Shape and Semantics

for 3D Anatomical Structure Retrieval

Davide Moroni

, Mario Salvetti

and Ovidio Salvetti

Institute of Information Science and Technologies (ISTI),

Italian National Research Council (CNR), Pisa, Italy

Department of Mathematics, University of Pisa, Pisa, Italy

Abstract. In this paper, we propose a framework for the description of anatomi-

cal structures based on topological and geometrical features and on semantic an-

notation. The main goal is to enhance the description of an anatomical structure

–understood as a 3D model– with other non-geometrical pieces of information

relevant to the particular problem-context. Hybrid methods for similarity searches

are then introduced and shown to be able to support effective case-based reason-

ing procedures. The approach is illustrated with examples from several medical

application ﬁelds in order to discuss its potential impact.

1 Introduction

In the ﬁeld of medical imaging, the analysis of the shape of anatomical structures may

shed new light in understanding their functional properties and may be used to support

the decision-making processes in diagnosis and treatment. For example, it has been

shown that irregular growth of the hippocampus is strongly correlated to epilepsy [1].

Thus, the development of computerized tools for hippocampus segmentation and re-

construction together with retrieval of similar cases in an annotated database may be

used as a clinical decision support in preoperative planning. Further, in the ﬁeld of neu-

rology, modelling and simulation of intracranial phenomena –such as haemorrhages,

neoplasm and hematoma– may be used to analyze the inﬂuences they have on neuro-

functional structures in the brain [2]. In cardiology, the modelling of the heart may be

used at different levels to analyze local and global myocardial performance and deﬁne

new quantitative parameters for injury evaluation [3].

Imaging modalities are the fundamental source of raw data on which to perform

such kind of shape analysis. Nowadays, the more and more increasing number of tech-

niques (e.g. MRI, fMRI, CT, Ultrasound, PET, SPECT, PAM and fPAM, . . . ) is able to

provide reliable anatomical images together with various and rich functional informa-

tion, ranging from perfusion to metabolism, from absorption to diffusion. In addition,

some of these modalities allow to acquire video sequences of dynamic phenomena,

involving for example the deformation of anatomical structures, and, thus, high dimen-

sional data (2 or 3 spatial dimensions plus time).

Further, such diagnostic resources are becoming more and more accessible and

common. This results in the production, on a daily basis, of a bunch of heterogeneous

Moroni D., Salvetti M. and SSalvetti O. (2009).

Shape and Semantics for 3D Anatomical Str ucture Retrieval.

In Proceedings of the 2nd International Workshop on Image Mining Theory and Applications, pages 73-83

DOI: 10.5220/0001962500730083

 SciTePress

image data, which undoubtedly represent a great richness for case-based reasoning and

data-mining procedures.

However, the organization and exploitation of such data cannot be fully accom-

plished unless with the help of suitable tools for image analysis, shape representation

and annotation.

In the last decade, much effort has been spent in developing methods for the geo-

metric representation of 3D models, especially from a general-purpose perspective (see

e.g. [4]). Among other scopes (e.g. classiﬁcation and categorization), such methods

are usually employed to accomplish the retrieval of similar shapes from an annotated

database. Given a query shape, the retrieved shapes can then be used for comparison

purposes; additional pieces of information available for the retrieved shapes (for exam-

ple as semantic tags) may also be used as “clues” for analyzing the case at hand.

The impact of such shape description and retrieval techniques has been clearly

strong; still, apart from several general-purpose approaches not suited for medical ap-

plications, the attempts have been conﬁned to particular and restricted problems without

moving towards generic anatomical structures retrieval.

In addition, the association of keywords to 3D models is still a subjective process,

often not even based on editable catalogue and, so, exhibiting very limited reusability.

Actually, the formalization of the process of geometric and semantic annotation is seen

as a necessary condition for enabling cross-modal access to 3D model/image reposito-

ries.

This being the general setting, the main aim of this paper is to present a framework

for the description of anatomical structures, based both on topological and geometri-

cal features and on semantic annotation. We argue that a 3D model –representing an

anatomical structure– may be enhanced with other non-geometrical pieces of informa-

tion relevant to the particular problem-context. Hybrid methods for similarity searches

are then introduced and shown to be able to support effective case-based reasoning pro-

cedures. This point is illustrated with three examples from various medical application

ﬁelds, namely neurology, radiotherapy and cardiology.

