Hubless 3D Medical Image Bundle Registration

R

´

emi Agier, S

´

ebastien Valette, Laurent Fanton, Pierre Croisille and R

´

emy Prost

Universit

´

e de Lyon, CREATIS; CNRS UMR5220; Inserm U1044; INSA-Lyon; CHU Lyon and St-Etienne

Universit

´

e Claude Bernard Lyon 1, Villeurbanne, France

Keywords:

Big Data, Medical Imaging, Points of Interest, Registration.

Abstract:

We propose a hubless medical image registration scheme, able to conjointly register massive amounts of

images. Exploiting 3D points of interest combined with global optimization, our algorithm allows partial

matches, does not need any prior information (full body image as a central patient model) and exhibits very

good robustness by exploiting inter-volume relationships. We show the efﬁciency of our approach with the

rigid registration of 400 CT volumes, and we provide an eye-detection application as a ﬁrst step to patient

image anonymization.

1 INTRODUCTION

The increasing availability of digital medical imag-

ing techniques such as Magnetic Resonance Imaging

(MRI), Computed Tomography (CT) and Ultrasound

(US) and the amount of data to process in health-

care networks has grown exponentially, thus illustrat-

ing the Big Data challenge in medecine. To perform

early screening, monitoring or to follow-up thousands

of patients throughout their healing, stress has to be

put on the ability to perform fast and robust image

analysis. This sums up to one question: how to pro-

cess several thousand volumes automatically and ro-

bustly? In this context, we propose a versatile feature-

based co-registration framework which can serve as a

ﬁrst step towards volume collections processing. The

aim of this paper is to register the volumes altogether.

this paper currently focus on robustness rather than

accuracy, with the belief that the challenge is in inter-

patient variability.

The Picture Archiving and Communication Sys-

tem (PACS) is at the center of image management in

healthcare networks. Medical images are stored in

the Digital imaging and communications in medicine

(DICOM) format which contains, in addition to im-

ages, informations such as acquisition parameters and

patient data. With cohort studies (Bild et al., 2002)

and mass computation, spatial consistency between

images is crucial. Despite the fact that DICOM con-

tains data about spatial positions, we can see in ﬁg-

ure 1 that they are not consistent. So, when one wants

to deal with large medical image datasets, an initial

Figure 1: Mass 3D image registration. (Top) a bundle of

heterogeneous images arranged according to DICOM em-

beded data. This shows that DICOM metadata are gen-

erally not consistent and may hinder subsequent computa-

tions. (Bottom) After mass hubless registration, images are

well aligned and the bundle may be used in further com-

putation. Registration is robust over heterogeneous images,

with, for example, only small body parts like heads. For

visualization purposes, images are distributed over an hori-

zontal grid.

global registration is needed. We propose to solve

this global challenge using a hubless approach. To

our knowledge, this is the ﬁrst time that an approach

which jointly process medical images is proposed.

This paper is organized as follows : Section 2 gives

a brief overview of related approaches both in Med-

ical Imaging and Computer Vision ﬁelds. Section 3

presents our hubless registration proposal. Section 4

shows experimental results and a conclusion follows.

Agier, R., Valette, S., Fanton, L., Croisille, P. and Prost, R.

Hubless 3D Medical Image Bundle Registration.

DOI: 10.5220/0005666702650272

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 3: VISAPP, pages 267-274

ISBN: 978-989-758-175-5

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

267

2 RELATED WORKS

2.1 Points of Interest

During the last decades points of interest (Harris and

Stephens, 1988; Lowe, 2004) have successfully been

exploited for tasks such as object recognition (Lowe,

1999; Lowe, 2004), action recognition, robotic navi-

gation, panorama creation, etc... They aim at being

fast while reducing the amount of data to process,

mainly to deal with realtime processing or tasks in-

volving large amounts of data. Their suitability to

medical imaging has been evaluated in (L

´

opez et al.,

1999), and various applications have been proposed

in this context, like image annotation (Datta et al.,

2005), image retrieval (Zheng et al., 2008). Most

of the applications relate to image registration and

matching. There are some 3D points of interest de-

velopment, like (Knopp et al., 2010), which use ras-

terized meshes to describe 3D shapes.

2.2 Image Registration

Image registration in medical application is a wide

research ﬁeld (Hill et al., 2001; Sotiras et al., 2013)

where a lot of different approaches have emerged. We

split the approaches in two categories:

• dense -or voxelwise- registration, with minimiza-

tion or maximization of an energy function (for

example mutual information (Pluim et al., 2003)).

