COLOR MODELS OF SHADOW DETECTION IN VIDEO SCENES

Csaba Benedek

azm

any P

eter Catholic University, Department of Information Technology, Pr

ater utca 50/A, Budapest, Hungary

Tam

as Szir

anyi

Distributed Events Analysis Research Group, Computer and Automation Institute, Kende u. 13-17, Budapest, Hungary

Keywords:

Shadow, color spaces, MRF.

Abstract:

In this paper we address the problem of appropriate modelling of shadows in color images. While previous

works compared the different approaches regarding their model structure, a comparative study of color models

has still missed. This paper attacks a continuous need for deﬁning the appropriate color space for this main

surveillance problem. We introduce a statistical and parametric shadow model-framework, which can work

with different color spaces, and perform a detailed comparision with it. We show experimental results regard-

ing the following questions: (1) What is the gain of using color images instead of grayscale ones? (2) What

is the gain of using uncorrelated spaces instead of the standard RGB? (3) Chrominance (illumination invari-

ant), luminance, or ”mixed” spaces are more effective? (4) In which scenes are the differences signiﬁcant?

We qualiﬁed the metrics both in color based clustering of the individual pixels and in the case of Bayesian

foreground-background-shadow segmentation. Experimental results on real-life videos show that CIE L*u*v*

color space is the most efﬁcient.

1 INTRODUCTION

Detection of foreground objects is a crucial task in vi-

sual surveillance systems. If we can retrieve the accu-

rate silhouettes of the objects, or object groups, their

high-level description becomes much easier, so it is

favorable e.g. in detection of people (Havasi et al.,

2006) or vehicles (Rittscher et al., 2000), respectively

in activity analysis (Stauffer and Grimson, 2000).

The presence of moving shadows on the background

makes difﬁcult to estimate shape or behavior of the

objects, therefore, shadow detection is an important

issue in the applications. However, we do not need

to search for shadows cast on the foreground objects,

since these ’self-shadowed’ scenario parts consist to

the foreground.

We ﬁnd a thematic overview on several shadow detec-

tors in (Prati et al., 2003). The methods are classiﬁed

in groups based on their model structures, and the per-

formance of the different model-groups are compared

via test sequences. The authors note that the methods

work in different color spaces, like RGB (Mikic et al.,

2000) and HSV (Cucchiara et al., 2001), however, it

remains open-ended, how important is the appropri-

ate color space selection, and which color space is

the most effective regarding shadow detection. More-

over, we ﬁnd also further examples: (Rittscher et al.,

2000) used only gray levels for shadow segmenta-

tion, other approaches were dealing with the CIE

L*u*v* (Martel-Brisson and Zaccarin, 2005), respec-

tively CIE L*a*b* (Rautiainen et al., 2001) spaces.

For the above reasons, the main issue of this paper

is to give an experimental comparison of different

color models regarding cast shadow detection on the

video frames. For the comparison, we propose a gen-

eral model framework, which can work with different

color spaces. During the development of this frame-

work, we have carefully considered the main ap-

proaches in the state-of-the art. Our presented model

is the generalization of our previous work (Benedek

and Szir

anyi, 2006).

225

Benedek C. and Szirányi T. (2007).

COLOR MODELS OF SHADOW DETECTION IN VIDEO SCENES.

In Proceedings of the Second International Conference on Computer Vision Theory and Applications - IFP/IA, pages 225-232

 SciTePress

2 BASIC NOTES

In (Prati et al., 2003), the authors distinguished de-

terministic methods (e.g. (Cucchiara et al., 2001)),

which use on/off decision processes at each pixel, and

statistical approaches (see (Mikic et al., 2000)) which

contain probability density functions to describe the

shadow-membership of a give image point. The clas-

siﬁcation of the methods whether they are determinis-

tic or statistical depends often only on interpretation,

since deterministic decisions can be done using prob-

abilistic functions also. However, statistical methods

have been widely distributed recently, since they can

be used together with Markov Random Fields (MRF)

to enhance the quality of the segmentation signiﬁ-

cantly (Wang et al., 2006).

