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Giuseppe Coppini a,*, Stefano Diciotti b, Guido Valli b

noise indicate considerable robustness against statistical variability. Applications to clinical images are presented.

preattentive processes to attentive tasks. A wide of paramount importance in modern medical

imaging. In the latter case, it is necessary to buildcomprehensive functional and anatomical repre-

sentations of the observed biological structures by

utilizing the partial views oered by basic imaging

procedures such as MRI, PET, CT (van den Elsen

qPartially founded by the Italian Ministry for Education,

University and Research (MIUR).*

Pattern Recognition Letters 25Corresponding author. Tel.: +39-503-153-480; fax: +39-

503-152-166. 2003 Elsevier B.V. All rights reserved.

Keywords: Image matching; Medical imaging; SOM neural network; Gabor wavelets

1. Introduction

Finding correspondences between images is a

central problem in many vision activities, from

category of image matching problems arises from

the need to integrate images generated by dierent

modalities. The importance of integration tasks

has rapidly grown in recent years and has becomea Consiglio Nazionale della Ricerche (CNR), Institute of Clinical Physiology, Via Moruzzi 1, 56124 Pisa, Italyb Department of Electronics and Telecommunications, University of Florence, Italy

Received 11 March 2003; received in revised form 21 October 2003

Abstract

A general approach to the problem of image matching which exploits a multi-scale representation of local image

structure and the principles of self-organizing neural networks is introduced. The problem considered is relevant in

many imaging applications and has been largely investigated in medical imagery, especially as regards the integration of

dierent imaging procedures.

A given pair of images to be matched, named target and stimulus respectively, are represented by Gabor Wavelets.

Correspondence is computed by exploiting the learning procedure of a neural network derived from Kohonens SOM.The SOM units coincide with the pixels of the target image and their weight are pointers to those of the stimulus images.

The standard SOM rule is modied so as to account for image features. The properties of our method are tested by

experiments performed on synthetic images. The considered implementation has shown that is able to recover a wide

range of transformations including global ane transformations and local distortions. Tests in the presence of additiveMatching of medical imneural nE-mail addresses: coppini@ifc.cnr.it (G. Coppini), diciotti@

asp.det.uni.it (S. Diciotti), valli@det.uni.it (G. Valli).

0167-8655/$ - see front matter 2003 Elsevier B.V. All rights reservdoi:10.1016/j.patrec.2003.10.012ges by self-organizingorks q

(2004) 341352

www.elsevier.com/locate/patrecet al., 1993). Several correspondence problems

have been faced which include mono-modal or

ed.

subject variability, nevertheless the observed

structures keep some general properties such asconnectedness and proximity among sub-struc-

tures. In general, it seems reasonable to search for

a correspondence law which is unique from T toS, 1 and which maps features in the T plane tosimilar features in the S plane by matching spa-tially contiguous features in T into spatially con-tiguous features in S. These conditions can berestated more concisely by saying that the desiredmapping is a feature- and topology-preserving

transformation from T into S. The importance oftopology preservation in image matching has been

ognition Letters 25 (2004) 341352multi-modal image correspondence and intra- or

inter-subjects matching. In addition, matching of

3D images has become an important issue along

with the mapping of imaged structures to reference

representations such as anatomical atlases. Much

eort has been devoted to nding global defor-mations, which has led to ecient algorithms

being able to recover linear transformations. A

popular method is based on the maximization of

the mutual information of the two images (Wells

III et al., 1996). More recently, the use of deform-

able models has been widely investigated so as to

recover local non-linear deformations. A number

of references on the subject can be found in(Maintz and Viergever, 1998). Thermodynamical

analogy with Maxwell demons has been also

investigated (Thirion, 1998).