The main advantage is to provide a dense regis-

tration, with an information about deformation at

each point of the space. However, voxelwise com-

putation is time-consuming.

• sparse registration, using points of interest (Al-

laire et al., 2008; Cheung and Hamarneh, 2007;

Khaissidi et al., 2009). This approach provides a

less accurate method because points of interest do

not always span the whole space. But if one has

to perform multiple registrations, this approach is

several orders of magnitude faster than dense reg-

istration, because points of interest have to be ex-

tracted only once per image.

Registration can be used directly for medical ap-

plications, as instance for therapy planning (Pelizzari

et al., 1989; Rosenman et al., 1998). It can also be

used as an essential step for other algorithms such as

atlas-based approaches (Gass et al., 2014).

2.3 Bundle Optimization

As ﬁrst applications in computer vision, points of in-

terest are generally used in the medical ﬁeld to match

two images. But novel approaches in computer vi-

sion have appeared, using multiple images in order to

tackle problems such as real time 3D reconstruction

(Triggs et al., 2000), efﬁcient tracking using low-end

cameras (Karlsson et al., 2005). More recent works,

like (Frahm et al., 2010), deal with large amount of

data to reconstruct a town.

Bundle optimization is a promising paradigm, that

paved the way to augmented reality and virtual real-

ity (Klein and Murray, 2007), and can contribute to

emerging challenges in medical image processing:

• Large Amounts of Images: nowadays, medical

imaging is a very spread technology and more and

more images are produced each day.

• Multiple Modalities: in order to be more accu-

rate, multiple modalities (CT, MRI, US, etc.) may

be used in order to establish a diagnostic. Algo-

rithms have to follow this trend and manage mul-

tiple modalities.

Note that some papers already have proposed the

use of multiple medical images such as Multi-Atlas

approaches (Gass et al., 2014). But these approaches

most often carry out several applications of one-to-

one matching with a hub model (Bartoli et al., 2013)

and are limited to completely overlapping input im-

ages (Marsland et al., 2008) contrary to image bundle

optimization. We call these approach hub-based, in

contrast with our hubless model (ﬁgure 2).

3 HUBLESS REGISTRATION

3.1 Multiple Views vs Multiple Patients

There is a fundamental difference between scene re-

construction and body registration. More precisely,

3D reconstruction assumes a unique scene acquired

with different points of view in contrast with mul-

tiple patients, variability breaks the hypothesis of a

unique scene. The challenge shifts from 3D estima-

tion with 2D data to inter-patient variability handling

among 3D images.

3.2 The ”Hub-based Model” Issue

If one wants to register two images I

1

and I

2

, one

containing an upper body part and one a lower body

part, one faces the overlap limit (August and Kanade,

2005). One solution is to use a third image I

re f

, a full

body image (the hub) and register it with I

1

and I

2

. Af-

terwards, the two registrations are composed in order

to obtain the upper body to lower body registration.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

268

hublesshub-based

Figure 2: Fundamental differences between hub-based and

hubless approaches. Here, 5 images are represented by 5

red dots. (Left) Hub-based approach : one needs an sixth

image as a central model. This approach allows only 5 links

between images, and its efﬁciency depends on the choice

of the model image. (Right) The hubless approach : no

image is picked as a model. This allows to compute 10

links between the 5 images.

In the case of image bundles, an image used as a

hub to register two images may not be the best hub for

other images. As a result, picking the right hub is a

complex task. Moreover, this ”one size ﬁts all” model

may be difﬁcult to register with some images due to

patient anatomy variability.

3.3 Challenges and Contributions

Our approach of registration is to deal with the whole

image bundle at once, which brings major improve-

ments compared to one-to-one registration. This pa-

per only deals with rigid registration, as a proof of

concept, with the intend to generalize it to non-rigid

registration in future works. A ﬁrst challenge is to

deal with a big amount of data. In this paper, each im-

age is a scanner acquisition which resolution ranges

between 200

3

and 600

3

, each voxel being encoded

with 16 bits. In the last experimentation, we have a

bundle of 400 images representing more than 100GB

of image data. We overcome this challenge by con-

verting the whole image bundle into a compact repre-

sentation such as Speeded Up Robust Features (SURF

(Bay et al., 2006)) that we extend to 3D in section 3.4.

Moreover, we need to be able to process images

containing not only full-body scans but also body

parts which is usually a problem. Indeed, incomplete

data (body parts) generally hinder the registration pro-

cess, due to the overlap limitation. In our case, we

overcome this difﬁculty, and use partial matches to

improve our results.

