基于迭代最近点方法对图像轮廓拟合多连接椭圆结构的技术研究资源-CSDN文库

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An iterative approach for ﬁtting multiple connected ellipse structure to silhouette

Richard Yi Da Xu

, Michael Kemp

School of Computing and Mathematics, Charles Sturt University, Australia

article info

Article history:

Available online 18 January 2010

Keywords:

Multiple connected ellipse ﬁtting

Iterative Closest Point

Contour ﬁtting

abstract

In many image processing applications, the structures conveyed in the image contour can often be

described by a set of connected ellipses. Previous ﬁtting methods to align the connected ellipse structure

with a contour, in general, lack a continuous solution space. In addition, the solution obtained often sat-

isﬁes only a partial number of ellipses, leaving others with poor ﬁts. In this paper, we address these two

problems by presenting an iterative framework for ﬁtting a 2D silhouette contour to a pre-speciﬁed con-

nected ellipses structure with a very coarse initial guess. Under the proposed framework, we ﬁrst

improve the initial guess by modeling the silhouette region as a set of disconnected ellipses using mixture

of Gaussian densities or the heuristic approaches. Then, an iterative method is applied in a similar fashion

to the Iterative Closest Point (ICP) (Alshawa, 2007; Li and Grifﬁths, 2000; Besl and Mckay, 1992) algo-

rithm. Each iteration contains two parts: ﬁrst part is to assign all the contour points to the individual

unconnected ellipses, which we refer to as the segmentation step and the second part is the non-linear

least square approach that minimizes both the sum of square distances between the contour points

and ellipse’s edge as well as minimizing the ellipse’s vertex pair (s) distances, which we refer to as the

minimization step. We illustrate the effectiveness of our methods through experimental results on several

images as well as applying the algorithm to a mini database of human upper-body images.

1. Introduction

Object recognition and shape registration is an important image

processing topic and its ﬁnding has been incorporated into many

real-life applications. Over the last decade, various techniques have

been developed for registering 2D and 3D models to images, from

simple geometrical shape models such as a vehicle (Yiu et al.,

2005) to more complex models such as human limbs tracking (Ber-

nier et al., 2009; Fossati et al., 2008) and hand model ﬁtting (Du

and Charbon, 2007).

Many works have used the joint ellipse models to represent

complex shapes (Fossati et al., 2008; Xu and Kemp, 2009; Jeune

et al., 2004). The advantage of using a connected ellipse represen-

tation is that the ellipse is easily parameterized and the parameters

convey information including the location, orientation and varia-

tion of data. The connectivity requirements of the adjacent ellipses

further reduce the number of degree of freedoms, and hence con-

strain their movements to reﬂect real-world problems. For exam-

ple, the upper and lower human limbs should always be joined.

However, some of the recent works suffer from two drawbacks:

ﬁrstly, they lack a continuous solution space to ensure only dis-

crete ‘‘valid” ellipse parameters are achieved and secondly most

of these methods require an accurate initialization.

A recent representative example which lacks in continuous

solution space is found in (Fossati et al., 2008), where the authors

use Generalized Expectation Maximization (GEM) to assign edge

pixels to body parts and to ﬁnd the body pose that maximizes

the likelihood of the resultant assignments. However, in the Max-

imization (M)-step of the algorithm, a ‘‘better” pose parameter is

selected from the predeﬁned data sets to increase the likelihood

probability. The use of only discrete number of classes can result

in misalignment between the image and the model, especially

when the number of predeﬁned models is small. In this paper,

we propose an effective and generalized approach to the ﬁtting

algorithm. Our algorithm does not use the predeﬁned model

parameter classes like (Fossati et al., 2008), but considers an inﬁ-

nite number of possible multiple ellipse representations under

the connectivity requirement.

It is natural to present the problem of ﬁtting as ﬁnding a solu-

tion for ellipse structure that minimizes the sum of squares of dis-

tances between the data points and the ellipse structure, in which

a numerical method can be used to ﬁnd the solution in a non-linear

least square fashion. For example, in (Jeune et al., 2004), the

authors ﬁt multiple ellipsoids to the noisy 3D hand points using

the geometrically constrained Levenberg–Marquardt (L–M) (Mad-

sen et al., 2004) algorithm to reﬂect the fact that ﬁngers can only

swing around the joints within an angular threshold. However,

when minimizing a single objective function for a complex struc-

ture containing many connected ellipses, the solution often aligns

doi:10.1016/j.patrec.2010.01.017

* Corresponding author. Fax: +61 2 633 84649.

E-mail addresses: rxu@csu.edu.au (R.Y.D. Xu), mkemp@csu.edu.au (M. Kemp).

Pattern Recognition Letters 31 (2010) 1860–1867

Contents lists available at ScienceDirect

Pattern Recognition Letters

journal homepage: www.elsevier.com/locate/patrec

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