Journal of Software Engineering and Applications, 2011, 4, 235-243
doi:10.4236/jsea.2011.44026 Published Online April 2011 (http://www.SciRP.org/journal/jsea)
235
Fractal Dimension Based Shot Transition
Detection in Sport Videos
Efnan Sora Gunal1, Selcuk Canbek2, Nihat Adar2
1Department of Electrical and Electronics Engineering, Eskisehir Osmangazi University, Eskisehir, Turkiye; 2Department of Com-
puter Engineering, Eskisehir Osmangazi University, Eskisehir, Turkiye.
Received March 23rd, 2011; revised March 28th, 2011; accepted April 2nd, 2011.
ABSTRACT
Increase in application fields of video has boosted the demand to analyze and organize video libraries for efficient
scene analysis and information retrieval. This paper addresses the detection of shot transitions, which plays a crucial
role in scene analysis, using a novel method based on fractal dimension (FD) that carries information on roughness of
image intensity surface and textural structure. The proposed method is tested on sport videos including so ccer and ten-
nis matches tha t co n tain co n siderab le amoun t of ab rup t and g radual shot trans itions. Exp erimenta l results indicate that
the FD based shot tran sition detection method offers promising performance with resp ect to pixel and histogram based
methods available in the literature.
Keywords: Sce ne An al ysis , Shot Transition, Fractal Dimension, Differential Box Counting
1. Introduction
Video can be simply defined as an audio-visual informa-
tion type. With the rapid advances on communication
technology, computer performance and storage media,
video is now available on various applications such as
internet conferencing, multimedia authoring systems, e-
education and video-on-demand systems. As the applica-
tion fields of video increase, the demand for organizing
video scenes and retrieving the desired information in
huge database increase as well. As a consequence, scene
analysis on video has become an important research topic
[1,2].
Scenes are formed by semantically related individual
shots that are uninterrupted segments of a video frame
sequence with static or continuous camera motion [3].
Accurate shot transition detection therefore plays a cru-
cial role to organize video contents into meaningful parts
for scene analysis [4]. Shot transitio ns may occur with ei-
ther abrupt or gr adual shot transition. In abrup t shot tran-
sition, the change of video content occurs over a single
frame. In gradual shot transition, however, the content
change takes place gradually through a short sequence of
frames. The gradual transition is also divided into several
subgroups such as fading, dissolving, wiping, noise and
camera movements (pan, tilt, zoom) [5].
Performance of shot transition detection methods di-
rectly depends on the features that are used to represent
the video content. Existing shot transition detection tech-
niques utilize differences on features over consecutive vi-
deo frames. Pixel differences and histogram differences
are the most widely used approaches among all [6-8].
In our study, we propose a novel shot transition detec-
tion approach which employs fractal dimension (FD) in-
formation. FD, which was introduced by Mandelbrot [9],
is an important tool to extract roughness of textural fea-
tures from images. Most of the real-world objects have
complex and irregular structures that cannot be described
by using ideal mathematical shapes such as cubes, cones
and cylinders defined in Euclidean geometry. It is how-
ever easier to characterize these objects by their FD. Us-
ing FD in image feature extraction and segmentation is
induced by the observation that FD has a strong correla-
tion with human judgment of surface roughness and is re-
latively insensitive to image deformation as well [10]. FD
has been previously applied to many areas in image pro-
cessing and pattern recognition. FD, which is calculated
from gray level images [11], can be used as a feature in
pattern recognition process. Textural segmentation, clas-
sification, shape analysis are applicable research areas of
FD in satellite, medical and natural images [12,13]. Im-
age zooming [14], video coding [15] and compression
[16,17] are other research topics where FD is used as a

