=1 are for a gray body and a black body, respectively. Since the temperature to radiance function of Equation (1) is not easy to estimate the temperature inversely from the radiance due to the integral operation, it is simplified as follows:
(2)LT≐εC1Δλλc5expC2/λcT−1,where Δλ and λc represent the given WB width and the central wavelength for the WB range. We assume that the emissivity is a constant, namely, the object is a gray body in the WB range. The above simplified formula is easy to estimate the temperature inversely from the radiance. According to the atmosphere transmission characteristics, an IR-WB range is classified into SWIR-WB (1.9~2.9 μm), MWIR-WB (3~5 μm), and LWIR-WB (8~12 μm). The output voltage from an IR detector for spectral transmittances τatm and τdet for an atmosphere and the IR detector is calculated as follows:
(3)Vdet=ApΩLT∫λ1λ2τatmλτdetλSλdλ,where S is the spectral responsivity of the IR detector in the given WB range. And Ω and Ap represent the solid angle of the IR detector from a target and the target area on the IR detector [27]. If τatm, τdet, and S are WB invariants with constants Ap and Ω, the IR detector’s output voltage is proportional to the target radiance, a function of the target temperature. The radiance formula of Equation (1) is a function of the spectral emissivity. However, for a black body or a gray body, the spectral emissivity becomes a constant and then the radiance formula of Equation (1) just becomes a function of temperature. In the case of a 2D imaging detector such as the imaging detector of Figure 1(d), the gray level of an IR image is also proportional to an output voltage of an IR detector. Therefore, the radiance of specific WB for an object temperature can be regarded as proportional to a gray level of an IR image.


### 2.2. Assumption of Transmittance and Emissivity

Many materials have different transmissivity, emissivity, and reflectivity properties according to the IR-WB. Among atmospheric gases, in particular, water vapor and carbon dioxide have specific emission and absorption characteristics according to the IR-WB. The LWIR-WB and MWIR-WB detect the thermal radiation emitted from a material itself, while the SWIR-WB uses active SWIR reflectivity of a material. Because of this reason, the IR-WB conversion is a very demanding research field. In this paper, the IR-WB conversion is limited to the conversion from LWIR-WB to MWIR-WB and SWIR-WB, and the IR image synthesis is performed on military targets composed of metals (e.g., tank, ship, helicopter, and airplane) and monotonous far-field backgrounds (e.g., sky, ground, and sea) that are frequently used in IRCM or IRST. Also, to reduce the complexity of our experiment, some assumptions about object emissivity and atmospheric transmissivity by the IR-WB are described as follows.First, our experiments have limitations in the WB conversion related to emissivity of a target that varies with the IR-WB. In fact, many materials are not a gray body with emissivity independent of the IR-WB. In a modern military IR imaging system such as IRST or IRCM, the criterion for dividing the target with a background is metal or nonmetal. The metal emissivity decreases rapidly with increasing IR-wavelength. The metal emissivity sharply decreases from about 75% to 25% in the SWIR-WB, then slowly decreases from about 20% to 10% for the MWIR-WB to LWIR-WB. On the contrary, the nonmetal emissivity is about 30%, 50~85%, and 90% for the SWIR-WB, MWIR-WB, and LWIR-WB. It can be seen that the emissivity of the metal and nonmetal is much higher in the MWIR- and LWIR-WB compared to the SWIR-WB. So assuming that the target and background are gray body or black body, the WB conversion between the LWIR-WB and MWIR-WB may be more reasonable compared to the WB conversion between the LWIR-WB and SWIR-WB.Second, our experiments have some WB conversion constraints related to transmittance of water vapor and carbon dioxide which greatly affects atmospheric transmittance. The IR-WB is affected by the concentration of water vapor and carbon dioxide. The concentration of these two materials is, respectively, about3×10-4 ppm for carbon dioxide and 0 to 8×10-3 ppm for water vapor from troposphere to ground (about 11 km or less). Because IR images used in an IRST or IRCM simulator are usually taken for distances less than 10 km from the viewing position, it can be assumed that the concentration of these two materials is constant. The transmittance of atmospheric gases including water vapor and carbon dioxide is nearly closed to 1 in the MWIR-WB and LWIR-WB, whereas it is uneven in the SWIR-WB. So assuming that the atmospheric transmissivity of Equation (3) is uniform, the WB conversion between the LWIR-WB and MWIR-WB may be more reasonable compared to the WB conversion between the LWIR-WB and SWIR-WB, similar to the relation between emissivity and WB conversion described above.


## 2.1. Radiance Estimation from WB and Temperature

For an object with temperatureT and spectral emissivity ε, the radiance for an WB width (λ1~λ2) is given by
(1)LT=∫λ1λ2ελC1λ5expC2/λT−1dλ,where C1=1.191×104Wμm4/cm2sr and C2=1.428×104μmK are the radiation constants [1, 20, 26]. ελ<1 and ελ=1 are for a gray body and a black body, respectively. Since the temperature to radiance function of Equation (1) is not easy to estimate the temperature inversely from the radiance due to the integral operation, it is simplified as follows:
(2)LT≐εC1Δλλc5expC2/λcT−1,where Δλ and λc represent the given WB width and the central wavelength for the WB range. We assume that the emissivity is a constant, namely, the object is a gray body in the WB range. The above simplified formula is easy to estimate the temperature inversely from the radiance. According to the atmosphere transmission characteristics, an IR-WB range is classified into SWIR-WB (1.9~2.9 μm), MWIR-WB (3~5 μm), and LWIR-WB (8~12 μm). The output voltage from an IR detector for spectral transmittances τatm and τdet for an atmosphere and the IR detector is calculated as follows:
(3)Vdet=ApΩLT∫λ1λ2τatmλτdetλSλdλ,where S is the spectral responsivity of the IR detector in the given WB range. And Ω and Ap represent the solid angle of the IR detector from a target and the target area on the IR detector [27]. If τatm, τdet, and S are WB invariants with constants Ap and Ω, the IR detector’s output voltage is proportional to the target radiance, a function of the target temperature. The radiance formula of Equation (1) is a function of the spectral emissivity. However, for a black body or a gray body, the spectral emissivity becomes a constant and then the radiance formula of Equation (1) just becomes a function of temperature. In the case of a 2D imaging detector such as the imaging detector of Figure 1(d), the gray level of an IR image is also proportional to an output voltage of an IR detector. Therefore, the radiance of specific WB for an object temperature can be regarded as proportional to a gray level of an IR image.


