文献翻译Mean Shift

英文翻译

分 院
专 业
届 别
学 号
姓 名
指导教师

2009年05月10日

<文献翻译一：原文>

NON-RIGIDOBJECT LOCALIZATION FROM COLOR MODEL USING

MEANSHIFT1

GaëlJaffré Alain Crouzil
Institutde Recherche en Informatique de Toulouse
UniversitéPaul Sabatier - 118 route de Narbonne - 31062 Toulouse Cedex 4 -France {jaffre,crouzil}@irit.fr

ABSTRACT

Thispaper deals with non-rigid object localization in an image, fromobject colors. Our method allows detection in an image of all theobjects which correspond to a color model, without a prioriinformation about their number. Our approach consists in creating abinary image, which represents the repartition of the most probablepixels to be part of the object. Considering this image as a cluster

in

R

2

, the object localization is done by finding all the cluster modes. This search is carried out by

applyinga statistical method: the mean shift procedure. To illustrate ourapproach, we use sport images, from which we try to detect all theplayers.

1. INTRODUCTION

Ourframework is sport image sequence analysis, especially playertracking. In this study, our topic search is non-rigid objectlocalization in an image, to automatically initialize trackingprocedures. This problem is often encountered in trackingapplications where search is local (tracking with snakes, mean shifttracking, …). The search being done in the neighborhood of theobject position in the previous frame, initialization is needed forthe first frame. Due to many difficulties, it is usually a manualinitialization [1, 2].

Ourproblem presents two main difficulties : the non-rigid and the 3Daspects of the objects. In order to solve both difficulties, we makeuse of color densities of the objects. In this paper, we assume thatobjects have a discriminant color, i.e. their color is characteristicof them. Thus, color density is robust to object non-rigidity,partial occlusions, camera zooming and camera position changing.

Amongpublications about object detection from their color, we wereinspired by [3] and [4]. In [3], Comaniciu proposes a face trackingapplication where, in the first frame, a face is iteratively detectedfrom multiple initializations. In [4], Vages, all the players aredetected by pixel classification. However, this approach needsvarious learning data, and no results with noisy models arepresented.

Weuse both method approaches. First, a classification of the pixels isdone: from an object model, a binary image is created, where eachpixel represents a belonging measure to the model (0 or 1). Thisimage represents the repartition of the most probable pixels to bepart of the searched object. An example is given in Fig. 1.b. Thisimage will be used in the sequel as a model to illustrate thedifferent examples.

Our approach consists in considering this binary image as a cluster in

R

2

: the task of object

1GaëlJaffré and Alain Crouzil. Non-rigid object localization from colormodel using mean shift[D]. IEEE. International Conference on ImageProcessing(ICIP 2003)

localizationreduces to the detection of local modes in the cluster. Each mode isassociated with an object, which corresponds to the model (a mode isa local density maximum).

(a) Original image

(b) Desired cluster

Fig.1. Exampleof cluster we would like to obtain from white player model. Blackpoints represent pixels with value 1, and white ones those with value0.

Inthe sequel, we will no longer use binary images, but weighted binaryimages, i.e. the belonging measure to the model will not be exactly 0or 1, but will be in the real interval [0, 1].

Thispaper is structured in four parts. First, we detail the statisticaltools used to estimate the cluster density and to search the clustermodes. Then, we discuss the used methods to create the cluster whichrepresents the most probable pixel repartition. Besides, we show howwe can extract the object coordinates from this cluster. In the lastpart, we present experiments of the applicationof our method on sportimages.

2.	STATISTICAL TOOLS	R	2	. In this section, we will
Our approach consists in considering binary images as clusters in

presentthe statistical methods used in this paper.

2.1.The Mean Shift Procedure

Themean shift is a nonparametric estimator of density gradient, proposedin 1975 by Fukunaga [5], in order to apply it for pattern recognitionproblems. However, it was really used only by Cheng [6] in 1995, thenby Comaniciu and Meer [7] since 1997.