Also, as seen on ﬁgure 2, registering a group of

n images with a hub-based approach, is performed

with n registrations. On the other hand, with a hub-

less approach, one can beneﬁt from a much higher

number of registrations. This number can be as high

as n(n − 1)/2, depending on the overlap between im-

ages. The advantage of this difference is the problem

which becomes more and more overdetermined with

the number of images. We exploit this fact to increase

robustness and accuracy of our approach. A second

challenge is to face the overdetemined nature of our

problem, for which we propose a novel solution in

section 3.6.

As a consequence, partially overlapping image

sets can easily be processed with our approach, and

incorrect registrations do not signiﬁcantly impact ac-

curacy as long as the problem remains overdeter-

mined.

3.4 3D Surf

The SURF approach comes as a fast and efﬁcient

points of interest extractor, but was originally created

for 2D images. We then developed a generalization of

the SURF descriptor to deal with 3D medical images.

3.4.1 Blob-like Structure Detection

The ﬁrst step is to extend the 3D scale-space of a 2D

image into a 4D function of a 3D image. In spirit

with 2D SURF, we compute a box-ﬁlter approximate

Hessian matrix H(x) at each point x = (x,y,z) of the

image. This results in a 3x3 Matrix H. Blob detection

is carried out by analysing the sign of the eigenval-

ues of H. But in contrast with 2D SURF, computing

the determinant of H is not sufﬁcient to check that

its eigenvalues are all negative or positive. In spirit

with what Allaire et al. proposed for 3D SIFT (Al-

laire et al., 2008), we use the trace of the Hessian

tr(H) and the sum of principal second-order minors

∑

det

P

2

(H) in addition to the determinant to have suf-

ﬁcient knowledge on the eigenvalues.

3.4.2 Description

For a 2D image, SURF splits the neighborhood of

each point of interest into smaller 4x4 square sub-

regions. For each sub-region, a set of features is com-

puted using Haar wavelet responses (2 responses per

direction). All responses are concatenated into a 64-

element vector which is normalized to be contrast-

invariant. We apply the same method but take bene-

ﬁt of the third dimension, by splitting neighborhoods

into 2x2x2 cubic-sub-regions, and extracting 3x2 re-

sponses. We build a 48-element vector, which is

smaller compared to 2D SURF but contains more lo-

cal information thanks to the third dimension.

3.4.3 Upright SURF

We chose to not extend the rotation-invariance of 2D

SURF to our case, as with most problems subject to

Hubless 3D Medical Image Bundle Registration

269

Figure 3: Points of interest extracted from a CT volume.

Clearly, important structures inside the patient such as lungs

are well detected. Blue and red circles represent dark and

light blobs, respectively.

the curse of dimensionality, giving the descriptor in-

variance to rotations would decrease robustness. Vari-

ous invariant solutions exist, as in (Allaire et al., 2008;

Cheung and Hamarneh, 2007). But in our current ap-

plication, we have the prior information that during

image acquisition, the patient is standing, which make

the principal orientation computing unnecessary as

long as inter-patient deformation remains reasonable.

3.5 Pairwise Registration

Once SURF descriptors are extracted from the whole

image bundle, we register all possible image pairs

using RANdom SAmple Consensus (Fischler and

Bolles, 1981). We currently deal with a rigid trans-

form model with 4 degrees of freedom : 3 translations

and 1 isotropic scale.

f : x 7→ s.x + t (1)

The output of this step is a set of n ∗ (n − 1)/2

transforms which link the images altogether. How-

ever this set contains incorrect transforms due to sev-

eral issues:

• non-overlapping images pairs.

• pairs with too few matches due to variability be-

tween patients.

e

Y =

1.5 −1

−1 −0.8

−1 1.8

t

3

2

= [−1, −0.8]

t

1

3

= [−1, 1.8]

t

2

1

= [1.5, −1]

Y =

2 −1

−1 −1

−1 2

n

1

n

2

n

3

Figure 4: A simple problem with 3 volumes (green dots)

and 3 translations: Blue arrows depict observed registra-

tions, orange dotted lines represent registration error. Ma-

trix Y depicts ground truth transforms between all images.

Matrix

e

Y represents estimated transforms.

3.6 Hubless Bundle Registration

3.6.1 Problem Statement

Once we have the set of transforms, we want to be

able to consistently register the images. Note that

we restrict ourselves to using transforms with 3 de-

grees of freedom (translations). Extension to 4 de-

grees of freedom is explained in a subsequent section.