## 2.2. Assumption of Transmittance and Emissivity

Many materials have different transmissivity, emissivity, and reflectivity properties according to the IR-WB. Among atmospheric gases, in particular, water vapor and carbon dioxide have specific emission and absorption characteristics according to the IR-WB. The LWIR-WB and MWIR-WB detect the thermal radiation emitted from a material itself, while the SWIR-WB uses active SWIR reflectivity of a material. Because of this reason, the IR-WB conversion is a very demanding research field. In this paper, the IR-WB conversion is limited to the conversion from LWIR-WB to MWIR-WB and SWIR-WB, and the IR image synthesis is performed on military targets composed of metals (e.g., tank, ship, helicopter, and airplane) and monotonous far-field backgrounds (e.g., sky, ground, and sea) that are frequently used in IRCM or IRST. Also, to reduce the complexity of our experiment, some assumptions about object emissivity and atmospheric transmissivity by the IR-WB are described as follows.First, our experiments have limitations in the WB conversion related to emissivity of a target that varies with the IR-WB. In fact, many materials are not a gray body with emissivity independent of the IR-WB. In a modern military IR imaging system such as IRST or IRCM, the criterion for dividing the target with a background is metal or nonmetal. The metal emissivity decreases rapidly with increasing IR-wavelength. The metal emissivity sharply decreases from about 75% to 25% in the SWIR-WB, then slowly decreases from about 20% to 10% for the MWIR-WB to LWIR-WB. On the contrary, the nonmetal emissivity is about 30%, 50~85%, and 90% for the SWIR-WB, MWIR-WB, and LWIR-WB. It can be seen that the emissivity of the metal and nonmetal is much higher in the MWIR- and LWIR-WB compared to the SWIR-WB. So assuming that the target and background are gray body or black body, the WB conversion between the LWIR-WB and MWIR-WB may be more reasonable compared to the WB conversion between the LWIR-WB and SWIR-WB.Second, our experiments have some WB conversion constraints related to transmittance of water vapor and carbon dioxide which greatly affects atmospheric transmittance. The IR-WB is affected by the concentration of water vapor and carbon dioxide. The concentration of these two materials is, respectively, about3×10-4 ppm for carbon dioxide and 0 to 8×10-3 ppm for water vapor from troposphere to ground (about 11 km or less). Because IR images used in an IRST or IRCM simulator are usually taken for distances less than 10 km from the viewing position, it can be assumed that the concentration of these two materials is constant. The transmittance of atmospheric gases including water vapor and carbon dioxide is nearly closed to 1 in the MWIR-WB and LWIR-WB, whereas it is uneven in the SWIR-WB. So assuming that the atmospheric transmissivity of Equation (3) is uniform, the WB conversion between the LWIR-WB and MWIR-WB may be more reasonable compared to the WB conversion between the LWIR-WB and SWIR-WB, similar to the relation between emissivity and WB conversion described above.


## 3. Proposed IR Composite Image Generation Method Using Temperature Synthesis

This paper proposes an IR composite image generation method for creating an (synthesized) IR image of three WBs (LWIR, MWIR, and SWIR) by synthesizing a modeled (or actual) IR target image and an IR background image of an arbitrary IR-WB as shown in Figure2. For a given IR target image and IR background image of certain WB, min and max temperatures are assigned to min and max gray levels. Also, the radiance intensities corresponding to the min and max gray level are obtained using Equation (2). The radiance intensities corresponding to the gray levels between the min and max gray levels can be obtained based on the proportional relationship of the radiance intensity and gray level, and then temperatures corresponding to the obtained radiance intensities for the gray levels between min and max gray levels are estimated using Equation (6). Then, the approximately estimated temperature is compensated by using the slope information of original temperature-radiance curve and the approximated one. Compensated temperature images estimated from the IR target image and the IR background image are synthesized together. Additionally, in order to synthesize the IR target temperature image in the IR background temperature image, the IR target size may be adjusted in consideration of a desired target distance between the IR background and an image detector [5]. The synthesized temperature image is converted into a radiance image using Equation (2); then the synthesized IR image is finally generated by the radiance to gray-level transfer function.Figure 2
Block diagram of the proposed IR synthesis image generation method.


### 3.1. Size Settings of IR Target

First, the size of a modeled (actual) IR target to be synthesized in an IR background image should be set according to an actual target distanceD between the target and an image detector. When the horizontal and vertical fields of view (FOV) of the image detector are given in the relationship between the target position and the visibility width for the FOV of the image detector, FOVh and FOVv from the target distance can be calculated as follows:
(4)FOVh=θ=tan−1Wb_hD,FOVv=θ=tan−1Wb_vD,where Wb_h and Wb_v mean the horizontal and vertical background visibility width in the actual background environment. In the case of the visibility width of the background image, Wb_h′ and Wb_v′ at a target distance D′, the actual target size is constant; however, the target on the obtained background image is largely shown comparatively. For the obtained background image size Xb×Yb, the background visibility is Wb_h×Wb_v. Therefore, if the actual target size Wt_h×Wt_v is known, the target size Xt and Yt on an image is given as follows:
(5)Xt=XbWt_hWb_h,Yt=YbWt_vWb_v.


### 3.2. Temperature Estimation from Radiance Intensity

When there is radiance intensity information per pixel for an IR target image and background image, the temperature corresponding to the radiance of individual pixels can be estimated using the inverse function of Equation (2). So the relation formula for calculating temperature T from radiance L can be derived as follows:
(6)TL≐C2λclnεC1ΔλLλc5+1−1.Since the IR-WB transformation method using a temperature of an object uses Equation (2) approximating Equation (1) including the integral operator, it is easy to estimate the temperature from the radiance through Equation (2), but the approximately estimated temperature contains some error due to the simplification of the equation. Figure 3(a) shows the original radiance obtained by Equation (1) and approximately estimated one calculated by Equation (2) in 200 K~600 K temperature range for three IR-WBs. Figure 3(b) shows the error of approximately estimated temperature from the original temperature for three IR-WBs. The temperature estimation error means the difference between the original temperature and the approximately estimated one. We can know that the radiance intensity for the temperature and the temperature estimation error have different characteristics for each WB.Figure 3
(a) Original radiance and approximately estimated one and (b) error of approximately estimated temperature from original temperature for three IR-WBs.
(a)
(b)Figure4 shows the original radiance curve L∗T and approximately estimated one LT according to arbitrary temperature. T^ represents the estimated temperature obtained from the radiance LT^ using Equation (6). The compensated temperature T~ obtained using only the first order tangent slope of L∗T^ for T^ is as follows:
(7)T~=T^−2⋅ΔT⋅eT^⋅L∗T^+ΔT−L∗T^−ΔT−1,where eT^=L∗T^−LT^. And L∗T^ is the original radiance for the approximately estimated temperature, and ΔT represents the microtemperature displacement value to obtain the tangential slope at the A point in the figure.Figure 4
The original radiance curve and approximately estimated one according to arbitrary temperature.