First, we developed a deterministic method which

classiﬁes the pixels independently, since that way, we

could perform a relevant quantitative comparison of

the different color spaces. After that we gave a prob-

abilistic interpretation to this model and we inserted

it into a MRF framework which we developed ear-

lier (Benedek and Szir

anyi, 2006). We compared the

different results after MRF optimization qualitatively

and observed similar relative performance of the color

spaces to the deterministic model.

Another important point of view regarding the cate-

gorization of the algorithms in (Prati et al., 2003) is

the discrimination of the non parametric and para-

metric cases. Non parametric, or ’shadow invariant’

methods convert the video images into an illuminant

invariant feature space: they remove shadows instead

of detecting them. This task is often performed by a

color space transformation, widely used illumination-

invariant color spaces are e.g. the normalized rgb

(Cavallaro et al., 2004),(Paragios and Ramesh, 2001)

and C

spaces (Salvador et al., 2004). (We re-

fer later to the normalized rgb as rg space, since

the third color component is determined by the ﬁrst

and second.) In (Salvador et al., 2004) we ﬁnd an

overview on these approaches indicating that several

assumptions are needed regarding the reﬂecting sur-

faces and the lightings. We have found in our experi-

ments that these assumptions are usually not fulﬁlled

in an outdoor environment, and these methods fail

several times. Moreover, we show later that the rg

and C

spaces are less effective also in the para-

metric case.

For the above reasons, we developed a parametric

model: we extracted feature vectors from the actual

and mean background values of the pixels and applied

shadow detection as solving a classiﬁcation problem

in that feature space. This approach is widespread in

the literature, and the key points are the way of feature

extraction, the color space selection and the shadow-

domain description in the feature space. In Section

3, we introduce the feature vector which character-

izes the shadowed pixels effectively. In Section 4,

we describe the chosen shadow domain in the feature

space, and deﬁne the deterministic pixel classiﬁcation

method. We show the quantitative classiﬁcation re-

sults with the deterministic model regarding ﬁve real-

world video sequences in Section 5. Finally, we in-

troduce the MRF framework and analyse the segmen-

tation results in Section 6.

We use three assumptions in the paper: (1) The cam-

era stands in place and has no signiﬁcant ego-motion.

(2) The background objects are static (e.g. there is no

waving river in the background), ad the topically valid

’background image’ is available in each moment (e.g.

by the method of (Stauffer and Grimson, 2000)). (3)

There is one emissive light source in the scene (the

sun or an artiﬁcial source), but we consider the pres-

ence of additional effects (e.g. reﬂection), which may

change the spectrum of illumination locally.

3 FEATURE VECTOR

Here, we deﬁne features for a parametric case where

a shadow model can be constructed including some

challenging environmental conditions. First, we in-

troduce a well-known physical approach on shadow

detection with marking that its model assumptions

may not be fulﬁlled in real-world video scenes. In-

stead of constructing a more difﬁcult illumination

model, we overcome the appearing artifacts with a

statistical description. Finally, the efﬁciency of the

proposed model is validated by experiments.

3.1 Physical Approach on Shadow

Detection

According to the illumination model (Forsyth, 1990)

the response g(s) of a given image sensor placed at

pixel s can be written as

g(s) =

e(λ, s)ρ(λ, s)ν(λ)dλ, (1)

where e(λ, s) is the illumination function, ρ(s) de-

pends on the surface albedo and geometric, ν(λ) is

the sensor sensitivity. Accordingly, the difference in

the shadowed and illuminated background values of

a given surface point is caused by the different local

value of e(λ, s) only. For example, outdoors, the il-

lumination function is the composition of the direct

(sun), diffused (sky) and reﬂected (from other non-

emissive objects) light components in the illuminated

background, while in the shadow the effect of the di-

rect component is missing.