In general, specic solutions have been pro-

posed for many matching problems. The related

algorithms usually exploit some form of prior

knowledge, and are often based on strong

assumptions. On the other hand many corre-spondence nding problems share important

common facets, such as the statement of image-

similarity criteria or the denition of adequate

computational schemes. In this view, the impor-

tance of general solutions for image matching

problems has been considered by several

researchers (Haralick and Shapiro, 1993). In par-

ticular, we believe that a self-organizing process isa natural and very promising setting. As reported

by Bellando and Kotari (1996), the computation of

topology preserving maps using Kohonen neural

networks (Kohonen, 2001) can provide valid

solutions to establishing image correspondence.

Wurtz et al. (1999) compare the behavior of Ko-

honens SOM with the Dynamic Link Architecture(Konen et al., 1994) paying particular attentionto the computational eciency of self-organizing

processes. It is worth mentioning that the appli-

cation of a SOM network to image registration is

described by Huwer et al. (1996).

In this work we will take the following general

problem into account. Let Itr and Isr0, twoimages (target and stimulus image, respectively)

with r x; y, and r0 x0; y0 co-ordinate vectorsdened in proper subsets T and S, respectively

342 G. Coppini et al. / Pattern Rec(image planes) of R2 space. We assume that afeature vector ftr ff it rg describing relevantproperties of Itr can be computed for each pointr in T . Similarly, fsr0 ff is r0g will indicate thefeature vector of Isr0 for each r0 2 S. We searchfor a correspondence rule M : T 7!S that mapspoints in T to points in S which have similarmorphological properties, as described by the

feature vectors (see Fig. 1). This is an ill-posed

problem, and further constraints must be consid-

ered to compute a useful solution, when stated so.We believe that powerful constraints can be de-

rived from the regularity of the observed world

even if the use of specic knowledge available for

each matching problem considered can lead to

adequate solutions. For example, images of nor-

mal anatomical structures exhibit a large inter-

tI (r)

sI (r)

r

r

T

Sstimulus image

target image

Fig. 1. A general matching procedure is expected to preserve

pictorial features and their neighborhood relationship.1 One-to-one mapping can be desirable in some cases.

given in the image planes I fT ; Sg and the fea-

ble image description to compute a useful set of

pictorial features f ff ig. This led us to investi-gate a self-organizing neural network coupled with

ognition Letters 25 (2004) 341352 343ture space F , respectively. Let us assume that forany given r1; r2 2 T , r01; r02 2 S are the correspond-ing transformed points, i.e. r01 Mr1, r02 Mr2. We will say that the transformation Mpreserves image topology if the following condi-

tions are met:

(1) Preservation of image plane topology:

limdI r1;r2!0

dIr01; r02 0

(2) Feature preservation:

limdI r1;r01!0

dF ftr1; fsr01 0

Though further constraints can be taken into

account (such as the high order smoothness of

the mapping), our aim is the investigation of the

preservation of the neighborhood relationship.

To this end we consider the computation of

image matching by using a topology preserving

neural network derived from Kohonens SOM.The resulting computation is typically data-drivenand no specic prior model is expected to con-

strain the obtained solution. In this sense our

approach is typically non-parametric. In order to

investigate the related capabilities, we outline the

basic scheme of the adopted computational para-

digm in the next section. Subsequently we present

and analyze the performances observed when a

set of known mathematical transformations wasapplied to phantom images in the presence of

additive noise. Applications to computing corre-

spondence between biomedical images are also

described.

2. Computational paradigm

Following the previous considerations, a gen-

eral framework of image matching problems re-

quires: (a) a proper computational architecture todiscussed by Musse et al. (2001) who propose the

use of hierarchical parametric models. A formal

denition of the meaning of topology preserving

transformation is useful for the following. To this

end we assume that proper metrics dI and dF are

G. Coppini et al. / Pattern Recimplement a topology preserving map, (b) a exi-image features computed by the Gabor Wavelet

Transform.

2.1. Matching through self-organization

The computation of topology preserving maps

between vector spaces can be carried out by using

Kohonen neural networks (Kohonen, 2001).

Basically, they include a grid of units, typically 2D,

each of which receives the same input ve