Joint Key-frame Extraction and Object Segmentation for Content-based Video Analysis

21 Pages·0.404 MB·English

by  Song X.

Joint Key-frame Extraction and Object Segmentation for
(cid:3)
Content-based Video Analysis
Xiaomu Song, Member, IEEE, and Guoliang Fan, Senior Member, IEEE. y
Abstract
Key-frame extraction and object segmentation are usually implemented independently and sepa-
rately due to the fact that they are on di(cid:11)erent semantic levels and involve di(cid:11)erent features. In this
work, we propose a joint key-frame extraction and object segmentation method by constructing a
uni(cid:12)ed feature space for both processes, where key-frame extraction is formulated as a feature selec-
tion process for object segmentation in the context of Gaussian mixture model (GMM)-based video
modeling. Speci(cid:12)cally, two divergence-based criteria are introduced for key-frame extraction. One
recommendskey-frameextractionthatleadstothemaximumpairwiseinterclassdivergencebetween
GMM components. The other aims at maximizing the marginal divergence that shows the intra-
frame variation of the mean density. The proposed methods can extract representative key-frames
for object segmentation, and some interesting characteristics of key-frames are also discussed. This
work provides a unique paradigm for content-based video analysis.
Index Terms | Key-frame extraction, object segmentation, Gaussian mixture model, feature
selection, cluster divergence.
(cid:3)ThisworkissupportedinpartbytheNationalScienceFoundation(NSF)underGrantIIS-0347613(CAREER)andthe
Department of Defense EPSCoR (DEPSCoR) under Grant W911NF-04-1-0221. This work is partially published in IEEE
Workshop on Motion and Video Computing, Breckenridge, Colorado, Jan. 5-6, 2005, and IEEE International Conference
on Acoustics, Speech and Signal Processing, Philadelphia, PA, March 18-23, 2005.
yX. Song was with the School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK
74078, USA. He is now with Northwestern University, Evanston, IL 60208, USA, email: [email protected]. G. Fan is
with the School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK 74078, USA, email:
[email protected]. Guoliang Fan is the contact author.
1
1 Introduction
How to bridge the semantic gap between low-level features and high-level concepts has been a long-
standing problem in content-based video analysis [1, 2, 3]. In this paper, we address this issue by jointly
studying two video analysis tasks, i.e., key-frame extraction and object segmentation. Key-frames are
those frames important to understand video content, and key-frame de(cid:12)nition is quite subjective. It
could be related to motion, or objects, or events. Objects usually refer to either regions with homoge-
neous features (e.g., color, motion), or meaningful real world entities, which may be composed of one
or multiple regions [4]. In this paper, we refer objects to the former one. Usually, key-frame extraction
and object segmentation are implemented independently and separately using di(cid:11)erent features. Low-
level color and motion features are often used for key-frame extraction [5], which are computationally
e(cid:14)cient for time-critical applications. The extracted key-frames usually indicates signi(cid:12)cant changes in
the feature space that have limited semantic meaning. We call key-frames semantically meaningful if
they can imply some object-related behaviors/events. Supervised methods are often used to enrich the
semantical meaning of key-frames by incorporating certain templates or domain knowledge [2, 3], e.g.,
news, sports, etc. The unsupervised process could also extract semantically meaningful key-frames if
object information is involved during key-frame extraction [1, 6]. Object segmentation provides better
interpretability and manipulability of video data than key-frame extraction, while it is more challeng-
ing. In [7], most object segmentation methods can be classi(cid:12)ed into three categories: segmentation with
spatial priority, with temporal priority, and joint spatio-temporal segmentation, which attracts more
and more attention [8, 9, 10]. The idea of joint spatio-temporal video segmentation is consistent with
the nature of human vision that recognizes salient video structures in space and time simultaneously
[11]. A mean shift clustering was proposed in [8] to segment objects in space and time. The Gaussian
mixture model (GMM) was applied for joint spatio-temporal video characterization in [9]. The method
using the graph partition theory was also suggested in [10] for joint spatio-temporal video modeling.