Although the validity of eq. (1) is already limited by

several scene assumptions (Forsyth, 1990), in general,

it is still too difﬁcult to exploit appropriate informa-

tion about the corresponding background-shadow val-

ues, since the components of the illumination func-

tion are unknown. With further strong simpliﬁcations

(Forsyth, 1990) eq.(1) implies the well-known ’con-

stant ratio’ rule. Namely, the ratio of the shadowed

(s) and illuminated value g

(s) of a given surface

point is considered to be constant over the image:

(s)

= A, (2)

where A is the shadow ’darkening factor’, and it does

not depend on s.

In the CCD camera model (Forsyth, 1990) the RGB

sensors are narrow banded and the constant ratio

rule is valid for each color channel independently.

Accordingly, the shadow descriptor is a triple

, A

] containing the ratios of the shadowed

and illuminated background values for the red, green

and blue channels. Due to the deviation of the scene

properties from the model assumptions (Forsyth,

1990), imprecise estimation of the background values

(Stauffer and Grimson, 2000) and further artifacts

caused by video compression and quantiﬁcation,

the ratio of the shadowed and estimated background

values is never constant. However, to prescribe a

domain instead of a single value for the ratios results

a powerful detector (Siala et al., 2004). In this

way, shadow detection is a one-class-classiﬁcation

problem in the three dimensional color ratio space.

3.2 Constant Ratio Rule in Different

Color Spaces

In this section, we examine, how can we use the pre-

vious physical approach in different color systems.

We begin the description with some notes. We as-

sume that the video images are originally available

in the RGB color space, and for the different color

space conversions, we use the equations in (Tkalcic

and Tasic, 2003). The ITU D65 standard is used for

calibration of the CIE L*u*v* and L*a*b* spaces. In

the HSV, CIE L*u*v* and L*a*b* spaces we should

discriminate two types of color components. One

component is related to the brightness of the pixel (V,

respectively L*; we refer them later as ’luminance’

components), while the other components correspond

to the ’chrominances’. We classify the color spaces

also: since the normalized rg and C

spaces con-

tain only chrominance components we will call them

’chrominance spaces’, while grayscale and RGB are

purely ’luminance spaces’. In this terminology, HSV,

CIE L*u*v* and L*a*b* are ’mixed spaces’.

As we stated in the last section, the ratios of the shad-

owed and illuminated values of the R, G, B color

channels regarding a given pixel are near to a global

reference value [A

, A

]. In the following, we

show by experiments that the ’constant ratio rule’ is a

reasonable approximation regarding the ’luminance’

components of other color spaces also.

While shadow may darken the ’luminance’ values of

the pixels signiﬁcantly the changes in the ’chromi-

nances’ is usually small. In (Cucchiara et al., 2001),

the hue difference was considered as a zero-mean

noise factor. This approach is sometimes inaccurate,

for example outdoors, due to the ambient light of the

blue sky, the shadow shifts to the ’blue’ color domain

(Fig 1, third column). We show that modeling the off-

set between the shadowed and illuminated ’chromi-

nance’ values of the pixels with a Gaussian additive

term is appropriate.

To sum it up, if the current value of a given pixel in a

given color space is [x

, x

] (the indices 0, 1, 2 cor-

respond to the different color components), the esti-

mated background value is there [m

, m

], we de-

ﬁne the shadow descriptor

ψ = [ψ

, ψ

] by the fol-

lowing. For i = {0, 1, 2}:

• If i is the index of a ’luminance’ component:

(s) =

(s)

. (3)

• If i is the index of a ’chrominance’ component:

(s) = x

(s) −m

(s). (4)

We classify s as shadowed point, if its

ψ(s) value lies

in a prescribed domain.

The efﬁciency of this feature selection can be ob-

served in Fig. 1, where we plot the one dimensional

marginal histograms of the occurring ψ

, ψ

and

values for manually marked shadowed and fore-

ground points of a 100-frames long outdoor surveil-

lance video sequence (’Entrance pm’). Apart from

some outliers, the shadowed ψ

values lie for each

color space and each color component in a ’short’ in-

terval, while the difference of the upper and lower

bounds of the foreground values is usually greater.

However, there is signiﬁcant overlap between the

one dimensional foreground and shadow histograms,

therefore, as we examine in the next section, an effec-

tive shadow domain description is needed.