Let

{

x i

} i

1 ...

m

be an arbitrary set of n points in

R

d

. The mean shift vector computed with

kernelKand kernel bandwidth his given by [7]

M

(

x

)



i1 n

x i

K

( x  x i h

)



x

h

i1 n

K

(

x  x i h

Inthis paper, we only deal with mean shift procedure in case ofEpanechnikov kernel [5]. The mean shift vector definition becomes

M

(

x

)



1



x i



x

h

n

x

x i

S h (

x

)

		(c)Noisy whiter player
(a) White player	(b) Red player

Fig.2.Player models used in the examples of this paper.

Where

Sh

(x

)

is the sphere centered on x, of radius h and containing

n

x

data points. The mean

shiftvector has the direction of the gradient of the density estimate atx.The mean shift procedure

isobtained by successive computations of the mean shift vector Mh (x),and translation of the

sphereSh(x)by Mh (x).The procedure is guaranteed to converge [7].

2.2. Mode Research

In[5], Fukunaga proposes an algorithm of mode seeking using the meanshift procedure. He applies the procedure to each point: when twodata points converge to the same final position, they are consideredto belong to the same cluster.

However, complexity is

O

(

n

2

)

, where n is the number of data points, what provides huge

computationaltime. In order to be usable to quickly initialize tracking procedure,complexity of mode seeking must be reduced. First, we use images asclusters, so data are in a regular grid, providing an efficientcomputation of the mean shift procedure [7]. To even reducecomplexity, we use the approach presented in [8]: instead of applyingthe mean shift procedure to every point, we only apply it to asubset. This is carried out as described below.

(1)Define a tessellation of the cluster with mspheres of radius h:
– thedistance between two neighbors should not be smaller thanh,
– (optional)the number of points inside the sphere should not be below athreshold

T1.

(2)Apply the mean shift procedure to the sphere centers. The differentpoints of convergence are themodes of the cluster.

(3)Merge modes whose distance is less than h.

(4)Discard modes whose density estimate is below a fraction T2of maximal density estimate.

3.CLUSTER CREATION FROM IMAGES

Thecolor models we used in this paper are presented in Fig. 2.

3.1.Binary Images

Themost naive approach consists in creating binary image with thefollowing way: each pixel whose color appears in the model has thevalue 1, and each pixel whose color does not appear has the value 0.Example is given in Fig. 3, where result seems satisfactory: densityestimate of the cluster

presentstwo maxima which can be distinguished, and which correspond to the“centers” of the two players. However, this approach is verylimited, because on real data the color model is often slightlydifferent from the color of the object in the image. Moreover,results are very sensitive to noise in the model, as we will see insection 3.3.

Todeal with slight changes in color, histograms can be used. To comparetwo pixels, we must now compare their index in the histogram insteadof directly comparing their color or gray level. The problem consistsin finding the optimal bin number. A small one will provide too manypoints in the cluster, whereas a too large one will not allowimportant changes in color.

(a)Cluster. (b)Density estimate
Fig.3.Cluster from the naive approach, with the model of Fig. 2.a.

Vandenbrouckeproposes another approach to get binary images from models, withsoccer images [4]. Learning data are drawn from various playermodels, for which many color representation systems are used.Finally, he only keeps the system which provides the best separationbetween the two classes of pixels according to the player soccersuits. Obtained clusters have a very good quality (like the desiredmodels shown in Fig. 1.b). However, this method needs many learningmodels, many color system changes, and particularly noise-free models(noise is manually removed).

3.2.Weighted Binary Images

Ourclusters are obtained from binary images. Each pixel has only twopossibilities: either it belongs to the model, or it does not. Theweighted binary image allows more degrees in model belonging. Largestvalues correspond to most probable pixels, whereas lower onescorrespond to unlikely pixels. Cluster is now obtained by taking onlythe pixels with strict positive value, each value corresponding to aweight: thus, most probable pixels will have a greater weight thanunlikely pixels.

Ourmethod to create cluster is the one proposed by Swain and Ballard in[9]: the measure of the object presence in image is defined from whatis called the backprojected image.

Letus denote by

{xi}i1... mthe location of the npixels in the image,

{qk}k1... mthe m-bincolor histogram (linearized color histogram with mbins) of the

image,



{

p

k

} k

1 ...

m

the

-bin color histogram of the model.