Interesting issues arise if the two processes can be jointly considered. For example, when objects are
representedasclustersinafeaturespace,thespatio-temporalrelationshipofclustersimpliessomeobject
behaviors or events, such as running away/toward, apprearing/disappearing, enlarging/shrinking, etc,
and extracted key-frames may imply such object behaviors. In [1], the position of segmented regions
is used to extract key-frames where objects merge. In [6], shape features are used to extract key-
frames implying changes of human gestures. Moreover, it was noted that key-frames may facilitate
object segmentation in the context of GMM-based video modeling [12]. An initial set of key-frames
is (cid:12)rst selected based on the color histogram and used to estimate GMM for object segmentation [5],
and segmentation results and the trained GMM are further used to re(cid:12)ne the initial key-frames. This
method signi(cid:12)cantly reduces the computational load and improve the robustness of video segmentation.
Since key-frame extraction and object segmentation are implemented sequentially in di(cid:11)erent feature
spaces and under di(cid:11)erent criteria in [12], this method is called a \combined" approach.
2
In this work, we propose a joint key-frame extraction and object segmentation method by extending
our previous work in [12]. The idea is to formulate key-frame extraction as a feature selection process
for object segmentation in a uni(cid:12)ed feature space. Speci(cid:12)cally, in the context of GMM-based modeling
[13, 9], a video sequence is represented by spatio-temporal feature clusters, which are characterized by
multivariateGaussiancomponents(MGC)ofaGMM.Theseparabilitybetweenclustersisestimatedby
the MGC-based divergence measurements, and the frames leading to the largest cluster separability are
extracted as key-frames. Two divergence criteria are used here: maximum average interclass Kullback
Leibler distance (MAIKLD), and maximum marginal divergence (MMD) that is de(cid:12)ned as the average
distance between each of the marginal class-conditional densities and their mean [14]. Compared with
previous GMM-based video segmentation methods [9, 13, 12], key-frames with large cluster divergence
can facilitate the GMM-based video modeling and support robust object segmentation, leading to more
homogeneous segmentation results. More interestingly, since key-frame extraction is guided by cluster
divergence-based criteria, the extracted key-frames, as the by-product of this process, may contain
some object behavior/event information characterized by these spatio-temporal clusters. The key-
frames extracted by the proposed method can carry some object-level semantic information that is not
available in the key-frames extracted by using low-level features only. However, the major limitation
of the proposed method and those under the same framework [12, 9, 13] is the ine(cid:14)ciency of GMM
to handle complex objects of di(cid:11)erent low-level features (e.g., colors and motions). Nevertheless, it is
an e(cid:14)cient step of early vision. By involving region-based features, it can be further integrated with
complementary techniques to produce higher level semantically meaningful results [4, 15]. It is worth
mentioning that the major purpose of this work is to improve the performance of object segmentation
by (cid:12)nding an optima/sub-optimal key-frame set for GMM estimation and key-frame extraction is a
by-product of this process. The proposed method is a preliminary study towards new tools for (cid:13)exible
and informative content-based video analysis that may introduce new frame/object descriptors and
functionalities for MPEG-4/-7 industrial standards.
2 Joint Key-frame Extraction and Object Segmentation
Key-frameextractionandobjectsegmentationhavebeenintensivelystudiedinthepast. We(cid:12)rstbrie(cid:13)y
review several relevant methods. In [9], a probabilistic framework for spatio-temporal video modeling
was proposed, where a object (homogeneous region) is characterized by a Gaussian \blob" in a spatio-
temporal feature space, which contains color (L, a, b), time (t), and coordinate (x and y). A video of M
objectsismodeledbyaM-orderGMM.TheEMalgorithmisappliedtoestimatemodelparameters,and
the MDL criterion is used to (cid:12)nd a proper M [16]. After GMM estimation, the video is segmented into
M spatio-temporal blobs via maximum a posteriori (MAP) classi(cid:12)cation. A piece-wise implementation
is proposed in [9] to handle nonlinear and non-convex motion patterns. One major bottleneck of this
method is the high computational load because all video frames are involved for GMM estimation.
