GROUPWISE NON-RIGID IMAGE ALIGNMENT
Results of a Multiscale Iterative Best Edge Algorithm
Bernard Tiddeman
Department of Computer Science, Aberystwyth University, Aberystwyth, Wales, U.K.
David Hunter
School of Psychology, University of St Andrews, St Andrews, Scotland, U.K.
Keywords:
Groupwise image alignment, Congealing, Active appearance models.
Abstract:
In this paper we present an algorithm for groupwise image alignment using an iterative best edge point algo-
rithm. Neighbouring image edge points are matched for similarity in a two directional fashion. The matches
found are used to drive a regularised warp of the images into alignment. The algorithm works from low to
high resolution, with the matches calculated across the set first at low resolution and towards progressively
finer scales. The regularisation decreases across iterations, and the search area remains constant, so covers
larger effective area in the low resolution images. We also extend the method to 3D surfaces by combining the
2D image search with a 3D ICP algorithm. The results show that this gives a very efficient algorithm that can
align many different sets of 2D images and 3D surfaces.
1 INTRODUCTION
Groupwise registration of images has received a great
deal of attention in recent years. Many applications
require the non-rigid alignment of different images
of the same class of object, such as medical images
or face images, for labelling of features or construc-
tion of morphable models such as active appearance
models (AAM) (Cootes et al., 2001). Models such
as AAM can be built using hand labelled examples,
but this is tedious and prone to error. Fully automatic
methods are therefore extremely valuable. Much of
the work performed in groupwise image alignment
thus far has followed the pattern:
choose a suitable metric for image alignment,
decide how to parameterise the non-rigid corre-
spondences, and
use a non-linear optimisation routine to minimise
the chosen metric by altering the image parametri-
sations.
Where the database contains multiple object
classes this basic framework can be extended to in-
clude assignment of class labels (e.g. (Liu et al.,
2009)), although that is not the focus of this paper.
For the single class alignment problem various
metrics have been proposed. Rueckert et al (Rueck-
ert et al., 2003) used mutual information for pairwise
matching. Wang et al (Wang et al., 2010) used the
Jansen-Shannon divergence (JSD) of multi-scale im-
age information to estimate matches between 3D MRI
images. Z
¨
ollei et al used a sum of voxel wise en-
tropies (Z
¨
ollei et al., 2005). Davies originally pro-
posed the minimum description length (MDL) met-
ric for alignment of similar 2D outline shapes (Davies
et al., 2001), which has subsequently been extended to
3D surfaces and volumetric data (Davies et al., 2008)
and also images (Cootes et al., 2005) (Cootes et al.,
2010). The MDL approach, whilst theoretically ele-
gant is computationally expensive, requiring repeated
building of morphable models and the use of (usu-
ally relatively slow) non-linear optimisation routines.
Others have found good results can be achieved with
far simpler metrics, such as the error from the current
estimate of the mean (Cootes et al., 2010) (Sidorov
et al., 2009).
The image alignment metric often includes a
shape component. For MDL this is usually based on
the shape statistics of the training set. In other work
the shape constraints usually take the form of a reg-
ularisation term or restriction of the warps to sim-
ple smooth deformations. In practice these can of-
ten achieve better alignment than a statistical shape
model, which can become trapped in local minima
22
Tiddeman B. and Hunter D..
GROUPWISE NON-RIGID IMAGE ALIGNMENT - Results of a Multiscale Iterative Best Edge Algorithm.
DOI: 10.5220/0003326800220029
In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2011), pages 22-29
ISBN: 978-989-8425-47-8
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
(a) (b)
(c) (d)
(e) (f)
Figure 1: Example output of our algorithm. (a), (c) and
(e) original blends without alignment, (b), (d) and (f) after
groupwise alignment on different images sets. (a-b) 434 im-
ages of men women and children of varying age and ethnic
origin, (c-d) 33 images of male faces from the IMM data set
and (e-f) 128 images from the FGNet Franck sequence.
(Cootes et al., 2010).
Parametrisation of the non-rigid registrations has
been achieved using a variety of methods, includ-
ing free form deformations (FFD) (e.g. (Rueckert
et al., 2003)) or piecewise affine warps (e.g. (Cootes
et al., 2005) (Cootes et al., 2010) together with FFDs
for moving groups of control points). Sidorov et al
(Sidorov et al., 2009) showed how to combine multi-
ple piecewise affine warps with arbitrary initial point
locations to create dense warping fields whilst keep-
ing the number of parameters to optimise over con-
stant across iterations.
Standard optimisation routines such as gradient
descent or the downhill simplex method can be
employed for minimising the error metric. Sev-
eral authors have elected to perform one-dimensional
searches along the current gradient direction (e.g.
(Cootes et al., 2005) (Wang et al., 2010). Sidorov et al
(Sidorov et al., 2009) used Simultaneous Perturbation
Stochastic Optimisation (SPSA) which can optimise
a function in approximately the same number of steps
as gradient descent, but using far fewer function eval-
uations (Spall, 1998). Their algorithm showed good
alignment but still required several hundred iterations
through the image set to achieve convergence.