### 3.3. Relationship of Radiance and Gray Level according to Temperature

Figure5(a) shows the meshing result for the Agusta helicopter model made by RadThermIR. Figure 5(b) shows the transformation relation between radiance and gray level according to the target temperature. In case the object is a gray-body (i.e., emissivity is constant), the function shape of the radiance intensity is similar with that of a black body; however, the height of the function is inversely proportional to the object emissivity. Figure 5(b) shows an example that the pixel with the max gray level Gmax corresponds to the window with max temperature Tmax (ε=0.8) and the pixel with the min gray level Gmin represents the interval engine with min temperature Tmin (ε=0.6) in the acquired IR image.Figure 5
(a) Modeled Agusta helicopter and (b) relation of radiance and gray level according to object temperature.
(a)
(b)The gray-level transfer functionGL using the radiance can be calculated as follows:
(8)GL=aL−LTmin+Gmin,where a (=Gmax−Gmin/LTmax−LTmin) is the slope of the transfer function. The radiances, LTmin and LTmax for the temperatures, Tmin and Tmax corresponding to the min and max gray level, Gmin and Gmax are obtained by Equation (2). Using Equation (8), the radiance LG from the gray level G can be inversely calculated by
(9)LG=G−Gmina+LTmin.This mentioned radiance estimation method using temperature and gray level assumes that the temperature and emissivity of objects corresponding to at least two pixels in an IR image are known. Larger pixel values and temperature differences for the two pixels ensure better radiance estimates.


### 3.4. Proposed IR Synthesis Image Generation Method Based on Temperature Synthesis

In this step, it is assumed that an IR target image size to be synthesized in an IR background image was adjusted according to a target distance as mentioned in Section3.1. The total procedure of the proposed IR synthesis image generation method using temperature synthesis is as follows.


#### 3.4.1. Step I: Min and Max Temperature Assignment to Min and Max Gray Level for IR Target and Background

In an original IR target (or background) image of arbitrary IR-WB to be converted, when assuming that min and max temperaturesTt.min and Tt.max (or Tb.min and Tb.max for the background image) are assigned to min and max gray levels Gt.min and Gt.max (or Gb.min and Gb.max for the background image), the radiance intensities LTt.min and LTt.max (or LTb.minand LTb.max for the background image) corresponding to the gray levels or the temperatures are calculated through Equation (2).


#### 3.4.2. Step II: Temperature Assignment to All Remaining Pixels for IR Target and Background

The target (or background) radiance intensityLGt (or LGb) for gray level Gt (or Gb) of all remaining pixels in the IR target (or background) is obtained using Equation (9). And the approximately estimated target (or background) temperature T^t (or T^b) corresponding to the obtained radiance intensity is calculated through Equation (6); then the compensated target (or background) temperature T~t (or T~b) is calculated through Equation (7).


#### 3.4.3. Step III: Synthesized Temperature Image with Target Embedded in Background Image

As the compensated target temperature imageT~t is synthesized at a desired location in the compensated background temperature image T~b with the desired size, the synthesized temperature image T~s with the target embedded in the background is created. The subscript s means the synthesis of the IR target and background. This step assumes that the target image was scaled as introduced in Section 3.1.


#### 3.4.4. Step IV: Radiance Intensity of Desired IR-WB for Synthesized Temperature

For the synthesized temperature imageT~s composed of the IR target and background, the radiance intensity Ls of the desired IR-WB is calculated using Equation (2) with the emissivity. ε=0.9 is experimentally used based on the assumption in Section. 2.2.


#### 3.4.5. Step V: Generation of Desired IR-WB Image for Radiance Intensity

Finally, the desired IR-WB image is generated by the radiance-to-gray-level transfer functionGLs using the radiance intensity Ls of the desired IR-WB obtained in the step III for the synthesized temperature image. The radiance-to-gray-level transfer function is given by
(10)GLs=α255Ls−Ls.minLs.max−Ls.min+β,0≤GLs≤255,where α0<α≤1 and β mean the contrast and brightness controlling constant. For α=1 and β=0, the gray level of the desired IR-WB image is distributed at 0~255.


## 3.1. Size Settings of IR Target

First, the size of a modeled (actual) IR target to be synthesized in an IR background image should be set according to an actual target distanceD between the target and an image detector. When the horizontal and vertical fields of view (FOV) of the image detector are given in the relationship between the target position and the visibility width for the FOV of the image detector, FOVh and FOVv from the target distance can be calculated as follows:
(4)FOVh=θ=tan−1Wb_hD,FOVv=θ=tan−1Wb_vD,where Wb_h and Wb_v mean the horizontal and vertical background visibility width in the actual background environment. In the case of the visibility width of the background image, Wb_h′ and Wb_v′ at a target distance D′, the actual target size is constant; however, the target on the obtained background image is largely shown comparatively. For the obtained background image size Xb×Yb, the background visibility is Wb_h×Wb_v. Therefore, if the actual target size Wt_h×Wt_v is known, the target size Xt and Yt on an image is given as follows:
(5)Xt=XbWt_hWb_h,Yt=YbWt_vWb_v.


## 3.2. Temperature Estimation from Radiance Intensity

When there is radiance intensity information per pixel for an IR target image and background image, the temperature corresponding to the radiance of individual pixels can be estimated using the inverse function of Equation (2). So the relation formula for calculating temperature T from radiance L can be derived as follows:
(6)TL≐C2λclnεC1ΔλLλc5+1−1.Since the IR-WB transformation method using a temperature of an object uses Equation (2) approximating Equation (1) including the integral operator, it is easy to estimate the temperature from the radiance through Equation (2), but the approximately estimated temperature contains some error due to the simplification of the equation. Figure 3(a) shows the original radiance obtained by Equation (1) and approximately estimated one calculated by Equation (2) in 200 K~600 K temperature range for three IR-WBs. Figure 3(b) shows the error of approximately estimated temperature from the original temperature for three IR-WBs. The temperature estimation error means the difference between the original temperature and the approximately estimated one. We can know that the radiance intensity for the temperature and the temperature estimation error have different characteristics for each WB.Figure 3
(a) Original radiance and approximately estimated one and (b) error of approximately estimated temperature from original temperature for three IR-WBs.
(a)
(b)Figure4 shows the original radiance curve L∗T and approximately estimated one LT according to arbitrary temperature. T^ represents the estimated temperature obtained from the radiance LT^ using Equation (6). The compensated temperature T~ obtained using only the first order tangent slope of L∗T^ for T^ is as follows:
(7)T~=T^−2⋅ΔT⋅eT^⋅L∗T^+ΔT−L∗T^−ΔT−1,where eT^=L∗T^−LT^. And L∗T^ is the original radiance for the approximately estimated temperature, and ΔT represents the microtemperature displacement value to obtain the tangential slope at the A point in the figure.Figure 4
The original radiance curve and approximately estimated one according to arbitrary temperature.