3
In[12],acombinedkey-frameextractionandobjectsegmentationapproachwasproposedtoimprove
the e(cid:14)ciency and robustness of GMM estimation. An initial set of key-frames are (cid:12)rst extracted using
the frame-wise 16(cid:2)8 2-D Hue and Saturation color histogram [5], and the GMM is estimated using
the key-frames. After object segmentation, each initial key-frame is modeled by a GMM that is used
for key-frame re(cid:12)nement. This method considerably mitigates the computational load, and improves
the robustness of model estimation by involving a compact and discriminative feature set from key-
frames. In addition, GMM-based key-frame re(cid:12)nement is able to provide more compact key-frames.
This combined approach further triggers three interesting issues: (1) How to warrant the optimality of
extracted key-frames in terms of GMM estimation or object segmentation? (2) Can we jointly optimize
key-frame extraction and object segmentation? (3) If the answer to question (2) is yes, is there any
semantically useful information (such as object’s behavior) carried by the extracted key-frames? In
this work, we address these issues by proposing a joint key-frame extraction and object segmentation
method to explore possible relationship and synergy between them.
2.1 Problem Formulation
Incontrasttoperformkey-frameextractionandobjectsegmentationwithdi(cid:11)erentfeatures, wepropose
to implement them within a uni(cid:12)ed feature space as shown in Fig. 1. In this (cid:12)gure, a video shot of
Frame index(cid:13) Key-frames(cid:13)
1(cid:13) 1(cid:13) 2(cid:13) 3(cid:13)
1(cid:13) 2(cid:13) 3(cid:13)
2(cid:13) 1(cid:13) 2(cid:13) 3(cid:13)
3(cid:13) 1(cid:13) 2(cid:13) 3(cid:13) 3(cid:13) 1(cid:13)
1(cid:13) 2(cid:13) 3(cid:13)
1(cid:13) 2(cid:13) 3(cid:13)
2(cid:13)
1(cid:13) 2(cid:13) 3(cid:13)
1(cid:13) 2(cid:13) 3(cid:13)
N(cid:13) 1(cid:13) 2(cid:13) 3(cid:13)
Video frames(cid:13) Feature space(cid:13) Video objects(cid:13)
Figure 1: An example of the uni(cid:12)ed feature space: an input video shot has three major objects.
N frames contains three major objects represented as three clusters in the feature space. Usually,
the frames within a shot represent a spatially and temporally continuous action, sharing the common
visual and often semantic-related characteristics. Consequently, there exists tremendous redundancy.
In addition, irrelevant outliers, which indicate noise and insigni(cid:12)cant objects that might randomly
appear around frame boundaries, increase the cluster overlap in the feature space. Both redundancy
and irrelevance decrease the e(cid:14)ciency of statistical modeling. Therefore, modeling performance can
be improved by removing redundant, irrelevant data/features, or in other words, by selecting most
relevant and compact data/features to boost the learning process [17]. In the case of GMM-based
object segmentation, this can be implemented by selecting most relevant key-frames for video modeling,
i.e., key-frame extraction is formulated as a feature selection process for object segmentation.
4
Feature selection methods have been intensively studied, as reviewed in [18]. Given an initial can-
didate feature set X0 = fxiji = 1;2;(cid:1)(cid:1)(cid:1);ng, feature selection aims at selecting a subset X~ from X0 so
that an criterion function F(X~) related to classi(cid:12)cation performance can be optimized:
X~ = arg max F(X): (1)
X(cid:18)X0
It is important to choose an appropriate F(X). One often used criterion is to select features to ap-
proximate the true density rather than to extract the most discriminative features. Although it is often
desired that this criterion could lead to good discrimination among classes as well, this assumption is
not always valid, and for robust classi(cid:12)cation, divergence-based feature selection criteria are preferred
[19]. In the following, we introduce two divergence-based criteria for feature selection, based on which
the new joint key-frame extraction and object segmentation method is developed.