2 Anatomical Structure Representation

Following the ideas of Grenander and Miller [5], an anatomical structure O embedded

in the background space Ω ⊂ R

(d = 2, 3) may be modeled as a collection:

O =

{

, P

)

}

α=1,2,...,k

where each V

is a smooth manifold (possibly with boundary) embedded in Ω and

: V

→ R

d(α)

is a smooth property function assuming its values in a suitable prop-

erties space. Notice that the collection

{

}

α=1,2,...,k

represents the underlying purely

geometrical structure, while the property functions are a structured representation of the

local attributes to the geometrical structure.

The smoothness assumption is a quite common hypothesis in computational anatomy

and it is satisﬁed in practice to a large extent; it implies for example that differential

geometric properties can be computed everywhere. We use, moreover, collection of

manifolds -instead of a single one- to be able to describe structure subparts (possibly

of different dimensionality) by attaching them speciﬁc salient attributes via a dedicated

property function. For example, in heart left ventricle modeling, the structure of interest

is the myocardium, that can be modeled as a 3D manifold, whose boundaries are two

surfaces: the epicardium and the endocardium. It is convenient to attach to the boundary

surfaces a different (actually richer) set of attributes than those used for internal points.

Time-resolved structures O = (O

)

t=0,1,...

may be represented as a temporal sequence of

structures satisfying some smoothness constraints. Each O

{

, P

)

}

1≤α≤k

should

be regarded as the snapshot of the deforming structure at time t.

We require that each manifold V

appearing in the snapshot at time t can be smoothly

deformed into V

t+1

in the subsequent snapshot. Such modelization is thus adaptable

and ﬂexible, permitting to represent geometrically 2D, 3D and time-resolved anatomi-

cal structures and their properties in just one framework. Since methods for recovering

such representation from raw image data have been extensively described in [6, 7], we

focus in the section below on shape characterization for anatomical structures.

3 Shape Characterization

The aim of this section is to provide methods for the representation of a structure which

are suitable for similarity searches and data mining procedures. After having recon-

structed an anatomical structure as a collection

{

}

α=1,2,...,k

, a ﬁrst step toward char-

acterization consists in assigning a signiﬁcant property function P

: V

→ R

d(α)

each manifold V

. Three types of properties may be considered:

– intensity-based properties;

– local shape descriptors;

– local dynamic behavior descriptors (for time-resolved structures only).

Intensity-based properties include gray level value, gradients, textures and the like. Such

intensity information may be extracted from the anatomical image leading to structure

reconstruction and may correspond to densitometric properties. In addition, data col-

lected from other imaging modalities may be fused (after performing some context-

dependent registration procedure) so as to further annotate the structure; for example,

in the case of the heart, information regarding perfusion and metabolism, obtained e.g.

by means of PET imaging, can be referred to the reconstructed myocardium. Geomet-

ric based properties, belonging to the second type, may be extracted directly from the

collection of manifolds {V

}, and are essential to describe locally the shape of the struc-

ture. It is possible to distinguish between context independent features (automatically

computable for every manifold of a given dimensionality, such as Gaussian principal

curvatures, shape index and curvedness [8] for surfaces) and problem-speciﬁc proper-

ties.

Notice however that this ﬁrst characterization (given by collection of manifolds de-

scribed by functions) is not suited for data mining or similarity searches. The reason

is twofold. First, the given description of the whole structures has a dimensionality too

high to make the problem computationally feasible. Even worse, a pointwise character-

ization does not permit, at least in a straightforward manner, the comparison of anatom-

ical structures belonging to different patients, because a point-to-point correspondence

should be ﬁrst established.

These issues could be addressed in two ways. The ﬁrst solution is by using a deformable

model (given for example by mass-spring models as presented in [2]) and normalizing

every instance of anatomical structure to that model: in this way anatomical structures

(belonging to the same family) are uniformly described and can be then compared

according to the feature-vector paradigm. The second solution, which can be used in

tandem with the ﬁrst, is to use derived global features, not depending of any problem-

speciﬁc model of the anatomical structure. Generally, the ﬁrst solution is able to perform

a ﬁne discrimination among the dataset; the latter instead may be used to make a ﬁrst

coarse discrimination in order to drastically reduce the search space. We review in the

sections below some recent methods for extracting such kind of more intrinsic features

using a geometrical approach (Section 3.1) and a topological one (Section 3.2).

