Relighting Backlight and Spotlight Images using the von Kries Model

Michela Lecca

Fondazione Bruno Kessler, Digital Industry Center, via Sommarive 18, 38123 Trento, Italy

Keywords:

Image Relighting, Image Enhancement, Backlight/Spotlight, von Kries Model.

Abstract:

Improving the quality of backlight and spotlight images is a challenging task. Indeed, these pictures include

both very bright and very dark regions with unreadable content and details. Restoring the visibility in these

regions has to be performed without over-enhancing the bright regions, thus without generating unpleasant

artifacts. To this end, some algorithms segment the image in bright and dark regions, re-work them separately

by different enhancing functions. Other algorithms process the input image at multiple scales or with different

enhancement techniques. All these methods merge the results together paying attention to the edge areas. The

present work proposes a novel approach, called REK and implementing a relighting technique based on the

von Kries model. REK linearly increases the channel intensities of the input image, obtaining a new brighter

image, which is then summed up to the input one with weights computed from the input image and taking

high values on the dark regions while low values on the bright ones. In this way, REK improves the quality

of backlight and spotlight pictures without needing for segmentation and multiple analysis, while granting

satisfactory performance at a computational complexity proportional to the number of image pixels.

1 INTRODUCTION

Good lighting is essential for capturing clear pictures.

Unfortunately, in some contexts, such important con-

dition is hard to meet. This is the case of environ-

ments with low light, backlight and spotlight. Under

low light, the acquired scene appears entirely dark,

while under backlight and spotlight the scene contains

both very bright and very dark regions. Precisely, in

the images with backlight, a foreground object is dis-

played against a very brilliant background, while in

the images with spotlight, the light source, which is

intense but not diffuse, is inside the acquired scene

and produces a very bright region, while the rest is

nearby black. In all these pictures, the content and the

details of the scene are unreadable and algorithms for

improving the quality of the dark areas are needed.

While several algorithms exist for low-light images,

e.g. (Lee et al., 2015), (Guo et al., 2017), (Lv et al.,

2018), (Kwok et al., 2018), (Wang et al., 2020), (Li

et al., 2020), (Wei et al., 2018), (Jiang et al., 2021),

(Guo et al., 2022), there are only few works on the

enhancement of backlight and spotlight images. The

main issue with these images is that the dark areas

must be reworked to increase their visual quality with-

out over-enhancing the bright ones. Some algorithms,

https://orcid.org/0000-0001-7961-0212

speciﬁcally designed for this task, segment the input

image in dark and bright region and enhance them

independently by different functions, e.g. (Ramirez

Rivera et al., 2012), (Li and Wu, 2018). The enhanced

regions are then merged together and the edge areas

are usually post-processed to prevent the formation

of undesired halos or artifacts. The use of different

enhancement functions for dark and bright areas en-

sures in general good results, that however strongly

depend on the segmentation. Multiscale Retinex ap-

proaches propose a different solution, not needing for

segmentation, e.g. (Petro et al., 2014), (Morel et al.,

2010), (Jobson et al., 1997). These algorithms pro-

cess the input image at multiple resolutions. At each

scale, the intensity of each pixel x is mapped onto a

new value based on the spatial distribution of a set

of colors sampled around x. The results obtained at

the various scales are averaged together, returning an

image where the details are preserved in the bright

regions and magniﬁed in the dark ones. Neverthe-

less, the output image often presents halos around the

edges and the computational time of such algorithms

is usually high. A recent Retinex inspired bilateral ﬁl-

ter for backlight and spotlight image enhancement has

been presented in (Lecca, 2021). This ﬁlter rescales

the color intensity of each pixel by a value depend-

ing both on spatial and intensity features of some pix-

226

Lecca, M.

Relighting Backlight and Spotlight Images using the von Kries Model.

DOI: 10.5220/0011107800003209

In Proceedings of the 2nd International Conference on Image Processing and Vision Engineering (IMPROVE 2022), pages 226-233

ISBN: 978-989-758-563-0; ISSN: 2795-4943

els regularly sampled over the image. The algorithm

performs well, but in some cases the output images

appear washed out. Another approach is proposed in

(Wang et al., 2016), where three different enhanced

images are computed from the input one: in the ﬁrst

image, the dark areas are over-enhanced, in the sec-

ond one the dynamic range of the bright regions is

compressed, while in the third one the contrast is im-

proved. The three images are smoothed by a Lapla-

cian operator to remove noise and halos, then they are

averaged together with weights controlling the over-

all brightness of the images. The results are generally

satisfactory, but in some cases the dark regions are

still quite dark.

