Analysis of Scattering Media by High-Frequency Polarized Light

Projection Using Polarizing Projector

Aigo Ohno, Fumihiko Sakaue and Jun Sato

Nagoya Institute of Technology, Nagoya, Japan

Keywords:

Scattering Medium, Polarized Light, First-Order Scattering, Multiple Scattering, Specular Reﬂection, Diffuse

Reﬂection.

Abstract:

This paper proposes a special projection method called high-frequency polarized light projection using a po-

larizing projector to analyze scenes ﬁlled with scattering medium, and proposes a method to separate reﬂected

lights and scattered lights by scattering medium in the observed image. In high-frequency polarized light

projection, a high-frequency pattern is created by light with different polarization directions, projected onto

a scattering medium, and the reﬂected light is observed. The light scattered by the medium and the reﬂected

light from the object have different polarization properties, and we show that these two types of light can be

easily separated.

1 INTRODUCTION

In recent years, due to the development of IoT and

image information processing technologies, camera-

based information analysis has been used in various

scenes. In many cases, such technologies are based

on the assumption that the scene is a clear scene in

which light can travel straight ahead, such as in the

air. However, when targeting outdoor scenes such

as in-vehicle video analysis, scenes are often ﬁlled

with medium called scattering medium such as fog or

smoke. In such scenes, light emitted from objects is

scattered before it reaches the camera. This results in

an unclear observed image, making it difﬁcult to use

techniques that assume a clear image. Therefore, a

method that can separate the effect of light scattering

by the scattering medium from the observed image

and obtain a clear image is required.

As a technique for this purpose, Nayar et al.(Nayar

et al., 2006) propose the separation of scattered light

using high-frequency projection. In this method, a

controllable light source such as a projector is used

to project and observe high-frequency patterns such

as ﬁne checker patterns on the object. This method

enables the acquisition of images in which the ef-

fects of the scattering medium are suppressed and

separated with only a simple calculation. However,

this method requires multiple projection of images

with large changes in brightness and darkness, mak-

ing it difﬁcult to use in driver assistance and other

applications that require human observation with the

naked eye. Mukaigawa et al.(Takatani et al., 2018)

have proposed a method for ﬁnely separating primary

scattered light, compound scattered light, specular re-

ﬂected light, and diffuse reﬂected light by an object

using a method called multiple weighted measure-

ment. Although this method enables more detailed

analysis than previous methods, it is time-consuming

because it requires taking a variety of images under

different conditions.

On the other hand, research has also been con-

ducted to remove the effects of scattering from the

image information alone. Kaiming et al.e(He et al.,

2010) deﬁne a dark channel as the degree of white-

ness, and use it to locally correct the captured image,

thereby achieving processing that is unaffected by the

shading of fog. However, such models approximate

the scattering of light to some extent using a simple

model, and therefore, when the density of the scat-

tering medium is high, they are not able to perform

proper separation. In recent years, there have been

studies of using deep learning to remove the effects

of scattering from image information alone(Cai et al.,

2016; Ren et al., 2016; Gupta et al., 2015; Li et al.,

2017; Zhang and Patel, 2018; Yang and Sun, 2018;

Tang et al., 2014). These methods have been shown to

be able to separate fog with very high accuracy com-

pared to the physics-based methods described above.

However, the estimation results of these methods are

highly dependent on training data, making it difﬁcult

772

Ohno, A., Sakaue, F. and Sato, J.

Analysis of Scattering Media by High-Frequency Polarized Light Projection Using Polarizing Projector.

DOI: 10.5220/0012473100003660

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 19th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2024) - Volume 3: VISAPP, pages

772-778

ISBN: 978-989-758-679-8; ISSN: 2184-4321

to guarantee their performance for unknown scenes.

This makes it difﬁcult to use these methods in situ-

ations where high reliability is required, such as in

driver assistance.

Therefore, this paper proposes a method of sepa-

rating scattered light and reﬂected light from an ob-

ject using a projection method called high-frequency

polarized light projection. For this purpose, we show

how to construct a polarized light projector to realize

such described above high-frequency polarized light

projection. Since the method proposed in this study

is based on a physical model, it can be used indepen-

dently of the scene conditions. It can be easily applied

to various scenes because it can be estimated from a

small number of images. High-frequency polarized

light projection changes only the polarization state

of the projected image, so there is almost no ﬂicker

when observed by the naked eye. This makes it pos-

sible to obtain an image that suppresses the effects of

scattering without changing the results of human ob-

servation, even in situations such as in-vehicle image

processing, where processing is performed simultane-

ously with human observation by the naked eye.