2.2 Maximum Average Interclass Kullback Leibler Distance (MAIKLD)
Kullback Leibler distance (KLD) can measure the distance or dissimilarity between two MGCs that
model two clusters. Given M clusters characterized by M MGCs, the average interclass KLD (AIKLD)
is de(cid:12)ned as:
M M
KLD(p ;p )+KLD(p ;p )
i j j i
AIKLD(X) = C ; (2)
X X 2
i=1j=1;j6=i
where KLD(p ;p ) = p (x)ln pi(x)dx is the KLD between MGCs p (x) and p (x), and C = 2 .
i j R i pj(x) i j M(M(cid:0)1)
Ideally, the larger the AKLD, the more separability between clusters. Since key-frame extraction is
formulated as a feature selection process, we want to extract key-frames where the average pairwise
cluster divergence is maximized. Let X0 = fx ; 1 (cid:20) i (cid:20) Ng be the original video shot with N frames
i
that is represented as a set with cardinality jXj = N. Let X = fx(cid:3); 1 (cid:20) i (cid:20) N(cid:3)g be any subset of X
i
with cardinality jXj = N(cid:3) (cid:20) N. If there are M objects in the shot, the objective function is de(cid:12)ned as:
X~ = arg max AIKLD(X); (3)
X(cid:18)X0;jXj(cid:20)N
where X~ is a subset of X0 that is optimal in terms of MAIKLD. According to [20], MAIKLD is optimal
in the sense of minimum Bayes error. If we use the zero-one classi(cid:12)cation cost function, this leads to the
MAPestimation. Thereforeanoptimalsolutionto(3)resultsinanoptimalkey-framesetthatminimizes
the error probability of object segmentation. An exhaustive searching can guarantee the optimality of
X~, nevertheless, it is computationally expensive and impractical for large X0, which needs to try 2N
frame subsets. Therefore, a suboptimal but computationally e(cid:14)cient solution is more practical. A
deterministic feature selection method called Sequential Forward Floating Selection (SFFS) is used here
[21],andthesequential forward selection (SFS)methodisappliedtoinitializeSFFS[18]. WhenN isnot
very large, SFFS could even (cid:12)nd the optimal X~. In this work, key-frames are extracted from N0 (cid:20) N
5
so-called key-frame candidates. After the GMM estimation obtains its optimal estimation in terms of
MDL,theKLDbetweenMGCsp ;p isapproximatelycomputedasKLD(p ;p ) = 1 K log p(omj(cid:18)i),
i j i j K Pm=1 p(omj(cid:18)j)
wherefo jm = 1;(cid:1)(cid:1)(cid:1);Kgareallpixelfeaturevectorsofkey-framecandidatesundertest,and(cid:18) denotes
m i
the parameters of the ith MGC. Then AIKLD is calculated using (2). The search process is as follows:
(1) Start with an empty set X~, and n is the cardinality of X~, i.e., n = jX~j and initially n = 0; (2)
Use SFS to generate a combination of 2 key-frame candidates that maximizes AIKLD, and jX~j = 2;
(3) Search for one key-frame candidate that maximizes AIKLD when jX~j = n+1 , and add it to X~,
let n = n+1; (4) If n > 2, remove one key-frame candidate from X~ and compute AIKLD based on
the remained key-frame candidates in X~, and go to (5), otherwise go to (3); (5) Determine if AIKLD
increases or not after removing the selected key-frame candidate. If the answer is yes, let n = n(cid:0)1,
and go to (4), otherwise go to (3).
The search stops when n reaches a prede(cid:12)ned number or after a given number of iterations. Besides
its e(cid:14)ciency compared with those using all frames [9], this method has two major advantages: (1)
The optimal or near-optimal key-frame sets in terms of MAIKLD are extracted for model estimation.
These key-frames can provide better discriminability for GMM-based object segmentation compared
with those extracted by the color histogram [12]. (2) The algorithm is (cid:13)exible and almost threshold-
0
free. However, some issues need further consideration. First, SFFS is not very e(cid:14)cient when N is
very large. Second, the MDL-based GMM estimation that is prior to key-frame extraction is time
consuming. An alternative approach is to perform SFFS based on a high-order GMM, and the MDL-
based GMM estimation is performed on key-frames only. However, with a high-order GMM, the video
isover-segmentedandmoreclustersareoriginatedfromonesemanticobject. Toincreasethedivergence
betweentheclustersfromthesameobject,MAIKLDfavorsframeswithmoreoutliersleadingto\noisy"
key-frames. Another possible approach is to use SFS for key-frame extraction. However, it is unable to
remove redundant key-frame candidates from the candidate sets under testing. In order to reduce the
computational load, we suggest another divergence-based criterion.