3.1 Geometrical Approaches

One of the most simple but ﬂexible geometric approach for the computation of global

features not depending on any problem-speciﬁc model is given by the so-called prop-

erty spectrum [7]. By deﬁnition, the property spectrum is the probability density func-

tion (PDF) of a given component of the property function P

(·). The property spec-

trum captures how the property is globally distributed; thus, comparison of different

property spectra is directly feasible; to reduce dimensionality, moreover, it could be ef-

fective to compute the momenta of the PDF (mean, variance,. . . ). However, property

spectrum does not convey any information at all about regional distribution of the prop-

erty. In clinical applications, this is a drawback which cannot be ignored: actually a

small highly anomalous region may not affect appreciably the property spectrum, but

its clinical relevance is, usually, not negligible. Hence, spatial distribution of proper-

ties has to be analyzed. One approach would be to estimate multidimensional property

spectrum. In this way, spatial relationship between different kinds of features could be

implicitly encoded. For example, considering the cords going from the center of mass

of a structure to its boundary, we may use the cord length and orientation as a property

function deﬁned on the structure boundary. See Figure 1.

Then, the associated multidimensional PDF implicitly codiﬁes the elongation axis

of the structure. A major issue in dealing with such sort of multidimensional shape

distributions is the accurate estimation of the PDF. Some methods, based on the fast

Gauss transform, have been reported [9]. Although, this approach may be conceivable

for general-purpose 3D structure indexing and retrieval, it has low relevance in medical

applications, due to the too implicit encoding and the poor characterization capabil-

ities of local anomalous regions. In the same vein, approaches which do not need a

reﬁned model of the structure (e.g., Gaussian image, spherical harmonics, Gabor spher-

ical wavelets and other general purposes shape descriptors used for content-based image

retrieval) may be suitable.

However, the introduction of models (or templates) for the anatomical structures

under examination should be considered so as to gain more description capability in

problem-speciﬁc scenarios. Indeed, using matching techniques, the template could be

propagated to any particular instance of the anatomical structure to be studied. Then,

Orientation

Fig. 1. An example of multivariate property function, encoding important spatial relationship

among features. We consider for each point of the structure the cord joining it with the center

of mass O of the structure. The length and orientation of such cord deﬁne a function in a 3-

dimensional property space.

using suitable averaging schemes for the property function on a model primitive (con-

sisting for example in a tetrahedron or in a polygon), a highly discriminative feature

vector may be coded.

3.2 Topological Approaches

The most known and well-established topological methods for the description of 3D

models include the medial axis transform [10–12], skeletal structures and Reeb graphs

[13]. Very often the extraction process is greatly sensitive to small perturbations in the

object to be studied. For this reason, in classical approaches, ad hoc cleaning of the

datasets has been used to achieve stability in the computation of the derived features.

Since topological noise is not always easily distinguishable from non-spurious topo-

logical features, multi-scale analysis should be generally preferred to ad hoc cleaning.

Persistency theory is a quite recent theory (see e.g. [14]) which offers the possibility to

build multi-scale hierarchical representations for 3D models, and to analyze and track

their topological features. In particular, persistency may describe at which scale a topo-

logical feature (e.g. a hole) is created and when it is annihilated (e.g. when the hole

has been ﬁlled) in a multi-scale representation. Topological features having long lives

are more robust and, likely, more salient. The interest in persistency theory has brought

several research groups to extend these ideas from the native 3D objects to derived

spaces in which geometrical properties are coded in a more explicit way. For example

in [15] the original object is replaced by its tangent complex, which, informally, may

be considered as the original space extended with the tangent directions in everyone of

its points. A multi-scale representation of the tangent complex is then obtained by con-

sidering a ﬁltration based on the curvature. Thus, a blending of geometric information

and topology is achievable by persistency analysis. Such synergy between the descrip-

tion power of geometry and the discriminative power of algebraic topology invariants

is clearly appealing for shape characterization and retrieval applications. For example,

in [16], the use of multidimensional Morse function and persistency is suggested for

building multiscale representation of anatomical structures, while in [17], persistency

of is applied to the skeletal graph of 3D models. The freedom in the choice of the func-

tion driving skeletal extraction coupled with the ﬁltrations arising from a wide-ranging

collection of shape descriptors allows the construction of suitable similarity measures

for 3D models.

3.3 Extension to Time-resolved Anatomical Structure

In [6] an extension to 3D+1 anatomical structures was proposed, with particular refer-

ence to the study of periodically deforming structures (such as the heart and the lungs).

Indeed, assuming that the deformations among the different phases of the cycle ﬁt into a

smooth family, modal analysis may be used to reduce the problem dimensionality, since

the anatomical structure has mainly low frequency excited deformation modes. See [3]

for an application to the study of the heart deformation pattern.