Fractal Dimension Based Shot Transition Detection in Sport Videos 236
feature. Reference [18] is one of the few studies where
FD is used for scene analysis purpose. FD is here emplo-
yed as one of the features for scene extraction process ra-
ther than shot transition detection. In the regarding study,
shot transition detection, which is an important part of
scene extraction job, is carried out by pixel-difference
based motion in tensity method with simple threshold ap-
proach. Furthermore, it has been indicated that the per-
formance of shot transition detection is not good at all es-
pecially for gradual transitions.
In our study, the proposed shot transition detection
method utilizes FD difference (FDD) values of consecu-
tive video frames. Using FD rather than pixel or histo-
gram information would help more to define roughness
of image intensity surface and textural information of vi-
deo frames so that locations of shot transitions can be de-
tected with higher precision. Benefits of using FD for shot
transition detection are previously shown in [19] particu-
larly for gradual transitions. In add ition to getting benefit
from FD information of video frames in shot transition
detection, this study (originated from [20]) offers addi-
tional novelties and improvements with respect to [19].
FD values are now estimated from sub-regions of video
frames. In this way, locations of the shot transitions are
emphasized much clearly. Another novelty of the study is
on computation of FD information itself. Standard FD es-
timation method is now simplified so that computational
complexity is drastically reduced with just a slight devia-
tion on the obtained FD value. FD based shot transition
detection method is tested on sport videos including soc-
cer and tennis matches, which contains considerable
amount of shot transitions with respect to other videos.
The proposed method is compared with well-known pix-
el and histogram based methods. Experimental results
reveal that the proposed method not only offers compa-
rable performance with respect to the abovementioned
detection methods but also surpasses them in some cases
as well.
Organization of the rest of the paper is as follows:
Section 2 summarizes the pixel and histogram based shot
transition detection approaches that are available in the
literature. In Section 3, computation of FD is briefly de-
scribed. Section 4 introduces the proposed shot transition
detection method based on FD. Section 5 includes expe-
rimental work and results. Finally, conclusions of the pa-
per are given in Section 6.
2. Pixel and Histogram Based Shot
Transition Detection
In the literature, as mentioned before, pixel differences
and histogram differences are the most widely used ap-
proaches for shot transition detection. Sum of Absolute
Differences (SAD) is the fundamental pixel difference
method. In this approach, the difference between two fra-
mes is obtained by calculating the value that represents
the overall chan ge in p ix el intensities o f imag es [4,6 ]. Th e
sum of absolute pixel-wise intensity differences between
two frames is used as a frame difference as shown in (1),
where 1
f
and 2
f
are intensity values of consecutive
frames, X and Y are the height and weight, x and y
represent pixel coordinates of the frames, respectively.
All pixel difference methods are very sensitive to noise
and camera motion [4].
  
11
121 2
00
1
,,,
XY
xy
SADf ff xyfxy
XY



 (1)
Histogram difference method is another widely used
approach in shot transition detection. Histogram repre-
sents the distribution of pixel values in an image. Gray
level and color histograms are very useful tools to meas-
ure difference between two frames [4,8,21,22]. There
exist various histogram difference methods such as bin to
bin difference (B2B) and histogram intersection (INT)
methods [23,24]. B2B is computed as in (2) where 1 h
and 2 h are histograms of consecutive frames and N is
the number of pixels in a single frame.
  
2121 2
1
,2
BB i
Dhh hihi
N

 (2)
Histogram intersection of two consecutive frames can
be obtained usi ng






12
12
min ,
Intersection ,i
hihi
hh N  (3)
Histogram difference (
I
NT
D) is then computed using

12
1 Intersection,
INT
Dhh (4)
In [6,8], pixel and histogram based methods are com-
pared and it is observed that the histogram methods pro-
vide a good trade-off between accuracy and speed. All
these methods however have several disadvantages in de-
termining the shot tran sitions. They are sensitive to cam-
era motion, large-sized object motion, noise, sudden ob-
ject appearance, pan and zoom which make it difficult to
determine gradual transitio ns particularly.
3. Fractal Dimension
Several FD calculation methods have been developed
following the increase in usage of fractal geometry for
different research fields. The choice of which method to
use depends on the application field and algorithmic
complexity. All these FD computation method s, however,
follow the same principles of Hausdorff-Besicovitch (D)
Dimension [25]. D dimension of a bounded set A in n

is a real number used to characterize the geometrical

Fractal Dimension Based Shot Transition Detection in Sport Videos 237
complexity of A. Here, the set A is called a fractal set if
its D dimension is strictly greater than its topological
dimension [26]. D dimension of a subset X of Euclidean
space can be replaced by counting number of open balls
used to cover X.
The box counting dimension (
B
D) of set A is defined
as



0
log
lim log 1
r
Br
N
Dr

 (5)
where r
N is the number of the boxes of size r needed to
cover A [9].
According to [11], gray level values are assumed to be
a 3D surface to calculate the FD of an image. Three di-
mensional view of gray scale image given in Figure 1(a)
is shown in Figure 1(b ).
FD can be estimated by using well known Differential
Box Counting (DBC) method, also known as Blanket
method. To calculate r N, the image of size M × M pix-
els is scaled down to a size s × s (Figure 2) where

12sM and s is an integer. r is the scaling ratio
and calculated using

rsM (6)
The image is considered as 3-D space with (x, y, z)
axes. While (x, y) is denoting 2-D position, the z axis
denotes gray level. After (x, y) space is partitioned into
grids of size (s × s), each grid contains column of boxes
of size s × s × h. If the total number of gray levels is G
then (G/h) is equal to (M/s). Let the minimum and max-
imum gray level of the image in the (i, j) th grid fall in
box number k and l, respectively. For each (i, j) th grid,
(,)
r
nij is the contribution of r N as shown in (7).
Considering the contributions from all grids, r N is then
obtained as in (8).