In a slightly more abstract formulation, our problem

is equivalent to compute point positions given only

relative positions between them. Figure 4 shows an

example where 3 nodes n

1

, n

2

and n

3

, have to be lo-

cated given their 3 ∗ (3 − 1)/2 = 3 relative positions

t

2

1

, t

3

2

and t

1

3

.

3.6.2 Solving Laplacian Equations

We propose to solve this problem by writing it as a

Laplace equation (Cohen-Or and Sorkine, 2006), us-

ing the image bundle complete graph. The graph car-

ries several kinds of information:

• Each node n

i

corresponds to one patient image I

i

,

with a local reference frame x

i

which will be ad-

justed consistently with the bundle.

• Each edge e

k

j

carries the translation t

k

j

between the

two images I

j

and I

k

as computed using pairwise

registration (section 3.3). Note that due to the

presence of incorrect registrations (section 3.3),

the set of translations is not always consistent.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

270

x

1

= [0, 2]

x

2

= [1.67, 1]

x

3

= [0.83, 0.2]

e

P =

0 2

1.67 1

0.83 0.2

P =

0 2

2 1

1 0

n

1

n

2

n

3

Figure 5: Reconstructed positions. Using our algorithm on

the problem shown in ﬁgure 4, we can reconstruct the po-

sitions. Blue arrows represent the corrected registrations

between all images. Matrix P depicts ground the truth posi-

tions. Matrix

e

P represents the estimated positions.

The problem now simpliﬁes to ﬁnding the best set of

local frames x

i

given the set of translations t

k

j

. In

graph theory, there is an analogy which can be done

in relation with relative / absolute information, based

on a matrix representation of the graph:

E

t

.P = Y (2)

where E is the incidence matrix that shows the rela-

tionship between vertices. P is the local frame matrix

which stores local frames x

i

, each row representing

one vertex, each column referring to one space dimen-

sion. Y refers to the observation matrix, where each

row contains the translation carried by one edge e

k

j

.

In our case, we aim at ﬁnding the best estimate of P

given an inconsistent observation matrix Y, which we

propose to solve using a Laplacian equation. Given

a graph, the matrix L = E

t

.E is known as the graph

laplacian operator matrix. This matrix is symmetric,

singular and positive semi-deﬁnite.

By left-multiplying equation (2), by E the Lapla-

cian matrix appear as follow :

L

t

.P = E.Y (3)

which cannot be solved as it is because the Lapla-

cian matrix is always singular, of rank n − 1. In a ge-

ometric point-of-view, this result in the fact that abso-

lute reconstruction from relative positions is deﬁned

up to an offset. Applying the same displacement to

all local frames doesn’t change relative positions be-

tween them. To make the Laplacian matrix non singu-

lar, we ﬁx the absolute coordinates of one vertex, re-

ferred to as anchor in (Cohen-Or and Sorkine, 2006).

Figure 6: Example of problem with 3 volumes (legs, head,

body) and 1 impossible registration. To successfully regis-

ter this bundle of 3 volumes, the registration between the

legs and head has to be discarded.

We solve equation 3 using least square minimization.

Figure 5 shows the solution to the problem depicted

in ﬁgure 4 with an anchor ﬁxed on vertex n

1

.

3.6.3 Graph Decimation

All possible image pairs are used to perform the

registration and construct the graph. As a conse-

quence, non-overlapping body parts create outliers in

the graph, as shown in ﬁgure 6. In other word, some

edges represent a wrong observation. As a reminder,

the breakdown of least square approaches is 0 (Meer

et al., 1991). Then in our case, the error caused by

one outlier edge will not be ﬁltered out but it will be

distributed over all the graph nodes. One solution is

to discard edges representing the worst registrations,

while keeping the graph connected. This requires the

deﬁnition of a quality criterion for each individual

transform. For robustness purpose, given two images

and their registration computed using RANSAC, we

simply use the number of inliers found by RANSAC.

We then sequentially remove edges according to this

criterion, avoiding the removal of any edge that would

break the graph connectedness. We chose to remove

edges until the graph contains k ∗ n edges. We experi-

mentally set k to 3.

Hubless 3D Medical Image Bundle Registration

271

3.6.4 Extension to Scale Computation

Our graph approach can only deal with summable val-

ues, allowing us to manage only translations between

images.