The present work proposes a new algorithm,

which relights the dark areas of backlight and spot-

light regions without over-enhancing the bright ones

and without needing for segmentation and/or multi-

ple scale analysis. Relighting is performed based on

the von Kries model (Finlayson et al., 1994), (Lecca,

2014), i.e. by rescaling the channel intensities of the

input image by a factor α greater than 1, so that the

brightness of the dark areas increases. This relighted

image is summed up to the input one with weights de-

pending on the input brightness and having high (low,

resp.) values on the dark (bright, resp.) regions. This

combination of images increases the visibility of con-

tent and details of the dark areas, while preserves the

appearance of the bright areas. The parameter α is

tunable by the user, but here an unsupervised estima-

tion of α is also presented. The proposed algorithm,

called REK from the keywords RElight and von Kries,

has been tested on different backlight and spotlight

images, showing good performance also in compari-

son with other state-of-the-art methods.

2 THE PROPOSED METHOD

The original von Kries model, presented in (Kries,

1905), provides a description of the human chromatic

adaptation, which is the mechanism regulating the re-

sponses of the human vision system to varying view-

ing conditions, such as illumination. This adaptation

is strictly related to the color constancy, i.e. to the hu-

man capability to discount light effects from the ob-

served scene (Hirakawa and Parks, 2005). In com-

puter vision, the von Kries model has been adapted

to describe how the colors of a digital image changes

when the illumination under which the image is ac-

quired changes. Speciﬁcally, this model approximates

such a change by a linear diagonal transform of the

RGB triplets (Finlayson et al., 1993). In image pro-

cessing, this transform has been widely employed

for correcting color shifts of an image with respect

to a reference one, showing very good performance

(Berens and Finlayson, 2000), (Lecca and Messelodi,

2011), (Lecca, 2014).

Mathematically, let I be a color image and let I

, I

be its color channels. Let x denote a pixel of I, and

let B be the brightness of I, i.e. the gray-level im-

age computed from I by averaging pixel-wise its three

color channels, i.e.:

B(x) =

∑

i=0

(x). (1)

The von Kries model states that any change of light

determines a rescaling of the values I

(x), I

(x),

i.e. for any i = 0, 1, 2:

(x) → α

(x) (2)

where the coefﬁcients α

, α

are real values

strictly greater than zero. This model was origi-

nally devised for narrow band sensors, but it has been

proved to be a good approximation also for standard

sensors (Finlayson et al., 1994).

When α

= α

:= α, the equation (2) de-

scribes a change of the image brightness, like that

caused by shadows. In particular, when α is greater

than 1, the image becomes brighter (i.e. the values of

B increase), while when α is smaller than 1, the image

becomes darker (i.e. the values of B decrease).

In agreement with this model, the algorithm REK

rescales the channel intensities of any input image I

by a parameter α > 1. This operation, which is per-

formed on the whole image I, enables improving the

visibility of content and details of the dark regions,

but at the same time it also increases the brightness

of the bright area, with the risk of saturating the col-

ors, removing edges and introducing unpleasant ar-

tifacts. To overcome this problem, REK combines

the relighted image I

with the input one through a

summation whose addends are weighted by values de-

pending on the brightness B of I and taking high val-

ues on the dark regions, while low values on the bright

ones. Thanks to these operations, REK improves the

visual quality of the dark regions, while preserves that

of the bright regions.

Operatively, REK works as follows. First, REK

maps I on a new image I

, obtained by relighting I

according to the von Kries model. Precisely, for each

pixel x, the color channels of I

are deﬁned pixel by

pixel as follows:

(x) = αI

(x) (3)

with α > 1 and i = 0, 1, 2.

Second, REK combines the input image I with I

and

Relighting Backlight and Spotlight Images using the von Kries Model

227

(a) Image Enhancement by REK and other algorithms:

(b) Enlargement of the Top Left Corner:

Figure 1: (a) On top, an image and its versions relighted by REK for p = 1, 3, 5, 7. In the middle: the weights corresponding

to the different values of p. On bottom: image enhancement by other algorithms (see text for more explanation). (b) An

enlargement of the top left corner of the input image and of its enhanced versions.

outputs a new, color image J, whose components J

= 0, 1, 2) are computed pixel-by-pixel as follows:

(x) = (1− w(x))I

(x) + w(x)I

(x), (4)

where w is a weighting function, deﬁned over the pix-

els of I, ranging over [0, 1], and taking high values on

the dark regions, while low values on the bright ones.