,1
r
nijlk  (7)

,,
rr
ij
Nnij (8)
r
N is obtained for different values of r, i.e., different
values of s. Then, using (5), FD is estimated using linear
least square fitting (LSF) of log(r N) against log(1/r).
4. FD based Shot Transition Detection
In this study, video frames, which will be segmented into
shots, are first converted to gray scale before computing
FD. Here, gray level values are assumed to be a 3D sur-
face just as in standard DBC method. Instead of compu-
ting FD value for complete frame, each frame is first par-
titioned into four regions of equal size as illustrated in
Figure 3.
Features that are used in the shot transition detection
(a) (b)
Figure 1. (a) 100 × 100 gray scale image; (b) Corresponding
3-D intensity surface.
Figure 2. Image intensity surface.
(a)
(b)
Figure 3. Regions in consecutive frames in (a) soccer video
(not shot transition), (b) tennis video (shot transition).

Fractal Dimension Based Shot Transition Detection in Sport Videos 238
are then obtained by calculating average of these regional
FD differences (FDD ) as in (9). Hence, four differ ent re-
gions in video frame have separate contributions to over-
all FDD value.


11
11
1
4kkkk
kk k k
aabb
ccdd
F
DDFDFD FD FD
FD FD FDFD




(9)
Figure 4 shows shot transitions and feature differences
for one of the test videos used in the study. The figure
indicates how the shot transitions are detected using one
(complete) and four sub-regions. It is obvious that divid-
ing frames into smaller sub-regions in feature extraction
stage provides a noise reduction on feature difference
values so that locations of the shot tran sitions are empha-
sized much more. It is verified that the same statement is
true for the other test videos. Therefore, video frames are
divided into four sub-regions to compute FDD in the
experiments.
While computing regional FD values, standard DBC
method [11], which is previously explained, may be used.
This method employs all possible point pairs between
two scales for LSF which is a time consuming task. In
our proposed method, instead of standard DBC, a simpli-
fied version is developed as another novelty. In this ver-
sion, only two pairs of

,
r
Nr are used to reduce com-
plexity and increase efficiency while calculating FD for
each frame. The two points (p1, p
2) corresponding to


,
r
Nr pairs provide together an equation of a line as
given in (10). Hence, the slope of the resulting line is
equal to FD. This process is called as simplified DBC
(SDBC) due to relatively less computation. Figure 5(a)
shows the graph of


loglog 1
r
Nr for a sample video
frame using DBC metho d in the range of (2 2)sM .
Figure 5(b) shows graph of
 
loglog 1
r
Nr and the
best fitted line joining p1 and p2 points for the same
video frame using SDBC.



  
21
21
21
21
log log
11
log log
rr
pNpN
FD
pp
rr


 


 

 

(10)
In standard DBC method [11], complexity of r
N cal-
culation, which is used to compute FD of an M × M im-
age, is


2
M. During this estimation, r N values are
calculated using the approximation given in (5) for


21M

different values of r. Subsequently, equation
of a line is obtained using all

,
r
Nr pair s through LSF
algorithm which has a complexity of

M
. Thus,
overall complexity of DBC algorithm, which is used to
compute FD of an image, equals to

3
M
. On the
other hand, SDBC method uses just two pairs of


,
r
Nr
for FD estimation as in (10). As a consequence, com-
plexity of SDBC algorithm is just

2
M.
(a)
(b)
Figure 4. FDD values for (a) Single FD per frame, (b) four FDs per frame in a video. Diamonds indicate actual locations of
shot transitions.