We also define the function

c

:

R

2



{ 1 ... m }

which associates to the pixel at location

x i

the

index

c

(

x i

)

of the histogram bin corresponding to the color of that pixel. The ratio histogram

{ r

}

1 ...

m

is defined as

r k

min(

p

k

, 1 )

. It associates to each color a belonging measure to the

k

k

q

k

model.It will allow the object presence in the image to be measured. Itsbackprojection onto the

image associates the value

r Cx i

)

to the pixel

x i

, for all

i



1 ... m

. Since the ratio histogram

emphasizesthe predominant colors of the target while diminishing the presenceof clutter and

background colors, the backprojected image

{ r Cx i

)} i

1 ...

m

represents a spatial measure of the

objectpresence.

In order to compute the mean shift vector for all

x

R

d

, we use a definition which takes the

weightsinto account

M

h

(

x

)

i

S

h

( x

)

w (

x i

)

x i



x

x i

S

h

( x

)

w (

x i

)

w (

x i

)

is the weight associated to the

Where

Sh

(x

)

is the sphere of radius h and center x, and

point

x i

.

(a)Cluster. (b)Density estimate. Fig.4.Backprojected image.

Backprojectedimage obtained from our soccer image is given in Fig. 4. We computedthe histogram in the RGB space with 16 bins for each color.

3.3.Comparison with Noisy Models

Withsynthetic models, we have similar results with naive approach andbackprojected image. However, this difference becomes obvious asmodels become noisy. In order to have a synthetic model from an imageof the object, we must select the image area where the object is,then manually remove the background [4]. This model could be used forvarious images.

However,we could expect to have a model from an image area, without manualcorrection. Background pixels will then be part of the model. Themethods previously presented have different behaviors in presence ofnoisy pixels, as we can observe in Fig. 5: with the naive approach,background pixel presence provides a too noisy cluster, which makesplayer localization impossible. One can see that in the rectangulararea where the model was extracted, every pixel was kept for the

cluster. On the other hand, with backprojected image, the ratio	p	k	allows the background pixel
	q	k

influenceto decrease [9], because in the image, the background pixels are morenumerous than the object pixels. In the area where the model isextracted, background pixels have low weights, whereas player pixelskeep large weights. Density estimate of the backprojected image hastwo maxima which can be distinguished, the most important beingobviously the one which corresponds to the player selected for themodel. This last method providing more reliable
resultson real (noisy) data, we will use it in our applications.

4. OBJECTLOCALIZATION

Whenthe cluster is computed, object localization is carried out byapplying the algorithm described in section 2.2, which allows thedetection of all the cluster modes, without knowledge about theirnumber. The only a priori information needed is the scale of thecluster, i.e. the radius hwe will use in the mean shift procedure. When mode computation isended, each mode corresponds to an object center.

Whenthere is only one object to find, its position corresponds to theglobal maximum of cluster density estimate. Even if pixel by pixeldensity computation is possible, the algorithm of section 2.2 is moreefficient in term of time computation because density is onlyestimated for a few number of points. Moreover, the last step of thealgorithm becomes useless, because we only keep the mode

with maximum density. Thus, threshold

T 2

is not used.

Thisapproach is inspired from [3], where face localization is carried outfrom various initializations. For each of them, the mean shiftprocedure is run, in order to compute the corresponding mode, and tokeep the one with the highest peak. However, we can point out somedifferences with our approach. First, initialization points are notrandomly taken in sufficiently populated region, but are alwayschosen in the same location, for all images. Besides, theoptimization is not the one of density estimate of the backprojectedimage, but the one of Bhattacharyya coefficient, which measures thesimilarity between color distributions of the model and an imagearea. The advantage of using backprojected image instead ofBhattacharyya coefficient is the computational time, which is lowerwith backprojected image.

(a)Cluster obtained from naive approach. (b) Density estimate.

(c)Cluster obtained from backprojected image. (d)Density estimate. Fig.5. Noiseinfluence on clusters. Models were drawn from an image area, without backgroundremoval. (Fig. 2.c).

When we know the number N of the objects in the image, the threshold

T 2

is useless. The

methodis the same than with only one object, but we keep the Nmodes with highest density estimate.

Whenwe do not know the number of objects in the image, which usuallyoccurs in applications, we then apply all the steps of the algorithmof section 2.2. With the last step, the modes with a too

small density estimate will be removed. In our experiments, we used

T 2

25 %

. This threshold is

notvery dependent on the current environment, i.e. we did not have tochange it in our different experiments.