There exist different equations for w. In the cur-

rent implementation of REK, w is deﬁned from B, pre-

cisely, for each pixel x:

w(x) =



1−

B(x) − m

− m



(5)

where m

and M

are respectively the minimum and

the maximum values of B and p is an integer number

greater or equal than 1. The value p = 0, that is not

considered here, is a special case, in which w is iden-

tically equal to the constant function 1. Therefore,

for p = 0, the input image does not contribute to the

computation of J and the output image is completely

deﬁned by the von Kries transform.

Figure 1(a) shows in the ﬁrst row an input image

and four versions of it improved by REK with p =

1, 3, 5, 7. The second row of the ﬁgure displays the

corresponding weighting functions: it is possible to

observe that the gap between the values of w on the

dark and bright regions increases with p. This means

that the contribution of the bright regions from I

de-

creases when p increases, so that the bright regions in

the output image J are very similar to those in the in-

put image, while the dark regions in the output image

are brighter than their counterpart in the input image.

3 EVALUATION

The performance of REK has been evaluated on two

datasets, called respectivelyPDB and SDB. PDB con-

IMPROVE 2022 - 2nd International Conference on Image Processing and Vision Engineering

228

sists of 20 real-world color images, that have been se-

lected from a personal collection of the author (’P’

stands for personal) and whose size range from 1580

× 1882 to 4160 × 3120 pixels. SDB contains 60 real

world color images with a lower resolution than those

of PDB (’S’ stands here for small): their size vary

from 102 ×76 to 432 × 576 pixels. SDB includes pic-

tures from Pixabay (https://pixabay.com), from some

datasets used to test image enhancement algorithms,

e.g. (Wang et al., 2016), (Li and Wu, 2018), (Ramirez

Rivera et al., 2012), and some images from PDB at

a low resolution. SDB was also employed to test

the backlight/spotlight image enhancer described in

(Lecca, 2021). In both the datasets, the images depict

indoor and outdoor environments, acquired under nat-

ural or artiﬁcial backlight and spotlight (see e.g. Fig-

ures 1 and 2).

The performance of REK has been evaluated by

analyzing three numerical features that are strongly

related to the human perception of the image quality

and are usually changed by enhancement. These fea-

tures are described here using the notation introduced

in Section 2:

The entropy of the color distribution (f

), which is de-

ﬁned as the L

distance between the probability den-

sity function (pdf) of B and the uniform probability

density function over [0, 255];

The mean value of the image brightness (f

), i.e. the

mean value of B;

The standard deviation of the image brightness (f

i.e. the departure of the image brightness from f

The features f

, f

and f

measure respectively

the colorfulness, the brightness level and the contrast

of the image I. These features usually change after

enhancement, but their behaviour is expected to be

different when they are computed on the bright re-

gions, on the dark regions and on the whole image.

Precisely, on the bright regions, where the visibility

of details and content are generally already good, f

and f

are expected to remain stable or change

slightly. In general, it may happen that the value of

increases slightly, consequently the histogram of B

on these regions becomes more peaked while the con-

trast diminishes because of saturation effects, i.e. f

increases and f

decreases. On the contrary, on the

dark regions, f

and f

are both expected to increase,

meaning that the areas become brighter and more con-

trasted, while f

is expected to decrease, since the en-

hancement tends to stretch the color distribution. Fi-

nally, on the whole image, f

is expected to increase,

because the dark regions are brighter, while f

is ex-

pected to remain unchanged or to decrease slightly. In

fact, brightening the dark regions decreases the con-

trast between the dark and the bright regions of the

original backlight/spotlightimage, that is usually very

high. Consequently, the mean value of f

over the

whole image generally decreases. Nevertheless, the

exact behaviour of f

depends on the content of the

dark regions: in fact, in case the dark regions contain

very high color variations, the global value of f

may

even increase. Moreover, it is to note that in the back-

light and spotlight images, the pdf of B is bimodal,

with the left and the right peaks correspondingrespec-

tively to the dark and bright regions. Brightening the

dark areas stretches the left peak toward the right one

and this diminishes the value of f

over the whole im-

age.

To capture these different trends, the values of the

measures listed above are here computed separately

on the whole image and on their bright and dark ar-

eas and indicated respectively with f

s, f

s and f

To this purpose, the dark regions P

and the bright

regions P

of the input image I are detected by a seg-

mentation procedure that partitions B using a thresh-

old τ. Speciﬁcally:

= {y ∈ D(I) : B(x) ≤ τ} (6)

= {y ∈ D(I) : B(x) > τ} (7)

where D(I) is the set of pixels of I and

τ =

− m

. (8)

Finally, it is to note that, for a fair assessment of

the performance of an enhancement algorithm, a sin-

gle measure does not sufﬁce. In fact, for example,

a very high value of brightness may correspond to a

saturated image, and thus to a loss of details and to

a peaked distribution. Therefore, all the features de-

scribed above, computed on the whole image or on its

parts, must be considered simultaneously in the eval-

uation process.