But scale information between two images depicts

a multiplicative relationship, as in Equation (1). We

address this problem in a separable way, with, on one

hand, the translation parameters and on the other hand

the scale parameters. Taking the logarithm of equa-

tion (1) changes the scale into an additive value.

We exploit this fact by processing log-scale as a

fourth dimension, supplementary to the three ﬁrst co-

ordinates.

4 RESULTS

We applied this method to register a bundle of het-

erogeneous Computed Tomography (CT) 3D images.

Images exhibit different dimensions, different reso-

lutions and most importantly may contain different

body parts. All computation have been carried out on

a 24-core workstation with 128 GB of RAM, using

the DESK framework (Jacinto et al., 2012).

In practice, SURF points of interest provide a very

compact representation of the data. As an example,

one image, which weighs from 200 to 600 MB, can

be turned into a 0.1 to 1MB SURF description. Com-

plexity of this part is linear with the number of im-

ages and can be easily parallelized. For a typical

full body acquisition (1.8*0.6*0.6 meters, resized into

an isotropic image with 1.5mm spacing), about 5000

points of interest are extracted in about 2 minutes.

Hubless bundle registration exhibits quadratic

complexity, as we have to register each possible im-

age pair. During RANSAC registration, we perform

6000 iterations with a distance threshold of 40mm.

As our metric reﬂects natural units, we add a crite-

rion about difference in scale during match computa-

tions: if the scale ratio between two points of inter-

est is larger than 1.5, we forbid the match between

these points. Thanks to a very compact representa-

tion, computing a transformation between two typical

full bodies (with full overlap) is done in a few sec-

onds.

Points of interest approaches were originally used

to register two images with different point of views

of the same scene. A main criterion to evaluate per-

formance of points extraction is repeatability. In our

case, repeatability is less signiﬁcant because we regis-

ter images from different patients. Moreover we cur-

rently only deal with global translations between im-

ages, as we currently focus on robustness rather than

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 50 100 150 200 250 300 350 400

Processing time(s)

Number of volumes

Figure 7: Processing time vs number of volumes.

accuracy. However we experimentally checked that

images containing overlapping body parts are well

registered together.

Figure 1 shows the registration of a bundle of 35

CT images, and ﬁgure 8 an example with 400 CT im-

ages. Our approach is able to register both bundles in

a very robust way. Figure 7 shows processing time for

a bundle depending on the number of images it con-

tains. This graph exhibits a slight quadratic behavior,

as computation time is still dominated by the points of

interest extraction stage, which has linear complexity.

Quadratic complexity will be more visible with bun-

dles containing more than 400 images.

A ﬁrst application of our algorithm is automatic

eye covering for anonymization. The only needed

user input is the head bounding box b

head

in one of

the images, and the eyes bounding box b

eyes

. After-

wards, we perform these steps:

1. compute the hubless bundle registration

2. extract images containing heads, by propagating

a human-made cut out of a head in one image, in

spirit with atlas-based approaches

3. apply a second pass of the whole hubless process,

using only points of interest located in the head.

4. transport the location of the pre-positioned eyes

on every images containing eyes using the previ-

ous registration.

Re-computation using only partial set of points of in-

terest allows the algorithm to be more accurate. Con-

ceptually, this can be considered as a ﬁrst step towards

deformable registration, with a locally-rigid registra-

tion. First results can be seen in ﬁgure 9. One can

note that the eyes are correctly covered except for

cases where the patient head is tilted. Solving these

cases will imply the use of transformation models

with more degrees of freedom than simple transla-

tions.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

272

Figure 8: Mass registration of 400 volumes. (Top Image) A bundle of volumes displayed with raw information about position

contained in DICOM. (Bottom Image) Registered bundle.

Figure 9: Covering eyes on meshes extracted from CT-images. Note that here the surface meshes are solely used for visual-

ization purposes, only the image is used for processing.

5 CONCLUSIONS AND

PERSPECTIVES

We have shown the beneﬁts of computing joint reg-

istrations compared to one-to-one registrations. This

brings robustness in the case of heterogeneous med-

ical datasets which may contain disjoint body parts.

Compact approaches, using point of interest extrac-

tion, allow us to deal with large datasets, in reason-

able time. Our approach provides an efﬁcient way

to background screening of large medical databases,

using a simple translation-and-scale transform model.

Future work may study the extension of this approach

to non-rigid transforms. We also plan to tackle the

complexity issues that will arise when dealing with

even bigger image bundles. Finally, our image graph

is currently connected, but sub-graph extraction is a

promising way to classify the patients, analyzing both

the graph inner properties and patient data.

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