## 3.3. Relationship of Radiance and Gray Level according to Temperature

Figure5(a) shows the meshing result for the Agusta helicopter model made by RadThermIR. Figure 5(b) shows the transformation relation between radiance and gray level according to the target temperature. In case the object is a gray-body (i.e., emissivity is constant), the function shape of the radiance intensity is similar with that of a black body; however, the height of the function is inversely proportional to the object emissivity. Figure 5(b) shows an example that the pixel with the max gray level Gmax corresponds to the window with max temperature Tmax (ε=0.8) and the pixel with the min gray level Gmin represents the interval engine with min temperature Tmin (ε=0.6) in the acquired IR image.Figure 5
(a) Modeled Agusta helicopter and (b) relation of radiance and gray level according to object temperature.
(a)
(b)The gray-level transfer functionGL using the radiance can be calculated as follows:
(8)GL=aL−LTmin+Gmin,where a (=Gmax−Gmin/LTmax−LTmin) is the slope of the transfer function. The radiances, LTmin and LTmax for the temperatures, Tmin and Tmax corresponding to the min and max gray level, Gmin and Gmax are obtained by Equation (2). Using Equation (8), the radiance LG from the gray level G can be inversely calculated by
(9)LG=G−Gmina+LTmin.This mentioned radiance estimation method using temperature and gray level assumes that the temperature and emissivity of objects corresponding to at least two pixels in an IR image are known. Larger pixel values and temperature differences for the two pixels ensure better radiance estimates.


## 3.4. Proposed IR Synthesis Image Generation Method Based on Temperature Synthesis

In this step, it is assumed that an IR target image size to be synthesized in an IR background image was adjusted according to a target distance as mentioned in Section3.1. The total procedure of the proposed IR synthesis image generation method using temperature synthesis is as follows.


### 3.4.1. Step I: Min and Max Temperature Assignment to Min and Max Gray Level for IR Target and Background

In an original IR target (or background) image of arbitrary IR-WB to be converted, when assuming that min and max temperaturesTt.min and Tt.max (or Tb.min and Tb.max for the background image) are assigned to min and max gray levels Gt.min and Gt.max (or Gb.min and Gb.max for the background image), the radiance intensities LTt.min and LTt.max (or LTb.minand LTb.max for the background image) corresponding to the gray levels or the temperatures are calculated through Equation (2).


### 3.4.2. Step II: Temperature Assignment to All Remaining Pixels for IR Target and Background

The target (or background) radiance intensityLGt (or LGb) for gray level Gt (or Gb) of all remaining pixels in the IR target (or background) is obtained using Equation (9). And the approximately estimated target (or background) temperature T^t (or T^b) corresponding to the obtained radiance intensity is calculated through Equation (6); then the compensated target (or background) temperature T~t (or T~b) is calculated through Equation (7).


### 3.4.3. Step III: Synthesized Temperature Image with Target Embedded in Background Image

As the compensated target temperature imageT~t is synthesized at a desired location in the compensated background temperature image T~b with the desired size, the synthesized temperature image T~s with the target embedded in the background is created. The subscript s means the synthesis of the IR target and background. This step assumes that the target image was scaled as introduced in Section 3.1.


### 3.4.4. Step IV: Radiance Intensity of Desired IR-WB for Synthesized Temperature

For the synthesized temperature imageT~s composed of the IR target and background, the radiance intensity Ls of the desired IR-WB is calculated using Equation (2) with the emissivity. ε=0.9 is experimentally used based on the assumption in Section. 2.2.


### 3.4.5. Step V: Generation of Desired IR-WB Image for Radiance Intensity

Finally, the desired IR-WB image is generated by the radiance-to-gray-level transfer functionGLs using the radiance intensity Ls of the desired IR-WB obtained in the step III for the synthesized temperature image. The radiance-to-gray-level transfer function is given by
(10)GLs=α255Ls−Ls.minLs.max−Ls.min+β,0≤GLs≤255,where α0<α≤1 and β mean the contrast and brightness controlling constant. For α=1 and β=0, the gray level of the desired IR-WB image is distributed at 0~255.


## 3.4.1. Step I: Min and Max Temperature Assignment to Min and Max Gray Level for IR Target and Background

In an original IR target (or background) image of arbitrary IR-WB to be converted, when assuming that min and max temperaturesTt.min and Tt.max (or Tb.min and Tb.max for the background image) are assigned to min and max gray levels Gt.min and Gt.max (or Gb.min and Gb.max for the background image), the radiance intensities LTt.min and LTt.max (or LTb.minand LTb.max for the background image) corresponding to the gray levels or the temperatures are calculated through Equation (2).


## 3.4.2. Step II: Temperature Assignment to All Remaining Pixels for IR Target and Background

The target (or background) radiance intensityLGt (or LGb) for gray level Gt (or Gb) of all remaining pixels in the IR target (or background) is obtained using Equation (9). And the approximately estimated target (or background) temperature T^t (or T^b) corresponding to the obtained radiance intensity is calculated through Equation (6); then the compensated target (or background) temperature T~t (or T~b) is calculated through Equation (7).


## 3.4.3. Step III: Synthesized Temperature Image with Target Embedded in Background Image

As the compensated target temperature imageT~t is synthesized at a desired location in the compensated background temperature image T~b with the desired size, the synthesized temperature image T~s with the target embedded in the background is created. The subscript s means the synthesis of the IR target and background. This step assumes that the target image was scaled as introduced in Section 3.1.


## 3.4.4. Step IV: Radiance Intensity of Desired IR-WB for Synthesized Temperature

For the synthesized temperature imageT~s composed of the IR target and background, the radiance intensity Ls of the desired IR-WB is calculated using Equation (2) with the emissivity. ε=0.9 is experimentally used based on the assumption in Section. 2.2.