2 SCATTERED MEDIUM AND

LIGHT SCATTERING

At ﬁrst, we will discuss the scattering of light and

its classiﬁcation. Light travels in a straight line in a

material-free vacuum. However, in a real environ-

ment, light is reﬂected and attenuated in various di-

rections due to collisions with various particles, such

as oxygen and nitrogen molecules in the air, small

water particles, dust, and dirt. This phenomenon is

called light scattering, and it has a greater impact on

the visibility of objects in medium with a large num-

ber of particles, such as fog, smoke, and water. Such

a medium in which a large number of particles exist

is called a scattering medium.

Scattering medium are classiﬁed according to the

size of their constituent particles. Based on the ra-

tio of particle size to wavelength, they can be classi-

ﬁed into Rayleigh scattering, Mie scattering, and ge-

ometric scattering. Since the projector used in this

study emits visible light and the scattering medium

is fog with a particle size of 1∼2µm, the scattering

phenomenon occurring in the scene is assumed to be

described by Mie scattering.

Also, scattering medium are classiﬁed according

to their optical thickness. Optical thickness is a mea-

sure of the opacity of a scattering medium, and the

greater the optical thickness, the opaquer the scatter-

ing medium. For light incident on an optically thin

scattering medium, the probability that the light will

incident on a particle in the medium and be reﬂected

in another direction is low, and is approximated by

a scattering model in which the number of scattering

events is limited to a single event. Such scattering is

called ﬁrst-order scattering or single scattering.

When multiple reﬂections occur in a medium, it is

called complex scattering. Such scattering can be di-

vided into cases that can be described above by scat-

tering as few as 2∼4 times, and cases in which a

sufﬁciently large number of reﬂections occur, called

higher-order scattering. Low-order scattering is ob-

served as light with some directionality because the

number of times it is scattered in the medium is

smaller than that of ﬁrst-order scattering, although

the number is larger. High-order scattering, on the

other hand, is caused by collisions with many parti-

cles in the medium, resulting in countless scatterings.

Higher-order scattering is represented as light spread-

ing in all directions with no directionality, since it

loses its directionality due to repeated reﬂections. In

this study, we use these scattering characteristics to

separate the light reﬂected from an object from the

light scattered by the scattering medium.

3 POLARIZATION PROPERTIES

3.1 Polarization

Next, we will discuss the characteristics of polarized

light used in this research. Although light is a trans-

verse wave that oscillates in various directions, polar-

ized light is light whose direction of oscillation is po-

larized in a speciﬁc direction. When polarized light is

observed through a polarizer, the observed intensity

changes as the polarizer is rotated. This intensity is

explained as described above using the polarizer ro-

tation angle φ, the maximum intensity of polarized

light I

max

, the minimum intensity I

min

, and the angle

(polarization direction) of the polarizer that gives

the maximum intensity.

I(φ) =

max

+ I

min

max

− I

min

cos(2φ − 2φ

) (1)

This allows the intensity change of polarized light to

be expressed as the addition of natural light I

min

and

polarized light with an intensity of (I

max

− I

min

) as

shown in Fig 1

This polarization intensity is known to change

with reﬂection and scattering.

Analysis of Scattering Media by High-Frequency Polarized Light Projection Using Polarizing Projector

773

Figure 1: Intensity change of partially linearly polarized

light.

3.2 Polarization in Reﬂection

Next, consider the polarization of light reﬂected from

an object. Reﬂection of light is broadly classiﬁed into

specular reﬂection and diffuse reﬂection. At ﬁrst, we

will discuss the change of polarization state in spec-

ular reﬂection. Specular reﬂection is represented as

a one-time reﬂection, and the change in polarization

state is expressed by Fresnel’s equation. In this case,

the direction of polarization and the intensity of the

light change, but the polarization is preserved. As

described above, the intensity reﬂectance R

parallel

to the plane of incidence and the intensity reﬂectance

perpendicular to the plane of incidence can be de-

scribed as follows:

tan(θ

− θ

)

tan(θ

− θ

)

, R

sin(θ

− θ

)

sin(θ

+ θ

)

(2)

where, θ

and θ

represent the angle of incidence and

refraction, respectively, and the reﬂection angle is as-

sumed to be equal to the angle of incidence assuming

that the object plane is optically smooth. In addition,

and R

are always R

≥ R

regardless of the angle

of incidence. At a certain angle of incidence, R

= 0,

and this angle of incidence is called the Brewster an-

gle. As described above, in specular reﬂection, the

polarization angle changes with the angle of incidence

of the ray.