2.3 Maximum Marginal Diversity
In [14], a maximum marginal diversity (MMD) criterion is proposed for e(cid:14)cient feature selection based
on the infomax principle [22], which recommends to preserve maximum information about input be-
havior while minimizing the information redundancy. In the context of classi(cid:12)cation, it tends to select
features that maximize the mutual information (MI) between the features and class labels [14]. When
the infomax principle is applied to this work, the objective function is written as:
X~ = arg max I(X;Y); (4)
X(cid:18)X0;jXj(cid:20)N
where I(X;Y) is the MI between the key-frame subset X and class label Y = f1;2;(cid:1)(cid:1)(cid:1);Mg: I(X;Y) =
p(x ;y )ln p(xi;yj) .
Pxi2XPyj2Y i j hp(xi)p(yj)i
6
Considering I(X;Y) = H(Y)(cid:0)H(YjX), where H(Y) is the entropy of the class label, and H(YjX)
is the conditional entropy. A relation between the tightest lower bound on Bayes error and H(YjX) is
derived in [14]. This relation indicates that minimizing H(YjX) (the infomax principle) is equivalent
to minimize a lower bound of Bayes error. I(X;Y) can be re-written as [14]:
I(X;Y) = p(y )KLD(p(Xjy );p(X))
X j j
yj2Y
= E [KLD(p(XjY = y );p(X))];
Y j
N(cid:3) N(cid:3) N(cid:3)
= MD(x(cid:3))+ I(x(cid:3);x(cid:3) jY)(cid:0) I(x(cid:3);x(cid:3) ) (5)
X i X i 1;i(cid:0)1 X i 1;i(cid:0)1
i=1 i=2 i=2
where MD(x(cid:3)) = E [KLD(p(x(cid:3)jY = y );p(x(cid:3)))], and x(cid:3) = fx(cid:3);x(cid:3);(cid:1)(cid:1)(cid:1)x(cid:3) g. MD(x(cid:3)) is called
i Y i j i 1;i(cid:0)1 1 2 i(cid:0)1 i
the marginal diversity (MD), and indicates the variance of the mean density. The analysis in [14] shows
that I(X;Y) can be approximated by a summation of MD values if the mutual information between
features is not a(cid:11)ected by class labels, i.e., N(cid:3) I(x(cid:3);x(cid:3) jY) = N(cid:3) I(x(cid:3);x(cid:3) ). Then maximum
Pi=2 i 1;i(cid:0)1 Pi=2 i 1;i(cid:0)1
MI becomes MMD. As generalized in [14], this condition is originated from recent studies about image
statistics, which suggest that a rough structure of pattern dependencies between some image features
followsgeneralstatisticallawsthatareindependentoftheirclasslabels. Thesefeaturesareextractedvia
various biologically plausible image transforms, such as the wavelet transform. Although this condition
is not always strictly held, at least it shows that MMD is near optimal in the sense of minimum Bayes
error.
When applying MMD to key-frame extraction, frames with the largest MD values are extracted
as key-frames. Similar to MAIKLD, MMD key-frame extraction is performed after the initial GMM
estimation. However,MAIKLDneedstotestdi(cid:11)erentcombinationsofkey-framecandidateswhileMMD
only considers the divergence in each frame and ignores the inter-frame dependence. The MD value
of key-frame candidate x(cid:3) is approximately calculated as MD(x(cid:3)) = M (cid:11)i K log p(omj(cid:18)i), where
i i Pi=1 K Pm=1 p(om)
fo jm = 1;(cid:1)(cid:1)(cid:1);Kg are all pixel feature vectors of x(cid:3), and N(cid:3) frames that have the largest MD values
m i
are selected as key-frames. N(cid:3) can be predetermined, or be adaptively determined given a threshold of
the MD value. We use the average MD of all key-frame candidates as the threshold, and any candidates
whose MD values are greater than the threshold are selected as key-frames.