## 3.4.5. Step V: Generation of Desired IR-WB Image for Radiance Intensity

Finally, the desired IR-WB image is generated by the radiance-to-gray-level transfer functionGLs using the radiance intensity Ls of the desired IR-WB obtained in the step III for the synthesized temperature image. The radiance-to-gray-level transfer function is given by
(10)GLs=α255Ls−Ls.minLs.max−Ls.min+β,0≤GLs≤255,where α0<α≤1 and β mean the contrast and brightness controlling constant. For α=1 and β=0, the gray level of the desired IR-WB image is distributed at 0~255.


## 4. Results and Discussion

### 4.1. Verification of Temperature Estimation

Figure6 shows the approximately estimated temperature T^, the compensated temperature T~, and their temperature error with the original temperature T∗ (given by Equation (1)) for the three IR-WBs. The temperature error represents the difference between the original temperature and the approximately estimated one or the compensated one. The errors of the approximately estimated temperature and the compensated one are given by e^T=T^−T∗ and e~T=T~−T∗, respectively. In the LWIR-WB of Figures 6(a) and 6(d), the sign of the approximately estimated temperature error changes from negative to positive at 410 K, and the compensated temperature error decreases significantly over all temperature ranges. In the MWIR-WB of Figures 6(b) and 6(e), the sign of the approximately estimated temperature error changes from positive to negative at 420 K, and it can be seen that after temperature compensation, the error is greatly reduced, similar to LWIR-WB. In the SWIR-WB of Figures 6(c) and 6(f), the approximately estimated temperature is higher than the compensated temperature from 300 K to 500 K. The errors for these two temperatures decreased with increasing temperature. And the error of the compensated temperature decreased significantly than that of the approximately estimated temperature. And the compensated temperature also caused an error of 4.5 K at 300 K.Figure 6
Approximately estimated temperature and compensated one for (a) LWIR-WB, (b) MWIR-WB, and (c) SWIR-WB; temperature error for (d) LWIR-WB, (e) MWIR-WB, and (f) SWIR-WB in 300 K~500 K.
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(f)Figure7 shows the comparison of the gray levels calculated from the approximately estimated temperature and the compensated temperature. The integral gray level, the approximately estimated gray level, and the compensated gray level represent the gray level obtained by the original temperature, the approximately estimated temperature, and the compensated temperature, respectively. The figure shows the differences of the integral gray level and the approximately estimated gray level and the compensated gray level in LWIR-WB-to-MWIR-WB and LWIR-WB-to-SWIR-WB conversion. The difference sums for the approximately estimated gray level are, respectively, 699 and 1041 in the level in the converted MWIR-WB and SWIR-WB. On the other hand, the difference sums for the compensated gray level are, respectively, 11 and 14 in the level in the converted MWIR-WB and SWIR-WB. We can know that the compensated temperature produces less gray-level difference than the approximately estimated temperature.Figure 7
Differences of integral gray level and (a) approximately estimated gray level and (b) compensated gray level in LWIR-WB-to-MWIR-WB conversion; differences of integral gray level and (c) approximately estimated gray level and (d) compensated gray level in LWIR-WB-to-SWIR-WB conversion for temperature range of 200 K~600 K and gray level of 0~255.
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(d)The IR-WB conversion simulations using the compensated temperature were performed. The IR images (SCENE1 and SCENE2) used in the simulation were acquired by TAU640, a LWIR camera of FLIR Corp., as shown in Figure8(a). In the test images, the ground structure has the brightest gray level (pixel value of 255). On the other hand, the sky background region has the lowest gray level (pixel value of 0). These temperatures measured using an IR thermometer were 320 K and 270 K, respectively. Figures 8(b) and 8(c) show the pseudocolor images of the approximately estimated temperatures and the compensated temperature extracted from the test LWIR images. In the LWIR-WB of Figure 6(a), it can be seen that the approximately estimated temperature is lower than the compensated temperature bellow 400 K so approximately estimated temperature is bluer than the compensated temperature in the pseudocolor as shown in the black box of the figure. As shown in the white box in the figure, the compensated temperature below 400 K rises above the approximately estimated temperature and becomes redder. Figures 8(d) and 8(e) show the WB-converted MWIR and SWIR images using the compensated temperatures.Figure 8
(a) Original LWIR image, pseudocolor image of (b) approximately estimated temperature and (c) compensated temperature, (d) converted MWIR image, and (e) converted SWIR image for SCENE1 and SCENE2.The IR-WB conversion is mainly performed from LWIR-WB to MWIR-WB or SWIR-WB. The LWIR-image is used more widely than other WB images, and its gray-level distribution according to temperature is relatively linear than those of other IR-WBs. On the other hand, SWIR image has little brightness change in the low temperature region because the radiance is very small in that region. This means that the IR-WB conversion using SWIR-WB may not be effective. Also, as shown in Figure6(e), because the compensated temperature for MWIR-WB has a very small error only below 350 K, the IR-WB conversion using the MWIR-image is more reasonable than that using the SWIR-image.


### 4.2. Preparation of IR Target and Background Images for Image Synthesis

For the verification of the proposed IR composite image method, we used modeled or actual LWIR target images consisting of three groups of IR target images (sky targets, ground targets, and sea targets) as shown in Figure9. The LWIR images for the modeled targets (mF16, mAgusta-helicopter, mTANK, mSHIP1, and mSHIP2) were produced from the respective 3D CAD models by RadThermIR [25] and MuSES [16], IR signature modeling tools of TAI corporation. The targets composed of mesh (or lattice) were modeled, and the radiance per each lattice was calculated through thermal analysis of the modeling tool. Then the LWIR target images were created as shown in the figure. We also used the actual LWIR target images (F35, BOEING, TANK1, TANK2, SHIP1, and SHIP2) actually photographed by thermal equipment. Similar to the LWIR target images, the actual LWIR background images are composed of three groups: sky backgrounds (SKY1 with high contrast and SKY2 and SKY3 with low contrast), ground backgrounds (GROUND1, GROUND2 with low contrast), and sea backgrounds (SEA1, SEA2 with high contrast). The FOVs of these IR background images were 10°×8° for the sky and sea backgrounds and 5°×3.3° for the ground backgrounds. If it is assumed that all objects in the prepared target and background images are the gray body, the temperature information of the target images and the background images can be, respectively, estimated by the proposed procedure. After generating one temperature synthesis image synthesizing a target temperature image and a background temperature image, an IR synthesis image of desired IR-WB is generated.Figure 9
Modeled and actual targets and background images for sky, ground, and sea.