We deﬁne the descriptor in grayscale and in the rg

space similarly to eq. (3) and (4) considering that

will be a one, respectively two dimensional vector in

these cases.

Figure 1: One dimensional projection of histograms of foreground (red) and shadow (blue) ψ values in the ’Entrance pm’ test

sequence.

Figure 2: Two dimensional projection of foreground (red) and shadow (blue) ψ values in the ’Entrance pm’ test sequence.

Green ellipse is the projection of the optimized shadow boundary.

4 SHAPE OF THE SHADOW

DOMAIN

The shadow domain is usually deﬁned by a mani-

fold having a prescribed number of free parameters,

which ﬁt the model to a given scene/situation. Previ-

ous methods used different approaches. The domain

of shadows in the feature space is usually an inter-

val for grayscale images (Wang et al., 2006). Re-

garding color scenes, this domain could be a three

dimensional rectangular bin (Cucchiara et al., 2001):

ratio/difference values for each channel lie between

deﬁned threshold; an ellipsoid (Mikic et al., 2000), or

it may have general shape, like in (Siala et al., 2004).

In the last case a Support Vector Domain Description

is proposed in the RGB color ratios’ space.

By each domain-selection we must consider overlap

between the classes, e.g. there may be foreground

points whose feature values are in the shadow do-

main. Therefore, the chosen shadow-domain should

be not only large enough, containing ’almost all’ the

feature values corresponding to the occurring shad-

owed points, but also ’narrow’ to decrease the num-

ber of the background or foreground points which are

erroneously classiﬁed as shadows.

Accordingly, if we ’only’ prescribe that a shadow

descriptor should be accurate, the most general do-

main shape seems to be the most appropriate. How-

ever, in practise, a corresponding problem appears:

the shadow domain may alter signiﬁcantly (and often

rapidly) in time due to the changes in the illumination

conditions, and adaptive models are needed to follow

these changes. It is sometimes not possible to train

a model with supervision regarding each forthcoming

case of illumination. Therefore, those domains are

preferred, which have less free parameters, and we

can construct an update strategy regarding them.

For these reasons, we used an elliptical shadow do-

main descriptor having parallel axes with the xyz co-

ordinate axes:

Pixel s is shadowed ⇔

∑

i=0



(s) −a



≤ 1, (5)

where {a

, b

| i = 0, 1, 2} are the shadow domain pa-

rameters. For these parameters, a similar update pro-

cedure can be constructed to that we introduced in

(Benedek and Szir

anyi, 2006). We found in the exper-

iments, that the parameters of the ’chrominance’ com-

ponents are approximately constant in time. Although

the mean darkening ratio of the ’luminance’ compo-

nents may change signiﬁcantly, it can be estimated

by ﬁnding the peak of the joint foreground-shadow ψ

histograms, which can be constructed without super-

vision, with an effective background subtraction algo-

rithm (e.g. (Stauffer and Grimson, 2000)).

We note that with the SVM method (Siala et al.,

2004), the number of free parameters is related to the

number of the support vectors, which can be much

greater than the six scalars of our model. Moreover,

for each situation, a novel SVM should be trained. For

these reasons, we preferred the ellipsoid model, and

in the following we examine its limits. For the sake

of completeness, we note that the domain deﬁned by

eq. (5) becomes an interval if we work with grayscale

images, and a two dimensional ellipse in the rg space.

We visualize the shadow domain of the ’Entrance pm’

test sequence in Fig. 2, where the two dimensional

projection of the occurring foreground and shadow

ψ values are shown corresponding to different color

space selections. We can observe that the components

of vector

ψ are strongly correlated in the RGB space

(and also in C

), and the previously deﬁned el-

lipse cannot present a narrow boundary. (It would

be better to ﬁt an ellipse with arbitrary axes, but that

choice would cause more free parameters in the sys-

tem.) In the HSV space, the shadowed values are not

within a convex hull, even if we considered that the

hue component is actually periodical (hue = k ∗ 2π

means the same color for each k = 0, 1, . . .). Based

on the above facts, the CIE L*u*v* space seems to

be a good choice. In the next section, we support this

statement by experimental results.