Next, we consider the change in polarization in

diffuse reﬂection. In diffuse reﬂection, multiple re-

ﬂections occur on the object surface or inside the

object, irradiating light uniformly in all directions.

In this case, even if the polarized light is incident,

its characteristics change in various directions as the

reﬂections are repeated. Therefore, the light ob-

served by diffuse reﬂection is a superposition of light

with various polarization directions, i.e., natural light.

Thus, when diffuse reﬂection occurs, the light ob-

served is natural light even when polarized light is

incident.

3.3 Polarization in Scattering

Next, we discuss the change in the polarization of

light due to scattering. When the medium is thin, scat-

tering in a scene can be represented by a ﬁrst-order

scattering model in which light is scattered only once.

This is because, if we focus on a single ray of light,

the ray is considered to be reﬂected and refracted by

a single fog droplet in the scene and scattered. There-

fore, ﬁrst-order scattering is considered to be similar

to specular reﬂection in fog droplets. Let n

and n

be the refractive indices of air and water, respectively,

and θ

be the angle of incidence to the fog drop. As

described above, the refraction angle θ

is expressed

by Snell’s law as follows:

= arcsin



sinθ



(3)

Next, we consider the change in polarization state

in complex scattering. Polarized light enters an opti-

cally thick scattering medium, and the ﬁrst-order scat-

tering described above is repeated multiple times. Al-

though each scattering can be described by the afore-

mentioned scattering model, the repetition of this pro-

cess results in reﬂections in various directions, i.e.,

a mixture of various polarizations. This means that

even if the incident light is polarized, the scattered

light is a superposition of various polarizations, just

like diffuse reﬂected light, so that the observed light

becomes closer to natural light as the number of

scatterings increases. Therefore, the light scattered

by lower-order scattering becomes partially polarized

light, while higher-order scattering becomes natural

light. In this paper, the composite scattered light is as-

sumed to be greatly affected by the higher-order scat-

tering and is treated as natural light.

4 SEPARATION OF SCATTERED

AND REFLECTED

COMPONENTS USING

POLARIZATION

4.1 Polarizing Projector

At ﬁrst, we describe the polarizing projector used in

this study. In general projectors, the intensity of light

emitted from a light source is partially changed by us-

ing liquid crystals or micro-mirror arrays to project a

variety of images. Let us consider liquid crystal dis-

plays (LCDs), which are used in many projectors. A

typical LCD consists of a liquid crystal sandwiched

between two orthogonally oriented polarizing plates.

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774

When no voltage is applied to the LCD, polarized

light incident from the back of the LCD is twisted

in various directions by the discretely arranged liquid

crystal molecules, resulting in a state close to unpo-

larized light. Therefore, a portion of the incident light

changes its direction of polarization to a state that al-

lows it to pass through the polarizer on the front sur-

face. On the other hand, when voltage is applied, the

orientation of the liquid crystal molecules is aligned,

and as a result, polarized light incident from the back

enters the front polarizer without changing its direc-

tion. Since the orientation of the two polarizers sand-

wiching the liquid crystal is orthogonal, light that has

passed through the liquid crystal cannot pass through

the polarizers. This makes it possible to control light

passing through the entire liquid crystal display. In

addition, by changing the voltage applied to the liquid

crystal, the alignment of the liquid crystal changes,

making it possible to observe light of various intensi-

ties.

Let us consider the case where the polarizer in-

stalled on the front surface is removed. In this case,

polarized light passing through the liquid crystal is

projected directly to the front surface. In other words,

the set of light rays whose intensity is adjusted by

passing through the polarizer is projected as a set of

light rays with different polarization directions. This

makes it possible to project light of various polar-

izations with different directions in the same way as

when projecting light of different intensities using an

ordinary projector. Regardless of the state of the liq-

uid crystal, the amplitude of the polarization, i.e., the

brightness of the observed image, remains almost un-

changed. Therefore, when observed by the naked eye,

an image with almost the same brightness is observed

regardless of the state of polarization. This makes it

possible to change the light source status of a scene

without signiﬁcantly disturbing human observation.