2.4 Proposed Algorithm
An overview of the joint method is presented in Fig. 2. The input key-frame candidates are either all
frames in a shot, or key-frames initially selected by the color histogram [5, 12]. (Y;u;v) color features,
x (cid:0) y spatial location, and time t are used to construct the uni(cid:12)ed feature space. The input video
is modeled by a GMM that is estimated via the EM algorithm and MDL criterion. After the initial
modeling, MAIKLD or MMD is used to guide the key-frame extraction. The extracted key-frames are
applied to re-estimate the GMM, which is used to segment all frames via the MAP classi(cid:12)cation. Even
7
Object(cid:13)
Input Key-frame(cid:13)
Segmentation of(cid:13) Objects(cid:13)
Candidates(cid:13)
All Frames(cid:13)
GMM-based(cid:13) GMM Re-(cid:13)
Learned(cid:13)
Object Modeling(cid:13) estimation using(cid:13)
Models(cid:13)
(EM+MDL)(cid:13) Key-frames(cid:13)
Divergence Computation and(cid:13)
Key-frames(cid:13)
Key-frame Extraction(cid:13)
Figure 2: The (cid:13)owchart of the proposed algorithm.
though the initial GMM estimation, key-frame extraction, and model re-estimation are implemented
sequentially and separately, the whole process is well-integrated by taking into account their mutual
in(cid:13)uence in the uni(cid:12)ed feature space. Compared with the method using all frames [9] or the combined
approach using key-frames extracted from color histogram [12], it is expected that the proposed method
not only improves the computational e(cid:14)ciency by minimizing feature redundancy, but also enhances
the robustness of video modeling by reducing feature irrelevance.
As mentioned before, MAIKLD extracts key-frames that maximize the pairwise cluster divergence,
and considers the statistical characteristics of clusters within and across frames by computing AIKLD
over a group of key-frame candidates, whereas MD values are estimated in each individual frame by
assuming frame independence, and MMD selects those with the largest MD values as key-frames. Ac-
cordingly, they could extract di(cid:11)erent key-frames, although both of them are lower bounded by the
Bayes error. In terms of GMM-based video modeling, MAIKLD could extract more discriminative
key-frames than MMD because maximizing the variance of mean density does not necessarily maximize
the pairwise cluster divergence or reduce the overlap between clusters. Moreover, MMD only considers
the cluster divergence in each frame, taking a risk of overlooking inter-frame dependency. Nevertheless,
MMD is computationally more e(cid:14)cient than MAIKLD because no combinatorial search is needed.
y(cid:13)
t=a(cid:13) t=b(cid:13)
t(cid:13)
B(cid:13)
I(cid:13) A(cid:13) II(cid:13) III(cid:13)
x(cid:13)
Figure 3: Two clusters in a joint spatio-temporal feature space.
8
B(cid:13) A(cid:13)
X(cid:13) A(cid:13) X(cid:13) A(cid:13) X(cid:13)
B(cid:13)
B(cid:13)
Y(cid:13) Y(cid:13) t(cid:13)
B(cid:13) B(cid:13) A(cid:13)
X(cid:13) A(cid:13) X(cid:13) A(cid:13) X(cid:13)
B(cid:13)
Y(cid:13) Y(cid:13) t(cid:13)
(a) Runing toward/away (b) Enlarged/shrinked (c) Appearing/disappearing.
Figure 4: Clusters A and B in the feature space are corresponding to two objects. Axes X and Y are
for the spatial coordinate, and Axis-t is for the time.