Fractal Dimension Based Shot Transition Detection in Sport Videos 239
(a)
(b)
Figure 5. Graph of log(Nr) – log(1/r) for single video frame
using (a) DBC for


22sM, (b) DBC and the line
fitted using SDBC method through points

12
p,p where


12
=14, =140
pp
rr .
FD values that are computed by SDBC are pretty close
to the ones obtained by standard DBC method. Moreover,
achieving low processing time in computing the FD dif-
ferences of consecutive video frames is much more im-
portant than computing the FD values precisely in shot
transition detection process. Figure 6 shows the similar-
ity between SDBC and standard DBC for the features of
a test video. Shot transition locations can be clearly ob-
served in both cases (Figure 6(a) and (b)). Figure 6(c)
shows the absolute error between FDD values obtained
by DBC and SDBC methods. Low error values prove that
SDBC provides quite similar FD values to DBC method.
As explained be fo re, when FD of images are computed
using DBC method, the images are divided into (s × s)
grids, where 12sM . Since the grids contain few
amounts of pixels for small values of s, r n would be
close to 1. Hence, r N gets close to2 1r. It is shown in
Figure 5 that the slope of the line starts changing for
small values of s. To overcome this problem, minimum
value of s is determined as 6. Thus, low limit of r value
at point 2
p is computed as 1/40 using (6). In DBC me-
thod, r N is an integer between 2
1r and 3 1r. For
s = M/2, r N is in the range of (4, 8). On the other hand,
for s = M/4, r N would have 49 possible values between
(16, 64). In this sense, high limit of r value at point 1 p
is defined as 1/4. Consequently, r N computation be-
comes more accurate. Additionally, minimum average
absolute error is achieved when FDD features, which are
obtained for different values of

12
,pp using DBC
and SDBC method, are compared (Figure 6(c)).
After computation of FDD values, shot transitions can
be located using a threshold approach. Thresholding is an
important tool in video shot transition detection. Among
different threshold techniques [27-29], typical approach
is to define a fixed threshold value. Nevertheless, this
approach may not provide good detection performance
because every video has different characteristics. While a
high threshold value increases the number of missed de-
tections, a lower threshold increases the number of false
detections. In our study, therefore, a dynamic threshold
method (DTM) is used where threshold is dynamically
changed during shot transition detection process [30].
The threshold in DTM is computed by considering the
presence of a shot transition and the variation of frame
contents. DTM consists of two threshold stages: fixed
and dynamic. Initially, a fixed threshold is used. After a
shot transition occurs, a dynamic threshold then takes
place of the fixed one. Dynamic value is determined as
given in (11), where low T is a fixed threshold, high T is a
dynamically raised threshold, and t is the elapsed time
after a shot transition occurrence.




dynlowhigh lowhighlow
TTTTftTT . (11)
In (11), time varying function


f
t can be linearly
defined as,
 
max
1 0max
t
ft t
t
 , (12)
where max
t is calculated by
1
max
0
max 1
nk
nk
t
tn



. (13)
In all shot transition detection methods, which are
tested in the study, DTM is used as the thresholding tool.
5. Experimental Study
In the experimental work, soccer and tennis match videos
containing various types of shot transitions are used to
justify the proposed method. The reason to use sport

Fractal Dimension Based Shot Transition Detection in Sport Videos 240
(a)
(b)
(c)
Figure 6. FDD values of a test video, (a) SDBC method (4 Partitions/Frame); (b) DBC method; (c) Absolute error between
DBC and SDBC


12
=14, =140
pp
rr . Diamonds indicate actual locations of shot transitions.
videos particularly for this study is that lots of object
moves and shot transitions are present in this type of
videos. A total of seven videos consisting of 17,985 fra-
mes are used in testing. The frame size is 240 × 320 pix-
els. Before testing, actual locations of shot boundaries
through the test videos are identified by a thorough ma-
nual analysis. Thus, total numbers of gradual (dissolve,
pan, wipe, zoom) and abrupt shot transitions are deter-
mined as 89 and 95, respectively. Figures 7-11 contain
sample video frames from the test set displaying abrupt,
dissolve, pan, wipe, and zoom type shot transitions.
After manual detection of shot transition locations on
the test videos, the method proposed in the current study
(FDDnew), the previously proposed FDD method (FDDold)
[19], and classic methods (SAD, B2B, INT) are conduc-
ted to detect the shot transition locatio ns tagged previou-
sly. Detection performances of the methods are measured
and compared using popular F1 measure [31], which uses
both recall and precision information. Recall and preci-
sion parameters are obtained as in (14) and (15). In these
formulas, NM, NC and NF represent missed, correct and
false detections, respectively.
C
Cm
N
RECALL NN  (14)
C
CF
N
PRECISIONNN  (15)
In case of our study, recall is the ratio of number of
correctly detected shot transitions obtained by a particu-
lar method to total number of actual shot transitions. Si-
milarly, precision is the ratio of number of correctly de-
tected shot transitions to total number of correctly and
incorrectly detected shot transitions. F1 measure is then
computed usin g
12precision recall Fprecision recall