In this paper, we call such a projector a polarizing

projector and show how to use it to separate scattered

light from reﬂected light.

Note that polarizing projectors do not directly

control the direction of polarization, but rather con-

trol the degree of polarization of the light that passes

through them, i.e., how close to perfect polarization

or how close to natural light the light is. Therefore, it

is not possible to directly project perfectly polarized

light that is orthogonal to the polarizer mounted on the

back of the liquid crystal. However, considering that

partial polarization and natural light can be expressed

as a linear combination of orthogonal perfect polar-

izations, the partial polarization obtained through the

LCD can be expressed as a linear combination of a

perfect polarization with an orientation equal to that

of the polarizer on the back and an orthogonal per-

fect polarization. Considering the linearity of light,

multiple images taken with varying partial polariza-

tion can easily be linearly combined to produce an

image when irradiated with perfect polarization.

Furthermore, polarization can be adjusted for each

pixel in a polarizing projector. This allows for the

synthesis of various polarizing projections, such as

the synthesis of polarization stripe patterns.

By using this to project various polarization pat-

terns, scattered light in an observed image can be sep-

arated.

4.2 Separation of Reﬂected and

Scattered Light Based on

Polarization

At ﬁrst, we consider the case where polarized light is

projected with the same orientation to the scene using

a polarizing projector, as shown in Fig 2.

Figure 2: Single polarized light projection.

As mentioned previously, the ﬁrst-order scattered

light from the scattering medium and the mirror re-

ﬂection light from the object retain the polarization

property. On the other hand, the compound scattered

light and the diffuse reﬂected light from the object

surface are natural light. Let us consider the case

where such light is observed by a polarization cam-

era. In this case, the observed light is partially po-

larized light that is a combination of natural light and

perfectly polarized light. Let us assume that the dif-

fuse reﬂected light and the composite scattered light

are perfect natural light. In this case, the natural light

indicated by the equation Eq.(1) is a combination of

diffuse reﬂection and complex scattered light. On the

other hand, perfectly polarized light is a composite of

ﬁrst-order scattered light and specular reﬂected light.

Both of these two components contain both re-

ﬂected and scattered light from the object. If all light

reﬂected from an object is diffuse reﬂected light or if

there is no compound scattered light, it is possible to

separate reﬂected and scattered light by this method.

Analysis of Scattering Media by High-Frequency Polarized Light Projection Using Polarizing Projector

775

However, in general scenes, such assumptions do not

hold, and it is difﬁcult to separate them by simple po-

larization alone.

4.3 Separation of Specular Reﬂection

by High-Frequency Polarized Light

Projection

In this study, we propose a method for separating ob-

ject specular reﬂection light by high-frequency polar-

ized light projection using a polarizing projector. To

separate the ﬁrst-order scattered light from fog and

the specular reﬂection light from the object surface,

this study takes advantage of the fact that fog has a

spatial thickness. In other words, we propose a light

separation method that takes advantage of the differ-

ence between fog, in which a ﬁrst-order scattered light

is integrated in the depth direction of the camera, and

an object, in which specular reﬂection occurs only on

its surface.

Figure 3: High-frequency polarized light projection.

Let us now consider the case where a polarization

pattern is projected onto the scene such that the di-

rection of polarization changes horizontally to 0

◦

and

◦

at a high-frequency polarized light projection, as

shown in Fig 3. When the scene is observed by a po-

larization camera from a different direction from that

of the projector, as shown in Fig 3, there will be dif-

ferent polarizations on the observed light path. There-

fore, the scattered light observed by the camera is a

combination of the ﬁrst-order scattered light with a

polarization of 0 degrees and the ﬁrst-order scattered

light with a polarization of 90 degrees, i.e., natural

light. On the other hand, the light reﬂected from the

specular surface of an object is generated only on the

surface of the object, and thus is observed with perfect

polarization. This makes it possible to easily separate

the perfectly polarized light from the specularly re-

ﬂected light, since the only perfectly polarized light

in the observed light is the specularly reﬂected light.

4.4 Separation of First-Order Scattered

Light

Finally, we describe a method for separating ﬁrst-

order scattered light from fog. The diffuse reﬂection

component from objects and the combined scattered

light from the medium are components that change to

natural light in the scene. Therefore, they are con-

sidered to have the same intensity in both cases of

high-frequency polarized light projection and single-

directional polarized light projection. Therefore, by

subtracting the natural light image obtained by single

polarized light projection from the natural light im-

age obtained by high-frequency polarized light pro-

jection, the ﬁrst-order scattered light from the fog can

be easily separated. This makes it possible to obtain

an image containing only scattered light from fog and

an image containing only reﬂected light from objects

with only two projection/photographing steps.