2.5 Key-frame Characteristics
So far, we have addressed the (cid:12)rst two issues raised in Section 2, and now we want to study the third
issue regarding the characteristics of key-frames extracted under the new formulation. Fig. 3 shows
two clusters in a feature space de(cid:12)ned in space and time, and two temporal slices (frames A and B),
which capture the spatial locations of two clusters at time t = a and t = b, splitting the feature space
into three regions. Two clusters are spatially closest when they overlap in the x(cid:0)y plane in Region
II (the shaded area). If the clusters are associated with two real objects, then the objects are spatially
adjacent in the frames of Region II, and far away in the frames of Region I or III. By understanding
the mechanism of MAILKD or MMD for key-frame extraction, a link between low-level features and
high-level concepts could be established. MAIKLD is equivalent to minimize the Bayes error, which is
caused by the cluster overlap in the feature space. In order to minimize the Bayes error, the cluster
divergence should be maximized. Therefore, MAIKLD tends to extract key-frames where clusters have
the least overlap, i.e., Regions I and III in Fig. 3. When applying MMD, the MD value is calculated
in each individual frame. Any frame whose mean density has a su(cid:14)ciently large variance, or in other
words, whose clusters are widely dispersed in the x(cid:0)y plane will be extracted as a key-frame. Hence
the location of such frames mainly depends on the cluster dispersion in space. Below we further discuss
three speci(cid:12)c cases of object behavior.
(cid:15) Running away/toward: When multiple objects are moving away from each other, the average
cluster divergence increases so long as their colors and sizes do not change signi(cid:12)cantly. MAIKLD
tends to extract key-frames where objects are spatially far away. Also, the cluster dispersion in
9
a frame measured by MD is large when objects are far away. Therefore, MMD also extracts key-
frames where object are well separated in space. Fig. 4 (a) and (b) show the cluster distribution
when the objects are spatially close and far away, respectively.
(cid:15) Enlarging/shrinking: When an object’s size is enlarging, AIKLD usually decreases, and the vari-
ation of the mean density increases because the cluster size of that object also increases in the
feature space. Therefore, MAIKLD tends to extract key-frames where the object is relatively
small, and MMD selects those where the object is relatively large, as shown in Fig. 4 (c) and (d)
where the clusters are de(cid:12)ned in the x(cid:0)y plane.
(cid:15) Appearing/disappearing: Fig. 4 (e) and (f), where the clusters are de(cid:12)ned in the x(cid:0)t plane of
Fig. 3, illustrate the cases of object appearing and disappearing. When an object appears in a
scene, usually AIKLD decreases due to the appearing of new clusters, and MD increases. Conse-
quently, MAIKLD tends to extract key-frames where the object disappears (or before it appears),
while MMD extracts key-frames where a new object appears (or before an object disappears).
In addition to above cases, it is possible to have other behaviors/events implied by the extracted
key-frames. For instance, if motion features are used, the objects’motion pattern could be indicated
by key-frames. If shape features are involved, the appearance of speci(cid:12)c objects can also be implied.
According to above analysis, it is possible that MAIKLD and MMD extract similar or even the same
key-framesiftheclusterdistributionineachframedoesnotchangeovert,i.e.,theprojectionsofspatial-
temporal clusters to any temporal slices (frames) are similar. In this situation, MMD is equivalent to
MAIKLD because the frames with the largest MD values also form the spatio-temporal clusters with
the maximum AIKLD. It is worth mentioning that the above discussion is based on a fundamental
assumption: the GMM-based spatio-temporal grouping can provide reasonable clusters in space and time
that correspond to objects and their spatio-temporal behaviors. With this assumption, the proposed
method can produce interesting key-frame extraction results. Especially, when the color distribution
does not signi(cid:12)cantly change over the time but the object is still moving (the object motion may not
necessarily a(cid:11)ect the color histogram), the key-frame extraction method using color histogram cannot
provide representative key-frames for object segmentation.
As we mentioned earlier, key-frame de(cid:12)nition is quite subjective. For instance, we may want frames
where objects are spatially close to study objects’ interactions; or those where objects have large sizes
to study objects’ detail, etc. The proposed method can still provide the key-frames of interest that may
not be the same used for object segmentation. Basically, during the process, all frames are evaluated
in terms of their contribution to object segmentation. We have the (cid:13)exibility to chose relevant frames
to best summarize the video content based on our preferences. Moreover, in terms of video content
organization [23], which groups video shots of similar content together by content-based matching or
via key-frame similarities, the extracted key-frames can imply salient points of video content related to
object behaviors/events and support more semantically e(cid:11)ective video grouping.
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