5. EXPERIMENTS

Weapplied this method with different sport images, and results1are satisfactory. When we deal with collective sports with two teams,we must run the procedure two times (one by team model).

Fig.6 and 7 present results of our method with different sport images.Sportsman locations are given by the circle centers. In both cases,we did not know the number of players in the images.

Thelimits of our method arise when conditions become difficult, as inFig. 8, where there is a billboard with the same color than whiteplayers, and those ones are only represented by few pixels.

Allthe players are detected, but there are two false alarms, thebillboard and the referee.

Fig.6. Soccerplayer localization.

(a)Noisy surfer model. (b)Result.
Fig.7.Surfer localization from a noisy model.

6.CONCLUSIONS AND DIRECTIONS OF FURTHER RESEARCH

Ourmethod allows non-rigid object localization from a color model, evenin the presence of noise, when they have enough pixels. This methodcan be used to automatically initialize tracking procedures, whichare often manually initialized in the first frame [1, 2].

Theinterest of our approach is the use of the mean shift procedure, which is a nonparametric statistical procedure, robust to noisealways present in real data. Mean shift procedure allows quickconvergence toward object locations, due to low complexity, lownumber of iterations and local search.

Anotheradvantage in our method is the low number of parameters: object colormodel,

approximate scale of the objects, and thresholds

T 1

and

T 2

. The threshold

T 1

is only used to

reducethe number of mean shift procedure uses, it can be removed if we donot want to determine

it. The threshold

T 2

is only used when we do not know the number of objects in the image. We

setit experimentally, and as it is not very dependent on the currentenvironment, we did not change it in all our examples.

So,the user only has to give a color model of the object, and itsapproximate size. To avoid manually creating a synthetic model, theuser can straightforwardly give the center object location:

themodel will be extracted from neighborhood (which depends on thescale) of the object. Finally, the user may not choose any scale, butselect an area in the image which corresponds to an object: the colormodel will be initialized from the colors of this area, and the scalewill be taken from the

size of the area. In this case, we can take two different scales

h x

and

h

y

for the height and the

widthof the object. Background pixels will only have a weak influence, asdiscussed in section 3.3.

However,a prior knowledge about the scale remains needed. We would like toremove this a priori knowledge, by automatically computing the scale.Thus, we will use the works presented in [10] and [11], where aredescribed clustering methods which use the mean shift procedure, butautomatically compute the scale from data.

7.ACKNOWLEDGMENT

Thiswork has been conducted on the behalf of the KLIMT project.

Fig.8.Soccer player localization : difficult case.

8. REFERENCES

[1]Chris Needham and Roger Boyle, “Tracking multiple sports playersthrough occlusion, congestion and scale,” in Proceedings of the12thBritish Machine Vision Conference, Manchester, UK, Sept. 2001, vol.1, pp. 93–102.

[2]Janez Perš and Stanislav Kovačič, “Tracking People in Sport:Making Use of Partially Controlled Environment,” in Proceedings ofthe 9th International Conference on Computer Analysis of Images andPatterns, Warsaw, Poland, Sept. 2001, pp. 374–382.

[3]Dorin Comaniciu and Visvanathan Ramesh, “Robust Detection andTracking of Human Faces with an Active Camera,” in Proceedings ofthe 3rd IEEE International Workshop on Visual Surveillance, Dublin,Ireland, July 2000, pp. 11–18.

[4]Nicolas Vandenbroucke, Ludovic Macaire, and Jack-Gérard Postaire,“Color image segmentation by supervised pixel classification in acolor texture feature space. Application to soccer imagesegmentation,” in Proceedings of the 15th International Conferenceon Pattern Recognition, Barcelona, Spain, Sept. 2000, vol. 3, pp.625–628.

[5]Keinosuke Fukunaga and Larry Hostetler, “The Estimation of theGradient of a Density Function, with Applications in PatternRecognition,” IEEE Transactions on Information Theory, vol. 21, no.1, pp. 32–40, Jan. 1975.

[6]Yizong Cheng, “Mean Shift, Mode Seeking, and Clustering,” IEEETransactions on Pattern

Analysisand Machine Intelligence, vol. 17, no. 8, pp. 790–799, Aug. 1995.