4 Anatomical Structure Semantic Annotation

The shape characterization features introduced so far may be understood as low level

features, which do not explain the case at hand, but just provide some –more or less

transparent– encoding of its appearance. Semantic annotation, on the other side, aims at

providing a meaningful, human understandable description of the case under examina-

tion. Semantic annotation generally consists in attaching (in a manual or assisted way)

textual labels (e.g. keywords) to objects. Such textual labels, however, should have fur-

ther structure in order to deﬁne a more powerful, clear and reusable language. Among

other models, ontologies appeared in artiﬁcial intelligence as computational artefacts

used for building conceptual models of a domain of discourse [18]. They can come in

different forms with increasing level of complexity, ranging from simple catalogues of

terms to thesauri till complex models with logical constraints that allow automated rea-

soning. Basically, an ontology contains a vocabulary of terms that states what exists in

the domain and, then, what can be predicated about.

In this sense, the Foundational Model of Anatomy (FMA, see [19]) deﬁnes concepts

and relations among anatomical structures; for instance relations such as has part are

included in FMA (e.g. Heart has part Heart Left Ventricle) and may be directly ex-

ploited in our framework for cross-modal access (for example a model of the heart

clearly represents also the heart left ventricle). Besides the use of a general medical on-

tology – like UMLS Semantic Network [20] – additional ontologies may be considered

to code reference terms for a speciﬁc domain, thus resulting in the use of a suite of

ontologies to gain modularity, scalability and extensibility.

5 Similarity Searches

The use of both shape and semantic tags for the annotation of anatomical structures

results into the possibility to gain cross-modal access to a repository, for example by

supporting the following two search strategies:

(a) (b) (c) (d)

Fig. 2. Sample neurofunctional systems: anterolateral (a), limbic (b), pyramidal (c) and auditorial

(d) systems.

– Searches based on similarity metrics for the feature vectors

– Concept-based searches

Well-established techniques are available for tuning similarity metrics for a given dataset

of feature vectors (see e.g. [4, 9]). Technologies are also available and mature to perform

concept-based searches using terms coded in an ontology and their semantic relations

(see e.g. the infrastructure presented in [21]). Our principal interest here is to use these

two methods for querying and accessing data and metadata in a hybrid way, for ex-

ample for supporting context-sensitive searches, as we describe next. Suppose indeed

that a query anatomical structure consists in a 3D model and that the user has already

stated that this model corresponds to a brain butterﬂy. In a basic way, the two searches

strategies above may be both triggered and, then, the two resulting sets of most similar

cases are compared to end up with just one set of most similar cases. An improvement

to this basic method consists in letting the semantic tag to inﬂuence the search based

on feature vector similarity. For example, the availability of the brain butterfly tag

may drive the system to the deﬁnition of a particular subset of features to be computed

and to the selection of a similarity metric ad hoc for the semantic class of brain but-

terﬂies. Other type of context-sensitive searches may take into account the scope of the

query (e.g. corresponding to a particular decisional task such as diagnosis or prognostic

stratiﬁcation) or general information about the patient (e.g. anamnesis). In both cases,

similar inﬂuences of the semantic tags on the similarity metric may be envisaged.

6 Application Scenarios

The aim of the following sections is to brieﬂy discuss sample scenarios for the applica-

tion of the ideas of this paper to neurology, radio-therapy and cardiology respectively.

6.1 Neurology

A still interesting problem in neurosurgery is represented by the morphological evalua-

tion of intracranial lesions, especially for what regards the identiﬁcation of surroundings

neurofunctional systems and vascular structures. For these reasons, neurofunctional at-

lases have been introduced since long time (see e.g. [22]). With this respect, the pro-

posed framework may be used for supporting case-based reasoning in the following

way. After having prepared a repository containing 3D models of neurofunctional sys-

tems (some samples are shown in Figure 2) and associated metadata (in the form of

geometric & topological features and semantic tags), several statistical similarity met-

rics may be learned, each one speciﬁcally designed for some particular sub-populations

in the dataset. For example, apart from a general-purpose similarity metric suitable for

all the anatomical structures in the repository, a speciﬁc similarity metric for the limbic

system may be included. This specialized similarity metric should be designed so as to

have a better retrieval performance on the subset of anatomical structure corresponding

to the limbic system. After this preparation step, the repository may be interrogated at

different context level; for example for answering a query consisting in just a 3D model

with no further information, the general purpose similarity metric should be used; if

semantic tags are available, more specialized similarity metrics together with concept-

based searches should be triggered instead. Of course, some strategies for on-line up-

dating the learned metrics on the basis of new annotated cases may be conceived.

6.2 Image Guided Radiation Therapy

Image-Guided Radiation Therapy (IGRT; see e.g. [23] for some introductional tech-

nical aspects) is a recent technique for the treatment of cancer, involving a workﬂow

even more complex than conventional conformal or intensity-modulated radio-therapy.