The performance of REK has been evaluated also

in comparison with the methods FUSION (Wang

et al., 2016), BACKLIT (Li and Wu, 2018) CD

(Ramirez Rivera et al., 2012), SuPeR-B (Lecca, 2021)

and MSR (Petro et al., 2014), brieﬂy described in

Section 1. For the comparative analysis, the codes

provided by the authors and/or available on the net

on GiThub (FUSION and BACKLIT) and MatLab

(MSR) repositories have been employed, within the

parameters set as per default. For SuPeR-B, the num-

ber of pixels sampled over the images and the other

three parameters, have been ﬁxed respectively to 100

and zero (see (Lecca, 2021) for more details).

Regarding REK, the experiments have been re-

peated for different values of p, i.e. p = 1, 3, 5, 7.

It is to note that, the parameter α must be chosen to

prevent the intersection of the brightness distribution

curves around the peaks correspondingto the dark and

Relighting Backlight and Spotlight Images using the von Kries Model

229

(a) Enhancement of an Indoor Backlight Image.

(b) Enhancement of an Outdoor Backlight Image.

Figure 2: Examples of backlight/spotlight image restoring by REK with different values of p and by other enhancers.

to the bright areas: violating this prescription may

cause the loss of the boundaries between the dark and

bright areas, worsing the global quality of the image.

To avoid this undesired effect, here α has been set as:

α =

− δ

, (9)

where µ

and δ

are respectively the mean value and

the standard deviation of B over P

, and µ

is the

mean value of B over P

. Of course, it is supposed that

> 0, i.e. the dark region is not uniformly black.

4 RESULTS

Tables 1 and 2 report the mean values of the objec-

tive measures f

s, f

and f

computed on the datasets

PDB and SDB. On both the datasets and for any value

of p, REK effectivelyimproves the quality of the dark

images, but the best results are obtained for p = 3

and p = 5. In fact, for these values the bright re-

gions are slightly modiﬁed, while the dark ones are re-

markably improved, reporting a much higher bright-

ness and contrast, while a lower entropy of the bright-

ness distribution. Globally, the input image is bright-

ened, while its contrast decreases because, as dis-

cussed in Section 3, after the enhancement, the dif-

ference between the dark and the bright regions di-

minishes. Consequently, the entropy of the brightness

distribution is lower and the pdf is more uniform: usu-

ally, this means that the range of colors in the image

has been widened and the image appears more pleas-

ant. On the contrary, for p = 1, the bright regions are

over-enhanced. their brightness increases very much,

IMPROVE 2022 - 2nd International Conference on Image Processing and Vision Engineering

230

Table 1: Evaluation of REK in comparison with other enhancers on the dataset PDB.

Algorithm f

[×10

−3

] [×10

−3

] [×10

−3

]

INPUT 4.16 71.00 65.89 4.93 197.76 31.45 5.12 33.86 25.88

BACKLIT 2.40 109.96 63.91 4.73 199.33 29.55 2.70 86.50 52.10

MSR 2.54 126.87 58.98 4.65 183.57 29.83 2.51 108.93 57.26

CD 4.07 89.46 79.97 6.13 235.28 17.29 4.34 45.00 40.87

FUSION 3.33 95.77 58.76 4.84 203.06 29.19 4.21 64.82 30.46

SuPeR-B 3.06 127.62 58.69 5.47 217.29 24.19 3.78 97.32 38.11

REK [p = 1] 3.54 134.21 63.81 6.11 214.63 18.14 3.48 110.89 57.16

REK [p = 3] 3.48 114.95 55.87 5.18 199.94 28.89 4.31 90.22 39.35

REK [p = 5] 3.72 105.23 55.12 4.98 198.02 31.04 4.77 77.79 30.79

REK [p = 7] 3.94 98.97 55.79 4.94 197.76 31.44 4.99 69.50 26.44

Table 2: Evaluation of REK in comparison with other enhancers on the dataset SDB.