[7]Dorin Comaniciu and Peter Meer, “Mean Shift: A Robust ApproachToward Feature Space Analysis,” IEEE Transactions on PatternAnalysis and Machine Intelligence, vol. 24, no. 5, pp. 603–619, May2002.

[8]Dorin Comaniciu and Peter Meer, “Distribution Free Decomposition ofMultivariate Data,” Pattern Analysis and Applications, vol. 2, no.1, pp. 22–30, 1999.

[9]Michael Swain and Dana Ballard, “Color Indexing,” InternationalJournal of Computer Vision, vol. 7, no. 1, pp. 11–32, Nov. 1991.

[10]Dorin Comaniciu, “An Algorithm for Data-Driven BandwidthSelection,” IEEE Transactions on Pattern Analysis and MachineIntelligence, vol. 25, no. 2, pp. 281–288, Feb. 2003.

[11]Hong Pan, Stan Li, and Guodong Guo, “Robust Unsupervised ClusteringUsing Generalized Annealing MEstimator,” in Proceedings of the 4thAsian Conference on Computer Vision, Taipei, Taiwan, Jan. 2000, vol.1, pp. 104–109.

<文献翻译一：译文>
基于MeanShift的颜色模型的非刚性物体定位 GaëlJaffré AlainCrouzil
Institutde Recherche en Informatique de Toulouse
UniversitéPaul Sabatier - 118 route de Narbonne - 31062 Toulouse Cedex 4 -France {jaffre,crouzil}@irit.fr

摘要
本文处理的是图像中基于颜色的非刚性目标定位。我们的方法可以在没有先验信息的前提下检测出图像中基于颜色模型的物体。我们的方法是创造一个二值图像，以便区分目

标最重要的像素。考虑图像作为在

R

2

中的一个簇，目标的定位就是找出所有的簇模型。该

搜索运用一个统计方法：MeanShift过程。为了说明我们的方法，我们采用运动图像，以从中找出所有的运动员。

1.介绍
我们的框架是运动图像序列分析，特别是运动员跟踪。在这项研究中，我们的目的是在图像中寻找非刚性物体的定位，自动初始化跟踪程序。当搜索是在本地（蛇形搜索，MeanShift搜索）时，这个问题会经常遇到。在跟踪时，需要在目标位置附近的前一帧初始化，由于诸多困难，往往需要一个手动的初始化[1,2]。

我们的问题主要两个难点：非刚性物体和三维物体。为了解决这两个难题，我们采用目标的颜色密度。在本文中，我们假设对象有一个差别颜色，例如，它们的颜色是容易区分的。因此，运用颜色密度对物体的非刚性、部分遮挡、摄像机的位置和远近变化等都有很好的鲁棒性。

在有关基于颜色的目标辨别的文献中，我们从文献[3]和[4]中受到启发。在文献[3]中，Comaniciu举了一个人脸跟踪的例子，在第一帧，一个脸由多个初始化检测出来。在文献[4]中，Vandenbroucke列举了一个不同的应用：从学习图像中，通过像素分类所有的运动员被检测出来。但是这种方法需要学习各种数据，并且在有噪声的图像中不能得到理想的结果。

我们同时使用两种方法：首先，我们先对像素分类：从目标模型中创建一个二值图

像，这样每个像素都被重新分类（0 或1）。此图像了代表了最重要目标像素信息被划分开

来。图1给出了例子，这个图像将作为模型被用于说明后面一同的例子中。

我们的方法是考虑这个二值图像作为

R

2

中的一个簇：目标定位的任务就减少为在簇中

对本地模型的区分。每一个模型是一个对象，它对应于该模型（一个模型就是一个本地密

度最大值）。
	(a) Original image	(b) Desired cluster

图1.簇的例子，我们想得到白色运动员的模型，黑点代表的像素值为1，白点代表的像素 值为0
在后续的实验中，我们将不再使用二值图像，但是使用加权的二值图像，例如，这些模型不在为单纯的0或者1，而是在[0,1]的区间内。