  (16)
Tables 1 and 2 show detection results for the abrupt
and gradual shot transitions respectively for all videos.
Additionally, Table 3 provides an overall analysis with-
out considering distinct types of the shot transitions. In
case of abrupt shot transitions, INT has the best perfor-
mance whereas FDDnew and B2B are runners up. More-

Fractal Dimension Based Shot Transition Detection in Sport Videos 241
(a) (b)
Figure 7. Abrupt shot transition in two consecutive frames.
(a) (b) (c)
(d) (e) (f)
Figure 8. Dissolve-type shot transition in consecutive frames.
(a) (b) (c)
(d) (e) (f)
Figure 9. Pan-type shot transition in consecutive frames.
(a) (b) (c)
(d) (e) (f)
Figure 10. Wipe-type shot transition in consecutive frames.
(a) (b) (c)
(d) (e) (f)
Figure 11. Zoom-type shot transition in consecutive frames.
Table 1. Detection results of abrupt sh ot transitions.
Method NCNFNMTotal Tr a nsitions F1
FDDnew 75 69 20 95 0.63
FDDold 69 13926 95 0.46
SAD 53 33 42 95 0.59
B2B 85 81 10 95 0.65
INT 61 5 34 95 0.76
Table 2. Detection results of gradual shot transitions.
Method NCNFNMT o tal Transitions F1
FDDnew 41 45 48 89 0.47
FDDold 49 64 40 89 0.49
SAD 9 15 80 89 0.16
B2B 35 49 54 89 0.41
INT 10 7 79 89 0.19
Table 3. Detection results of all types of shot transitions.
Method NCNFNMTotal Transitions F1
FDDnew 11611468 184 0.56
FDDold 11820366 184 0.47
SAD 62 48 122184 0.42
B2B 12013064 184 0.55
INT 71 12 113184 0.53
over, FDDnew offers a considerable improvement against
FDDold thanks to less number of false detections. In case
of gradual shot transitions, FDDnew and FDDold methods
offer the best performance. Again, number of false detec-
tions is much smaller in FDDnew method with respect to
FDDold.
If the results of overall analysis are examined in Table
3, it is obvious that the proposed method (FDDnew) sur-

Fractal Dimension Based Shot Transition Detection in Sport Videos 242
passes all the other approaches. This analysis verifies that
the proposed method offers a promising performance in
detection of shot transitions with respect to classical de-
tection methods. Moreover, it surpasses the other me-
thods in detection of gradual transitions, which is a more
challenging job than detecting abrupt transitions, as well.
6. Conclusions
In this work, FD based shot transition detection method
is proposed as alternativ e to classical pixel an d histogra m
based methods available in the literature. The proposed
method employs FD differences of consecutive video
frames to detect the shot transitions where roughness of
image intensity surface and textural information of video
frames are taken into consideration. Difference of FD
values for consecutive frames depends on the variations
of frame contents. Since these variations are very large
during the shot transitions, FD can be employed as an
alternative tool in detection of these transitions. There are
also additional novel approaches in the study other than
use of FD information for shot transition detection. The
first novelty is to utilize regional FD values instead of
single FD per video frame in detecting the difference
between consecutive frames. Using regional FD based
feature differences reduces noise that may cause false
alarm in detection process. Thus, locations of shot transi-
tion are strongly emphasized and detection performance
is improved. Another novel approach of the study is the
development of SDBC which reduces the computational
complexity of standard DBC in computation of FD val-
ues. Due to high processing cost of DBC algorithm, the
use of FD information in detection of shot transitions
may not be suitable at all. In our study, however, com-
plexity of FD calculation is significantly reduced so that
FD can be easily employed for detection purpose. More-
over, the reduction in FD computation time would speed
up not only the shot transition detection process but also
the other processes using fractal information in different
research fields. The proposed shot transition detection
method is tested on sport videos including soccer and
tennis matches and efficacy of the method is compared
with the classical pixel and histogram based methods.
Experimental results verify that the proposed method not
only offers comparable performance with respect to the
abovementioned detection methods but also surpasses
them in case of gradual shot transitions as well. As a fu-
ture work, a hybrid shot transition detection algorithm
combining classical and FDD based methods is planned
to develop.
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