Algorithm f

[×10

−3

] [×10

−3

] [×10

−3

]

INPUT 4.17 67.79 64.13 4.92 179.33 28.56 5.26 29.74 28.00

BACKLIT 2.78 100.65 65.67 4.68 189.30 29.14 3.47 73.26 51.58

MSR 2.21 118.12 61.97 4.69 185.23 27.82 2.35 97.24 58.55

CD 4.04 89.45 83.03 5.86 228.30 18.82 4.53 41.49 44.58

FUSION 3.23 89.54 60.81 4.84 189.51 26.62 4.22 56.82 34.50

SuPeR-B 3.17 119.31 64.77 5.51 213.03 21.25 3.95 84.12 41.38

REK [p = 1] 3.80 122.76 68.53 6.24 204.04 14.21 3.76 97.15 63.13

REK [p = 3] 3.51 103.75 57.55 5.23 182.86 25.44 4.35 78.60 44.68

REK [p = 5] 3.61 95.29 55.36 4.98 179.80 28.03 4.72 67.98 35.80

REK [p = 7] 3.76 90.21 55.18 4.92 179.34 28.54 4.90 61.10 31.13

their brightness histogram become more peaked, and

their contrast decreases, meaning that some edges are

lost. An example of these effects is shown in Fig-

ure 1, where the elephant’s trunk becomes almost

white and its ﬁnal part tends to disappear (see Fig-

ure 1(b)), getting worse the quality of the entire im-

age. It is to note that an excessive brightening may

introduce artifacts also in the dark areas, as illustrated

in Figure 2(b). Here, the image obtained for p = 1

presents some bluish halos on the bell tower, while

the branches of the tree are poorly visible. For p = 7,

the bright regions after enhancement are highly simi-

lar to the input one, while the dark regions have still

a low contrast, very close to that of the input images.

This means that the enhancement poorly improved the

visibility of the details in the dark areas. As already

observed in Section 2, these results are due to the dif-

ferent shape of the function w.

From the comparative analysis of REK with other

methods, it results that CD often returns images where

the dark regions are still quite dark, while the contrast

of the bright regions is signiﬁcantly reduced. MSR

returns very good values of the f

s, f

s and f

, but

a qualitative inspection of the images showed that

the MSR images are poorly natural and look as car-

toonized, with strong, thick edges between the dark

and the bright regions. BACKLIT performs quite

well, but sometimes generates undesired artifacts, like

the halos visible on the bell tower of Figure 2(b)

and the greenish, thin boundary around the elephant’s

trunk in Figure 1(b). SuPeR-B works generally well,

but on average the edges in the bright regions are

quite attenuated and, despite the visibility of the con-

tent and details is generally good, the global image

appears often washed out. FUSION provides satis-

factory results, but the improvement of the dark re-

gions is less than that performed by REK. From the

theoretical point of view, REK behaves similarly to

FUSION, because both these methods merge images

with different enhancement levels. Nevertheless, FU-

SION has an higher computational complexity since

it computes three different enhancement versions of

the input image and requires smoothing operations,

while REK computes only one new image, i.e. that

relighted by the von Kries model, and does not need

for further processing.

Relighting Backlight and Spotlight Images using the von Kries Model

231

5 CONCLUSIONS

The experiments described in Section 4 show that al-

gorithm REK is a new, computational efﬁcient back-

light/spotlight image enhancer, outperforming other

algorithms in the state-of-the-art. This result is ob-

tained by up-scaling the channel intensities of the in-

put image by the von Kries transform and blending

the relighted image with the input one. In this op-

eration the choice of the up-scaling factor α and of

the weighting function w is crucial. In particular, the

value of α must prevent over-enhancement effects as

well as the removal of important edges, while w must

grant simultaneously the improvement of the visibil-

ity of the dark regions and the ﬁdelity of the bright

regions to the original versions. The unsupervised es-

timate of α and the choice of an exponential function

of the image brightness for w proposed here havebeen

demonstrated to work well, especially when the expo-

nent of w is equal to 3 and 5. In particular, for p = 3,

after enhancement, the appearance of the bright re-

gions is preserved, while on average, the values of the

brightness and the contrast of the dark regions are in-

creased by 165% and 56% with respect to their origi-

nal values, while the color distribution entropy is de-

creased by 16.6%. Although these results are good,

future research will investigate alternativechoices, es-

pecially for the value of α. This latter currently re-

lies on the analysis of the bimodal density function of

the input brightness, but other possible choices could

be considered also the weight w. Moreover, it is to

note that the level of enhancement could be also made

dependent on the application scenario, e.g. making

the pictures more pleasant for entertainment, enabling

visual inspection or computer vision tasks requiring

high detail visibility, as for instance unsupervised im-

age description and matching.

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