本文的结构分为四个部分：首先，我们详细地介绍了统计工具用来估计簇密度和搜索

簇模型。然后，我们讨论用使用过的方法来创建簇，此外，我们还会展示我们能从簇中提

取对象坐标。在最后一部分，我们将用我们的方法在这些运动图像中进行实验。 2.统计手法

我们的方法在考虑二值图像作为

R

2

中的一个簇。在本节中，我们将讲述一下本文所使

用一统计方法。

2.1.Mean Shift 过程
MeanShift是一个无参密度梯度估计。有Fukunaga[5]在1975年为了解决图像识别而提出。然而，它真正的应用还在于1995年从Cheng[6]开始的，然后是1997年的Comaniciu和Meer[7]。

设

i i

1 ...

n

为

R

d

中的n 个点的集合。核函数为K 且核带宽为h 的Mean Shift 向量在

文献[7]给出：

M

(

x

)



i1 n

x i

K

( x  x i h

)



x

h

i1 n

K

(

x  x i h

在本文中，我们仅用Epanechnikov核函数[5]和处理MeanShift过程。MeanShift向量的定义就变成

M

(

x

)



1



x i



x

h

n

x

x i

S h (

x

)

(a) White player

(b) Red player

(c) Noisy white player

图2在本文例子中使用的运动员模型

Sh

(x

)

是一个以x 为中心的球形，半径为h 并且包含

n

x

个数据点。Mean Shift 向量的方向就

是在x 点概率密度梯度估计的方向。Mean Shift 过程就是计算Mean Shift 向量

M h

(x

)

的过程，

运用

M h

(x

)

对球形

Sh

(x

)

的转化。在个过程在文献[7]中得到保证。

2.2.模型搜索
在文献[5]中，Fukunaga提出了一个运用MeanShift过程模型搜索的算法。他把这一过程运用到每一点：当两个数据点收敛到相同的位置时，认为它们属于相同的簇。

然而，当数据点的个数为n 时，复杂度为

O

(

n

2

)

，这将耗费很大的计算时间。为了能

快速地初始化跟踪过程，节点搜索的复杂度就必须减少。首先，我们把图像分成簇，因此，数据就在一个正则网络中，提供了一个有效的MeanShift过程的计算[7]。为了更加减少复杂度，我们使用文献[8]提到的方法：我们仅仅使用MeanShift在一个集合内，而不是运用到每点。下面是该算法描述：
（1）定义一个簇的分布，m个半径为h的圆：

	两个相邻的距离要大于或等于h，	T 1	。
	圆内的点的个数不能低于一个阈值

（2）在这些圆的中心使用MeanShift过程，不同的收敛点是这些簇的模型。（3）合并距离小于h的模型。

（4）舍弃密度估计小于最大概率密度估计的一个小数的

T

2

模型。

3.图像中簇的创建

本文中使用的颜色模型在图2中给出。

3.1.二值图像

最简单的构建二值图像的方法如下：在模型中出现的颜色的像素值为1，否则为0。以

图3为例，结果看起来令人满意：簇的密度估计呈现两个可以区分的极大值，并分别对应于

两个运动员的“中心”。然而，这种方法还是有一定的局限性，在真实的颜色模型中目标的

颜色模型往往有背景相差不大。此外，结果对模型中的噪声非常敏感，这些我们将在3.3中

看到。

为了处理颜色的轻微变化，可使用直方图。为了比较两个像素，我们必须用比较它们的

直方图索引来代替比较它们的颜色的灰度级。问题就在于寻找最优的bin数。小的在簇中提

供的点太多，而在大的则不允许颜色的大的变化。

Vandenbroucke提出了从模型中得到二值图像的另一种方法，运用足球图片[4]。学习数

据来自于大量的运动员模型，他们的很多颜色系统被使用。最后，他只保留了能通过球衣区

分运动员的两个像素类。获得的簇有很高的质量（像在图1.b中所示的所需要的模型）。然

而，这种方法需要很多学习模型，很多颜色系统的变化，特别是无噪声模型（噪声被移除）。

3.2.加权二值图像

我们的簇从二值图像中获得。每一个像素只有两种可能：属于模型或者不属于模型。加

权二值图像允许模型中更多的度。最大的值对应最有可能的像素，同样，最小的值对应最不

可能的像素。簇现在有有着严格正值的像素获得，每个值对应一个权重：因此，最有可能的

像素有一个更大的权重。

我们创建簇的方法是Swain和Ballard在文献[9]中提出的：图像中目标的度量由投影图

像定义。

让我们用以下表示：



{

x i

} i

1 ...

m

为图像中n 个像素点的个位置，

(

x i

)

对应像素的颜色。直方图比率



{ q

k

} k

1 ...

m

图像的m-bin 颜色直方图，



{

p

k

} k

1 ...

m

模型的m-bin 颜色直方图。

我们同样定义函数c：

R 

{ 1 ... m }

，直方图的索引

c

{ r

} k

1 ...