Indeed, in IGRT, high-resolution imaging modalities (usually CT) are used ﬁrst for ac-

quiring reliable anatomical images and reconstructing the boundary of the tumor and

of the sensible nearby structures (e.g. the spinal cord or genital organs). Then, a radio-

therapy plan is made, trying to maximize fraction delivery to tumoral cells and minimiz-

ing risk of exposing sensible structures. After the registration of radio-therapy plan to

physical world coordinates, the actual treatment delivery starts and is repeated for sev-

eral days or weeks (without repeating from scratch the radio-therapy planning). During

radio-therapy delivery, in addition, images (normally Cone-Beam CT images) of the pa-

tient anatomy are acquired on-line and may be used to make more effective and safe the

treatment, by checking that sensible structures are not irradiated (e.g. due to registra-

tion errors) and tuning the radio-therapy plan according to the actual growth/shrinkage

of the tumor during the treatment period. With respect to this scenario, the proposed

framework could be used to integrate the several available pieces of information, some

of which are depicted in Figure 3.

In particular, we may foreseen the following applications:

– Using as a query the reconstruction of a tumor, the framework may support retrieval

of already-available radio-therapy plans. Retrieved plans should be suitable as a

starting point for working out a new plan.

– The availability of annotated sensible structures may be used to setting up a deci-

sion support system to prevent their exposition to radiation. Such decision support

should run in the background and should present its suggestions in the proper con-

text during treatment planning and tuning. Since the latter is made on-line, preven-

tion of trivial mistakes is particularly important.

– Finally, retrieval using as query a temporal sequence of the tumor (for instance

depicting the tumor before treatment, after one week of treatment and after two

weeks) may be useful to evaluate the success of the therapy.

Shape Integration

Integrate the realm of shapes in the problem context

 Gain support for:

 More Powerful KDD

 Case

reasoning

 Effective Decision

Support

Demographics

/ History

LAB

Planning

Functional

Imaging

3D Model

Fig. 3. Integration of shape information in the general process of IGRT.

Fig. 4. Wall thickness at end diastole and systole, shown as a property function for the epicardial

surface.

Notice that the above applications demand for the management of scope-sensitive

queries, as deﬁned in Section 5. Of course, if a sufﬁciently rich dataset is available, such

procedures may also take into account patient demographic/anamnesis information, to-

ward a more personalized treatment.

6.3 Cardiology

The analysis of the shape of the heart and of its deformation pattern may be used to sup-

port case-based reasoning procedures for diagnosis of several cardiological pathologies

and for preoperative planning. For example, we consider here ventricular dyssynchrony.

Dyssynchrony is a complex phenomenon whose origins are to be tracked back to elec-

trical conduction disturbances that affect both regional and global function of the heart

and which results into incoordinate ventricular wall motion due to activation delay. De-

spite its relevance, the only dyssynchrony marker that has received some consensus is

an ECG-derived parameter, which however is poorly correlated to the outcome of resyn-

chronization therapy, usually consisting in pacing device implantation [24]. Since there

is a lack of generally accepted evidence about dyssynchrony therapy, the retrieval of

similar cases from a repository may help the physician to make appropriate therapeutic

choices. Indeed, after having reconstructed a time-resolved model of the heart of the

patient and having computed meaningful features (like activation time, wall motion and

thickening; see e.g. Figure 4), the patient anatomy, enriched possibly with demographic

and drug assumption information, may be compared with other patients which already

underwent resynchronization therapy.

7 Conclusions and Further Work

In this paper, a framework for the description of anatomical structures has been pre-

sented. The framework takes into account 1) topological and geometrical features and

2) semantic annotation. In this way, a 3D model representing an anatomical structure

may be extended with non-geometrical pieces of information, ranging from metadata

inherent to the instance of the structure (such as textual description of a lesion) to other

patient-speciﬁc data (regarding age, sex, anamnesis,. . . ).

Possible hybrid methods for similarity searches are then envisaged and shown to be

useful for reﬁned scope-sensitive retrieval. In this way, enhanced support for case-based

reasoning procedures is provided, as illustrated with three sample scenarios extracted

from various medical application ﬁelds.

In the future, we plan to integrate this work with other already developed infras-

tructures. Indeed, the presented framework may happily coexist with the system pre-

sented in [21], which introduces and uses an ontology for shape descriptors that –after

a suitable extension– may be proﬁtable also for the scopes of this paper. Another im-

provement towards a more ontology-centered framework is seen in the exploitation of

the algorithm ontology presented in [25], so as to provide semantic insight also in the

feature extraction process.

Acknowledgements

This work was partially supported by European Project HEARTFAID “A knowledge

based platform of services for supporting medical-clinical management of the heart

failure within the elderly population”(IST-2005-027107).

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