### 4.3. Synthesis Experiments for IR Target and Background

Figures10 and 11 show the resulting images from synthesizing the modeled sky targets (mF16 and mAgusta-helicopter) and the real sky background images (SKY1, SKY2, and SKY3) for the three IR-WBs. For a variety of temperature distributions, FOVs, and target distances, various IR synthesis images were created for the three WBs based on the compensated temperature and the compensation of the approximately estimated temperature. In the temperature extraction from the modeled targets and the LWIR background images, it can be seen that the compensated temperature rises slightly higher than the approximately estimated temperature in the pseudocolor. The MWIR and SWIR images were, respectively, transformed using the synthesized temperature images estimated from the LWIR images of the modeled targets and the real sky background images. In the conversion of high-WB to low-WB for the mF16 and mAgusta-helicopter model, the body region in the low temperature region became darker due to reduction of radiance intensity, while the engine region in the high temperature region became brighter by the increase of radiance intensity. In the conversion of high-WB to low-WB for the sky background images, the high temperature regions are highlighted by radiance intensity increased by the conversion function, for example, the structures near the road in SKY1, the small structures on the mountain in SKY2, and the partial cloud regions above in SKY3. On the other hand, lower temperature regions are darkened due to the decrease in radiance intensity, for example, the upper cloud region and low hill region in SKY1, the upper cloud region in SKY2, and the lower cloud region in SKY3.Figure 10
Resulting images from synthesizing modeled sky target (mF16) and sky background images for three IR-WBs.Figure 11
Resulting images from synthesizing modeled sky target (mAgusta-helicopter) and sky background images for three IR-WBs.Figure12 shows the resulting images from synthesizing the modeled ground target (mTANK) and the modeled sea targets (mSHIP1 and mSHIP2) with the ground backgrounds (GROUND1 and GROUND2) and the real sea backgrounds (SEA1 and SEA2) for three IR-WBs. Similar to the conversion for the modeled sky targets, the body region of the modeled tank and ship, which have low temperature, is darkened on the whole, while the moving rotational axis and caterpillar region of mTANK with high temperature, the upper region of mSHIP1 by direct sunlight, are highlighted. GROUDN1 and GROUND2 have somewhat wide temperature range and gray-level distribution; on the other hand, SEA2 and SEA3 have narrow ones. In the converted MWIR and SWIR images, the high temperature regions are highlighted by radiance increased by the conversion function, for example, the structures near the road in GROUDN1 and GROUND2 and the partial ground regions in SEA1 and SEA2. On the other hand, low temperature regions are darkened due to the decrease in radiance intensity, for example, the mountain and the hill region in GROUDN1 and GROUND2 and the sea region in SEA1 and SEA2. We can see that the pixel values of the high temperature region expand due to the increase of radiance, whereas the pixels of low temperature region decrease due to the decrease of radiance (i.e., expansion and compression effect of pixel values by the conversion function with exponential shape) in the brightness of the converted MWIR and SWIR images. In the case of the SWIR and MWIR synthesis images, it is difficult to distinguish the background because the radiance at low temperatures is very low. On the other hand, in the case of the LWIR synthesis images, it is easier to distinguish even objects with low temperature.Figure 12
Resulting images from synthesizing modeled ground, sea target (mTANK and mSHIP1, mSHIP2) and ground, and sea background images for three IR-WBs.Figures13, 14, and 15 show the synthesis result for each IR-WB, applying the actual sky targets (F35 and BOEING), the ground targets (TANK1 and TANK2), and the sea targets (SHIP1 and SHIP2) for the same sky, ground, and sea backgrounds. We can see that the IR-WB conversion results using the actual targets are similar to those obtained by applying the modeled targets.Figure 13
Resulting images from synthesizing the real sky target (F35) and sky background images for three IR-WBs.Figure 14
Resulting images from synthesizing real sky target (BOEING) and sky background images for three IR-WBs.Figure 15
Resulting images from synthesizing modeled ground, sea target (TANK1, TANK2, SHIP1, and SHIP2) and ground, and sea background images for three IR-WBs.Figures16 and 17 show the pixel value of the red, green, and blue lines (solid line for target line and dot line for background line) on the converted LWIR, MWIR, and SWIR image. Figures 16(a)–16(d) are, respectively, corresponding to the result of Figures 10(a), 11(c), 12(a), and 12(c) including the modeled targets, and Figures 17(a)–17(d) are, respectively, corresponding to the result of Figures 13(e), 14(e), 15(b), and 15(d) including actual targets. In the case of Figure 16 applying the modeled targets, it can be seen that the pixels of the targets were made of almost metal and the backgrounds decrease proportionally from high-WB to low-WB as a whole. However, in Figures 16(a) and 16(b), since the pixel values of the engine part of mF16 and mAgusta-helicopter are very high, it can be seen that there is almost no change in the pixel values even if the WB conversion is performed. In addition, the pixel values of the normal backgrounds of Figures 16(b)–16(d) are monotonously decreased at the WB conversion, whereas very low pixel values of the dark clouds in Figure 16(a) are not decreased proportionally due to very low pixel values. The mentioned features are similar in Figure 17 applying the modeled targets. It can be seen that the pixel values corresponding to the actual targets and backgrounds also decrease proportionally at the WB conversion. This is because the almost targets are mostly composed of metals and the backgrounds in the IR system are relatively monotonous, so the pixel value of such a region exists between 0 and 255, in spite of the fact that emissivity changes for specific objects in the IR-WBs are irregular in general. We also can see that saturation phenomenon of pixel value occurs even if the IR-WB is changed, because the pixel value is very high in the plume region of F35 in Figure 17(a), the engine region of BOEING in Figure 17(b), and the caterpillar region of the tank in Figure 17(c). We confirmed that the IR background images can be synthesized with modeled or actual targets by setting temperature of the target and background, target distance, and FOV arbitrarily. To make a more precise synthesis, it needs information about an IR camera for IR background photographing and climatic conditions during an image acquisition. In particular, environmental information of IR photograph, such as time, longitude, weather, temperature, humidity, and altitude at the photograph location, can be used for more exact temperature estimation of an object.Figure 16
Pixel values of the target line and background line in (a) Figure10(a), (b) Figure 11(c), (c) Figure 12(a), and (d) Figure 12(c) including modeled targets.
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(d)Figure 17
Pixel values of the target line and background line in (a) Figure13(e), (b) Figure 14(e), (c) Figure 15(b), and (d) Figure 15(e) including actual targets.
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## 4.1. Verification of Temperature Estimation