5 COMPARATIVE EVALUATION

WITH THE ELLIPSE MODEL

In this section, we show the tentative limits of the el-

liptical shadow domain deﬁned by eq. (5). The evalu-

ations were done through manually generated ground

truth sequences regrading the following ﬁve videos:

• ’Laboratory’ test sequence from the benchmark

set (Prati et al., 2003). This shot contains a simple

indoor environment.

• ’Highway’ video (from the same benchmark set).

This sequence contains dark shadows but ho-

mogenous background without illumination arti-

facts.

• ’Entrance am’, ’Entrance noon’ and ’Entrance

pm’ sequences captured by the ’Entrance’ (out-

door) camera of our university campus in different

parts of the day. These sequences contain difﬁcult

illumination and reﬂection effects and suffer from

sensor saturation (dark objects and shadows).

The evaluation metrics was the foreground-shadow

discrimination rate. Denote the number of correctly

identiﬁed foreground pixels of the evaluation se-

quence by T

. Similarly, we introduce T

for the num-

ber of well classiﬁed shadowed points, A

and A

the number of all the foreground, respectively shad-

owed ground truth points. The discrimination rate is

deﬁned by:

D =

+ T

+ A

. (6)

Since the goal is to compare the limits of the dis-

crimination regarding different color systems, we op-

timized the parameters in eq. (5) through the training

data with respect to maximize the discrimination rate.

We summarized the discrimination rates in Fig. 3,

regarding the test sequences. We can observe that

the CIE L*a*b* and L*u*v* produce the best re-

sults. However, the relative performance of the other

color systems is strongly different in different videos

(see also Table 1). In sequences containing dark

shadows (Entrance pm, highway), the ’chrominance

spaces’ produce poor results, while the gray, RGB and

Lab/Luv results are similarly effective. If shadow is

brighter (Entrance am, Laboratory), the performance

of the ’chrominance spaces’ becomes reasonable, but

the ’luminance spaces’ are relatively poor. (In this

case, shadow is characterized better by the illuminant

invariant features than the luminance darkening do-

main). Since the hue coordinate in HSV is very sensi-

tive to the illumination artifacts (Section 3), the HSV

space is effective only in case of light-shadow.

Figure 3: Foreground-shadow discrimination coefﬁcient (D in eq. (6)) regarding different sequences.

Figure 4: MRF segmentation results with different color models. Test sequences (up to down): ’Laboratory’, ’Highway’,

’Entrance am’, ’Entrance pm’, ’Entrance noon’.

6 SEGMENTATION BY USING

BAYESIAN OPTIMIZATION

For practical use, the above color model should be

inserted into a background-foreground-shadow seg-

mentation process. Since we want to test the color

model itself, we use a Markov Random Field (MRF)

optimization procedure (Geman and Geman, 1984) to

get the globally optimal segmentation upon the above

model.

The results in the previous section conﬁrm that using

the deﬁned elliptical shadow domain, the CIE L*u*v*

color space is the most effective to separate shadowed

and foreground pixels only considering their colors,

if we have enough training data. However, in several

applications, we should consider the following facts:

1. Representative ground truth foreground-shadow

points are not available, the optimal ellipse param-

Table 1: Indicating the two most successful and the two less

effective color spaces regarding each test sequence. We also

denote the mean of the darkening factor for shadows in the

third column.

Video Scene Dark Worst Best

Laboratory indoor 0.73 gray,

RGB

Luv,

Lab

Entrance am outdoor 0.50 gray,

RGB

Luv,

Lab

Entrance pm outdoor 0.39 C

Luv,

Lab

Entrance

noon

outdoor 0.35 C

Luv,

Lab

Highway outdoor 0.23 C

Luv,

RGB

eters should be estimated somehow.

2. The classiﬁcation of a given pixel is usually done

considering not only its color, but also the class of

the neighbors (MRF).

Here we suit the proposed model to an adaptive

Bayesian model-framework, and show that the advan-

tage of using the appropriate color space can be mea-

sured directly in the applications.