Note that it is difﬁcult to completely separate the

complex scattered light by the medium and the diffuse

reﬂected light by this method alone because of their

close polarization characteristics. However, since the

complex scattered light are weaker than the ﬁrst-order

scattering, their effect is small in scenes with low fog

density. Furthermore, by combination with the usual

high-frequency projection with varying brightness, it

is possible to separate these components as well.

5 EXPERIMENTAL RESULTS

5.1 Environment

The results of the separation of reﬂected light and

scattered light using the proposed method are pre-

sented. In this experiment, fog was generated in

a plastic greenhouse in which observation targets

were set up. High-frequency polarized light projec-

tion patterns and single polarized light projection pat-

terns were projected onto the scene, which was pho-

tographed by a polarization camera. Fig 4 shows the

scene.

Figure 4: Experimental environment.

Fig 5 shows an image taken under high-frequency

VISAPP 2024 - 19th International Conference on Computer Vision Theory and Applications

776

Figure 5: Images under high-frequency polarized light pro-

jection.

Figure 6: Images under single polarized light projection.

polarization, and Fig 6 shows an image taken under

single polarization, respectively. These four images

were taken simultaneously by the polarization cam-

era through ﬁlters with polarization angles of 0

◦

(up-

per left), 45

◦

(upper right), 90

◦

(lower left), and 135

◦

(lower right), respectively. The results of these two

types of images show that the brightness of the fog

only around the object in the images taken under sin-

gle polarization is different for each polarization an-

gle. This is thought to be due to the fact that the scat-

tered light from the fog is strongly partially polarized,

resulting in a large change in the intensity observed at

each angle. On the other hand, when high-frequency

polarized light projection is used, the fog is observed

to be almost equally bright in all polarized light im-

ages. This is considered to be a result of the fact that

the ﬁrst-order scattered light from the fog is observed

as natural light due to the high-frequency polarization.

5.2 Results of Separation

Next, we show the results of separating the observed

light using the proposed method. At ﬁrst, the results

of separating natural light and polarization compo-

nents for each captured image are shown in Fig 7 and

Fig 8. The results show that almost no polarized

light is observed outside of the object surface at the

base of the high-frequency polarized light projection.

Figure 7: Polarized light (left) and natural light (right) in

high-frequency polarized light projection.

Figure 8: Polarized light (left) and natural light (right) in

single polarized light projection.

This may be due to the fact that the high-frequency

polarized light projection allows the thicker parts of

the object to be observed as natural light. On the other

hand, in the case of single polarized light projection,

polarization is also observed in the fog area, indicat-

ing that ﬁrst-order scattering from the fog is observed

as polarized light.

The results of the separation of the scattering

and reﬂection components based on these images are

shown in Fig 9. The results show that the brightness

of the fog ﬁrst-order scattering image decreases in

the area where the object is placed. This is thought

to be due to a decrease in the fog thickness caused

by the placement of the object. In the specular re-

ﬂection component, the brightness increases in areas

where the normal direction is the same, indicating that

it is observed as a specular reﬂection. In the com-

posite image of diffuse reﬂection and composite scat-

tering, diffuse reﬂection from the entire object sur-

face is observed. The brightness of the areas where

there are no objects is suppressed, conﬁrming that

composite scattering was not strong in this environ-

ment. These results conﬁrm that the combination of

single-frequency polarized light projection and high-

frequency polarized light projection can achieve sepa-

ration according to the characteristics of the observed

image with only two projection and imaging.

Figure 9: Results of separation of reﬂection and scattering

components: fog ﬁrst-order scattering (left), specular reﬂec-

tion (center), diffuse reﬂection + complex scattering (right).

Analysis of Scattering Media by High-Frequency Polarized Light Projection Using Polarizing Projector

777

6 CONCLUSION

In this paper, we propose a method for separat-

ing various components in an observed image, such

as reﬂected and scattered components, by means of

high-frequency polarized light projection and high-

frequency projection using a polarizing projector. We

also show how to conﬁgure a polarizing projector to

realize this method. In the future, a method to com-

pletely separate the scattering and reﬂection compo-

nents by separating diffuse and composite scattering

will be investigated.

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