Figure6 shows the approximately estimated temperature T^, the compensated temperature T~, and their temperature error with the original temperature T∗ (given by Equation (1)) for the three IR-WBs. The temperature error represents the difference between the original temperature and the approximately estimated one or the compensated one. The errors of the approximately estimated temperature and the compensated one are given by e^T=T^−T∗ and e~T=T~−T∗, respectively. In the LWIR-WB of Figures 6(a) and 6(d), the sign of the approximately estimated temperature error changes from negative to positive at 410 K, and the compensated temperature error decreases significantly over all temperature ranges. In the MWIR-WB of Figures 6(b) and 6(e), the sign of the approximately estimated temperature error changes from positive to negative at 420 K, and it can be seen that after temperature compensation, the error is greatly reduced, similar to LWIR-WB. In the SWIR-WB of Figures 6(c) and 6(f), the approximately estimated temperature is higher than the compensated temperature from 300 K to 500 K. The errors for these two temperatures decreased with increasing temperature. And the error of the compensated temperature decreased significantly than that of the approximately estimated temperature. And the compensated temperature also caused an error of 4.5 K at 300 K.Figure 6
Approximately estimated temperature and compensated one for (a) LWIR-WB, (b) MWIR-WB, and (c) SWIR-WB; temperature error for (d) LWIR-WB, (e) MWIR-WB, and (f) SWIR-WB in 300 K~500 K.
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(f)Figure7 shows the comparison of the gray levels calculated from the approximately estimated temperature and the compensated temperature. The integral gray level, the approximately estimated gray level, and the compensated gray level represent the gray level obtained by the original temperature, the approximately estimated temperature, and the compensated temperature, respectively. The figure shows the differences of the integral gray level and the approximately estimated gray level and the compensated gray level in LWIR-WB-to-MWIR-WB and LWIR-WB-to-SWIR-WB conversion. The difference sums for the approximately estimated gray level are, respectively, 699 and 1041 in the level in the converted MWIR-WB and SWIR-WB. On the other hand, the difference sums for the compensated gray level are, respectively, 11 and 14 in the level in the converted MWIR-WB and SWIR-WB. We can know that the compensated temperature produces less gray-level difference than the approximately estimated temperature.Figure 7
Differences of integral gray level and (a) approximately estimated gray level and (b) compensated gray level in LWIR-WB-to-MWIR-WB conversion; differences of integral gray level and (c) approximately estimated gray level and (d) compensated gray level in LWIR-WB-to-SWIR-WB conversion for temperature range of 200 K~600 K and gray level of 0~255.
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(d)The IR-WB conversion simulations using the compensated temperature were performed. The IR images (SCENE1 and SCENE2) used in the simulation were acquired by TAU640, a LWIR camera of FLIR Corp., as shown in Figure8(a). In the test images, the ground structure has the brightest gray level (pixel value of 255). On the other hand, the sky background region has the lowest gray level (pixel value of 0). These temperatures measured using an IR thermometer were 320 K and 270 K, respectively. Figures 8(b) and 8(c) show the pseudocolor images of the approximately estimated temperatures and the compensated temperature extracted from the test LWIR images. In the LWIR-WB of Figure 6(a), it can be seen that the approximately estimated temperature is lower than the compensated temperature bellow 400 K so approximately estimated temperature is bluer than the compensated temperature in the pseudocolor as shown in the black box of the figure. As shown in the white box in the figure, the compensated temperature below 400 K rises above the approximately estimated temperature and becomes redder. Figures 8(d) and 8(e) show the WB-converted MWIR and SWIR images using the compensated temperatures.Figure 8
(a) Original LWIR image, pseudocolor image of (b) approximately estimated temperature and (c) compensated temperature, (d) converted MWIR image, and (e) converted SWIR image for SCENE1 and SCENE2.The IR-WB conversion is mainly performed from LWIR-WB to MWIR-WB or SWIR-WB. The LWIR-image is used more widely than other WB images, and its gray-level distribution according to temperature is relatively linear than those of other IR-WBs. On the other hand, SWIR image has little brightness change in the low temperature region because the radiance is very small in that region. This means that the IR-WB conversion using SWIR-WB may not be effective. Also, as shown in Figure6(e), because the compensated temperature for MWIR-WB has a very small error only below 350 K, the IR-WB conversion using the MWIR-image is more reasonable than that using the SWIR-image.


## 4.2. Preparation of IR Target and Background Images for Image Synthesis

For the verification of the proposed IR composite image method, we used modeled or actual LWIR target images consisting of three groups of IR target images (sky targets, ground targets, and sea targets) as shown in Figure9. The LWIR images for the modeled targets (mF16, mAgusta-helicopter, mTANK, mSHIP1, and mSHIP2) were produced from the respective 3D CAD models by RadThermIR [25] and MuSES [16], IR signature modeling tools of TAI corporation. The targets composed of mesh (or lattice) were modeled, and the radiance per each lattice was calculated through thermal analysis of the modeling tool. Then the LWIR target images were created as shown in the figure. We also used the actual LWIR target images (F35, BOEING, TANK1, TANK2, SHIP1, and SHIP2) actually photographed by thermal equipment. Similar to the LWIR target images, the actual LWIR background images are composed of three groups: sky backgrounds (SKY1 with high contrast and SKY2 and SKY3 with low contrast), ground backgrounds (GROUND1, GROUND2 with low contrast), and sea backgrounds (SEA1, SEA2 with high contrast). The FOVs of these IR background images were 10°×8° for the sky and sea backgrounds and 5°×3.3° for the ground backgrounds. If it is assumed that all objects in the prepared target and background images are the gray body, the temperature information of the target images and the background images can be, respectively, estimated by the proposed procedure. After generating one temperature synthesis image synthesizing a target temperature image and a background temperature image, an IR synthesis image of desired IR-WB is generated.Figure 9
Modeled and actual targets and background images for sky, ground, and sea.