The segmentation framework is a Markov Random

Field (Geman and Geman, 1984), more speciﬁcally

a Potts model (Potts, 1952). An image S is consid-

ered to be a two-dimensional grid of pixels (sites),

with a neighborhood system on the lattice. The pro-

cedure assigns a label ω

to each pixel s ∈ S form the

label-set: L = {bg,sh,fg} corresponding to the three

classes: foreground (fg), background (bg) and shadow

(sh). Therefore, the segmentation is equivalent with

a global labeling Ω = {ω

| s ∈ S}. Each class at

each pixel position is characterized by a conditional

density function: p

(s) = P(x

|ω

= k), k ∈ L, s ∈ S.

Eg. p

(s) is the probability of the fact that the back-

ground process generates the observed color value x

at pixel s.

Following the Potts model, the optimal segmentation

corresponds to the labeling which minimizes:

Ω = argmin

Ω

∑

s∈S

−p

(s) +

∑

r,q∈S

Φ(ω

, ω

), (7)

where the Φ term is responsible for getting

smooth, connected regions in the segmented image.

Φ(ω

, ω

) = 0 if q and r are not neighboring pixels,

otherwise:

Φ(ω

, ω

) =



−β if ω

= ω

+β if ω

6= ω

The deﬁnition of the density functions p

(s) and

(s) s ∈ S is the same, as we deﬁned in (Benedek

and Szir

anyi, 2006). We use a mixture of Gaus-

sian model for the pixel values in the background,

where the parameters are determined using (Stauf-

fer and Grimson, 2000). The foreground probabilities

come from spatial pixel value statistics (Benedek and

Szir

anyi, 2006).

Before inserting our model in the previously deﬁned

MRF framework, we give to the shadow-classiﬁcation

step deﬁned in Section 4 a probabilistic interpretation.

We rewrite eq. (5): we match the current

ψ(s) value

of pixel s to a probability density function f (

ψ(s)),

and decide its class:

pixel s is shadowed ⇔ f (ψ(s)) ≥ t. (8)

The domains deﬁned by eq. (5) and eq. (8) are equiv-

alent, if f is a Gaussian density function (η):

f (

ψ(s)) = η(ψ(s), µ

, Σ

) =

(2π)

detΣ

exp



−

(

ψ(s) − µ

)

−1

(ψ(s) − µ

)



with the following parameters: µ

= [a

, a

]

= diag{b

, b

}, while t = (2πb

)

−

Using Gaussian distribution for the occurring fea-

ture values is supported also by the one dimensional

marginal histograms in Fig. 1.

In the following, the way of using the previously de-

ﬁned probability density functions in the MRF model

is straightforward: p

(s) = f (

ψ(s)). The ﬂexibil-

ity of this MRF model comes from the fact that we

deﬁned ψ(s) shadow descriptors for different color

spaces differently in Section 3. The method sets the

parameters of the class models adaptively, similarly to

(Benedek and Szir

anyi, 2006). Using a desktop com-

puter, and the ICM MRF-optimization technique, the

algorithm runs with 3fps on 320×240 video frames.

We compared the segmentation results using differ-

ent color spaces in the MRF model (Fig. 4), and ob-

served that the quality of the segmentation depends

on the used color space similarly to that we measured

in Section 5 .

7 CONCLUSION

This paper examined the color modeling problem of

shadow detection. We developed a model framework

for this task, which can work with different color

spaces. Meanwhile, the model can detect shadows un-

der signiﬁcantly different scene conditions and it has

a few free parameters which is advantageous in prac-

tical point of view. In our case, the transition between

the background and shadow domains is described by

statistical distributions. With this model, we com-

pared several well known color spaces, and observed

that the appropriate color space selection is an impor-

tant issue regarding the segmentation results. We val-

idated our method on ﬁve video shots, including well-

known benchmark videos and real-life surveillance

sequences, indoor and outdoor shots, which contain

both dark and light shadows. Experimental results

show that CIE L*u*v* color space is the most efﬁ-

cient both in the color based clustering of the indi-

vidual pixels and in the case of Bayesian foreground-

background-shadow segmentation.

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