被定义为

r k

min(

p

k

, 1 )

。它允许图像中目标的描述是可度量的。它的在图像上

k

m

q

k

像素

x i

的投影值为

r cx i

)

。由于强调目标颜色直方图的比率，同时减少杂波和背景颜色，投

影图像

{ r cx i

)} i

1 ...

m

代表了目标的空间度量。

为了计算所有

x

R

d

的Mean Shift 向量，我们使用了加入权重的定义

M

(

x

)





x iS h ( x ) w ( x iS h ( x )

x i

)

x i



x

h

x i

这里，

Sh

(x

)

半径为h 的圆并且中心为x，

w (

x i

)

为

x i

点的权重。

投影图像由图4中的足球图像所得，我们计算在RGB空间内计算直方图，每个颜色为

16bin。

(a) Cluster

(b) Density estimate

图4投影图像

3.3.噪声模型对照

对于综合模型，我们用简单的方法和背面投影图像得到简单的结果。然而，当模型带有

噪声时，这种差异就变得非常明显。为了从一个对象图像中得到一个综合模型，我们必须选

择其中的图像目标区域，然后手动删除背景[4]。这模型可用于各种图像。

然而，我们期望有通过手工矫正而从图像区域中得到一个模型。背景像素将会是模型的

一部分。先前提到的方法在噪声像素面前有不同的表现，我们能在图5中看到：用最简单的

方法，背景像素为一个噪声很大的簇，使得运动员定位变得不可能。我们能看到模型被抽出

的矩形区域，每一个像素都被簇保留。另一方面，对于背面投影图像，比率	p	k	允许背景像
	q	k

素的影响减少[9]。因为在图像中，背景像素比目标像素要多得多。在模型被抽出的区域，

背景像素有较低的权重，而运动员像素有较大的权重。背面投影的密度估计有两个可以区分

的极大值，最重要的一个对应选择的运动员模型区域。最后一个方法在真实（噪声）数据上

提供了较真实结果，我们将在我们的应用中使用它。

4.目标定位

当簇被计算出时，目标的定位就可以由2.2描述的算法得出，在没有簇的个数的先验知

识的情况下，允许所有簇的检测。仅仅需要的先验信息是簇的宽度，例如，在MeanShift过

程中使用的半径h。当计算结束时，每一个模态对应一个目标的中心。

当只有一个寻找的目标时，它的位置对应一个簇密度估计的全局最大值。如果一个像素

一个像素地密度计算是可能的，则2.2提到的算法是更有效的，因为密度的估计仅仅是很少

的数据点。此外，算法的最后一步变得无用，因为我们仅仅保留模态的最大密度。因此阈值

T

2

是没有用的。

这种方法在文献[3]中得到启发，其中脸部的定位从不同的大量初始化中得到。它们中

的每一个都是有MeanShift过程得到，为了计算出对应的模态，并且保留最高的尖峰。然而，

我们能指出我们方法的一些不同之处。首先，初始化点不是随机的在稠密的区域取得，而是

一直在所有图像中选择同一个位置。此外，最优位置不是背面投影图像的密度估计，而是

Bhattacharyya系数，其表示目标颜色描述与图像区域的相似程度。用背面投影图像代替

Bhattacharyya系数的优点是计算时间，用背面投影的时间要短。

当我们知道图像中目标的数目N 时，阈值

T 2

就变得无用。方法就变得与一个目标一样，

但是我们保留有最高密度估计的N个模型。

当我们不知道图像的目标个数时，我们就使用2.2提到的算法的每一步。到了最后一步，

具有太少密度估计的模型就会被移除。在我们的实验中，我们使用T225%。这个阈值并

不是太依赖当前环境，例如，我们不会在不同的实验中去改变它。

5.实验

我们在不同的运动图像中使用我们的方法，结果1效果是别人满意的。当我们处理两个