## 4.3. Synthesis Experiments for IR Target and Background

Figures10 and 11 show the resulting images from synthesizing the modeled sky targets (mF16 and mAgusta-helicopter) and the real sky background images (SKY1, SKY2, and SKY3) for the three IR-WBs. For a variety of temperature distributions, FOVs, and target distances, various IR synthesis images were created for the three WBs based on the compensated temperature and the compensation of the approximately estimated temperature. In the temperature extraction from the modeled targets and the LWIR background images, it can be seen that the compensated temperature rises slightly higher than the approximately estimated temperature in the pseudocolor. The MWIR and SWIR images were, respectively, transformed using the synthesized temperature images estimated from the LWIR images of the modeled targets and the real sky background images. In the conversion of high-WB to low-WB for the mF16 and mAgusta-helicopter model, the body region in the low temperature region became darker due to reduction of radiance intensity, while the engine region in the high temperature region became brighter by the increase of radiance intensity. In the conversion of high-WB to low-WB for the sky background images, the high temperature regions are highlighted by radiance intensity increased by the conversion function, for example, the structures near the road in SKY1, the small structures on the mountain in SKY2, and the partial cloud regions above in SKY3. On the other hand, lower temperature regions are darkened due to the decrease in radiance intensity, for example, the upper cloud region and low hill region in SKY1, the upper cloud region in SKY2, and the lower cloud region in SKY3.Figure 10
Resulting images from synthesizing modeled sky target (mF16) and sky background images for three IR-WBs.Figure 11
Resulting images from synthesizing modeled sky target (mAgusta-helicopter) and sky background images for three IR-WBs.Figure12 shows the resulting images from synthesizing the modeled ground target (mTANK) and the modeled sea targets (mSHIP1 and mSHIP2) with the ground backgrounds (GROUND1 and GROUND2) and the real sea backgrounds (SEA1 and SEA2) for three IR-WBs. Similar to the conversion for the modeled sky targets, the body region of the modeled tank and ship, which have low temperature, is darkened on the whole, while the moving rotational axis and caterpillar region of mTANK with high temperature, the upper region of mSHIP1 by direct sunlight, are highlighted. GROUDN1 and GROUND2 have somewhat wide temperature range and gray-level distribution; on the other hand, SEA2 and SEA3 have narrow ones. In the converted MWIR and SWIR images, the high temperature regions are highlighted by radiance increased by the conversion function, for example, the structures near the road in GROUDN1 and GROUND2 and the partial ground regions in SEA1 and SEA2. On the other hand, low temperature regions are darkened due to the decrease in radiance intensity, for example, the mountain and the hill region in GROUDN1 and GROUND2 and the sea region in SEA1 and SEA2. We can see that the pixel values of the high temperature region expand due to the increase of radiance, whereas the pixels of low temperature region decrease due to the decrease of radiance (i.e., expansion and compression effect of pixel values by the conversion function with exponential shape) in the brightness of the converted MWIR and SWIR images. In the case of the SWIR and MWIR synthesis images, it is difficult to distinguish the background because the radiance at low temperatures is very low. On the other hand, in the case of the LWIR synthesis images, it is easier to distinguish even objects with low temperature.Figure 12
Resulting images from synthesizing modeled ground, sea target (mTANK and mSHIP1, mSHIP2) and ground, and sea background images for three IR-WBs.Figures13, 14, and 15 show the synthesis result for each IR-WB, applying the actual sky targets (F35 and BOEING), the ground targets (TANK1 and TANK2), and the sea targets (SHIP1 and SHIP2) for the same sky, ground, and sea backgrounds. We can see that the IR-WB conversion results using the actual targets are similar to those obtained by applying the modeled targets.Figure 13
Resulting images from synthesizing the real sky target (F35) and sky background images for three IR-WBs.Figure 14
Resulting images from synthesizing real sky target (BOEING) and sky background images for three IR-WBs.Figure 15
Resulting images from synthesizing modeled ground, sea target (TANK1, TANK2, SHIP1, and SHIP2) and ground, and sea background images for three IR-WBs.Figures16 and 17 show the pixel value of the red, green, and blue lines (solid line for target line and dot line for background line) on the converted LWIR, MWIR, and SWIR image. Figures 16(a)–16(d) are, respectively, corresponding to the result of Figures 10(a), 11(c), 12(a), and 12(c) including the modeled targets, and Figures 17(a)–17(d) are, respectively, corresponding to the result of Figures 13(e), 14(e), 15(b), and 15(d) including actual targets. In the case of Figure 16 applying the modeled targets, it can be seen that the pixels of the targets were made of almost metal and the backgrounds decrease proportionally from high-WB to low-WB as a whole. However, in Figures 16(a) and 16(b), since the pixel values of the engine part of mF16 and mAgusta-helicopter are very high, it can be seen that there is almost no change in the pixel values even if the WB conversion is performed. In addition, the pixel values of the normal backgrounds of Figures 16(b)–16(d) are monotonously decreased at the WB conversion, whereas very low pixel values of the dark clouds in Figure 16(a) are not decreased proportionally due to very low pixel values. The mentioned features are similar in Figure 17 applying the modeled targets. It can be seen that the pixel values corresponding to the actual targets and backgrounds also decrease proportionally at the WB conversion. This is because the almost targets are mostly composed of metals and the backgrounds in the IR system are relatively monotonous, so the pixel value of such a region exists between 0 and 255, in spite of the fact that emissivity changes for specific objects in the IR-WBs are irregular in general. We also can see that saturation phenomenon of pixel value occurs even if the IR-WB is changed, because the pixel value is very high in the plume region of F35 in Figure 17(a), the engine region of BOEING in Figure 17(b), and the caterpillar region of the tank in Figure 17(c). We confirmed that the IR background images can be synthesized with modeled or actual targets by setting temperature of the target and background, target distance, and FOV arbitrarily. To make a more precise synthesis, it needs information about an IR camera for IR background photographing and climatic conditions during an image acquisition. In particular, environmental information of IR photograph, such as time, longitude, weather, temperature, humidity, and altitude at the photograph location, can be used for more exact temperature estimation of an object.Figure 16
Pixel values of the target line and background line in (a) Figure10(a), (b) Figure 11(c), (c) Figure 12(a), and (d) Figure 12(c) including modeled targets.
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(d)Figure 17
Pixel values of the target line and background line in (a) Figure13(e), (b) Figure 14(e), (c) Figure 15(b), and (d) Figure 15(e) including actual targets.
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## 5. Conclusions

This paper proposes an IR composite image generation method for modeled (or actual) IR targets and real IR backgrounds. The synthesized temperature image is generated by combining, respectively, estimated temperature information from IR targets and IR backgrounds. The gray level on WB-converted images for real IR backgrounds and IR targets is adjusted based on their estimated temperature and radiance information. For the actual test, we synthesized various modeled targets and real backgrounds. We confirmed that IR background images can be synthesized with IR targets with setting temperature of the target and background, target distance, and FOV arbitrarily. The IR composite image can be used for the simulation of image seekers for IR-guided missiles. In case the IR composite images are used by overlapping them on IR reticle patterns for DIRCM, they can also be applied to an IR reticle seeker simulation.



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*Source: 9423976-2019-12-10.xml*