An entirely different approach to non-rigid align-
ment is the iterative closest point algorithm which is
usually applied to 3D data sets. Both rigid and non-
rigid variation on the algorithm exist, it can be imple-
mented very efficiently and is guaranteed to converge
to a local minimum when one dataset is a subset of
another. Previous attempts have been made to com-
bine edge point matching into a groupwise alignment
algorithm. Hugnafel et al (Hufnagel et al., 2008) de-
veloped a groupwise expectation-maximisation ICP
algorithm for matching 3D surface shapes. Wang et
al (Wang et al., 2008) represented the points using
mixtures of Gaussians and iteratively minimised the
JSD. For image data Di et al (Di et al., 2007) devel-
oped a spatio-temporal generative model to automat-
ically align image sequences, but the algorithm was
not demonstrated on sets of independent images.
In this paper we develop a method for groupwise
image shape parametrisation and alignment based on
a multi-resolution ICP variant in which we find the
best match of edge maxima in a local neighbour-
hood of the search point. The algorithm developed is
simple to implement, efficient and shows promising
alignment results.
2 METHOD
In this section we first give an overview of the group-
wise alignment algorithm and then describe parts of
the algorithm in more detail. Multi-resolution has
been used in previous work, but in this algorithm it
plays a crucial role in the matching. Very localised
searches are used for matching points in the low reso-
lution version of the problem, which brings the points
in higher resolutions sufficiently close for matching
using an equally localised search. All images are reg-
istered to the current estimate of the average at a low
resolution, then the average estimate is recalculated
and the process is repeated at the next higher resolu-
tion (Algorithm 1).
2.1 Point Selection and Matching
Starting at the lowest resolution, maxima of the local
image intensity are found (Mallet, 1989) (Canny,
GROUPWISE NON-RIGID IMAGE ALIGNMENT - Results of a Multiscale Iterative Best Edge Algorithm
23
Algorithm 1: Groupwise registration algorithm.
Require: Images {I
i
} = {I
1
,...,I
N
}
iΦ
i
= 1 {Initialise all warps to the identity}
r = 2
k
{initialise resolution parameter}
while r 1 do
A =
1
N
N
i=1
I
i
(Φ
i
(x)) {Estimate average}
for i = 1 to N do
W = I
i
(Φ
i
(x)) {Warp current image}
φ = warpU pdate(A,W,r) {Get warp update,
Algorithm 2}
Φ
i
(x) = φ(Φ
i
(x)) {Compose warp update
with current warp}
end for
¯
Φ =
1
N
N
i=1
Φ
i
{Average warps}
iΦ
i
=
¯
Φ
1
(Φ
i
) {Normalise warps by removing
average warp}
r = r/2 {increase resolution}
end while
return Warps {Φ
i
}
1986). At each edge point found in the source image
a search is made in a small neighbourhood (currently
just the adjacent 9 pixels) in the target image (Figure
2). The most similar point (in terms of first or first and
second image derivatives) is selected as a potential
match (Algorithm 4). If a potential match is found
the same search is performed for matching edges in
the source image for the target point. If the points
in the source and target images agree the points are
added to the list of matches (Algorithm 3). Once the
search for matches is complete the estimated match-
ing points are used to drive a regularised warp from
the source to the target image. The process is repeated
until the number of matching edges doesn’t increase
(Algorithm 2).
2.2 Warping and Regularisation
Warping is performed using a multi-scale B-spline
based warping function (Lee et al., 1995) that in-
cludes an affine term. We store the non-affine part of
the warping function on a discrete grid. At the lower
scale the non-affine part of the warping function is
regularised. In this work we regularise by filtering
with a B-spline function whose width increases lin-
early with decreasing image resolution. This can be
achieved by repeated filtering with dilated versions of
the same discrete filter. We ensure that all the par-
tial warps are one-to-one by scaling the warp update
based on the size of the Jacobean at each point in the
warp (Tiddeman et al., 2001). Partial warps are con-
catenated at each iteration, which preserves the one-
to-one property. Each image is warped using the cur-
(a) (b)
Figure 2: (a) For each edge point in the first image (top) a
small neighbourhood is searched in the target image (bot-
tom). The most similar edge point (if any) is selected,
and an identical search is made of its neighbourhood in the
first image. If the most similar point in this second search
matches the original point the point pair are added to the
warp constraints. (b) Example edges from two images dur-
ing two iteration of our algorithm at different resolutions.
The current estimate of the average is shown in magenta,
the subject in cyan and overlapping pixels in blue.
Algorithm 2: Warp update algorithm.
Require: Images A and B, resolution parameter r
A
r
(x,y) = f
r
A(rx,ry) {Get low resolution ver-
sion}
B
r
(x,y) = f
r
B(rx,ry) {Get low resolution ver-
sion}
N
old
= 0
N
new
= 0
Φ = 1 {Initialise warp to identity}
repeat
N
old
= N
new
W
r
(x) = B
r
(Φ(x)) {Warp image using current
estimate}
({p
i
},{q
i
}) = match(A
r
,W
r
) {Get matching
edge maxima points, Algorithm 3}
N
new
= length({p
i
}) {store the number of
matches found}
φ = interpolate({p
i
},{q
i
}) {Interpolate con-
straints}
φ = f
r
φ {Low pass filter non-affine part of
warp}
φ = overlap(φ) {Ensure one-to-one property of
partial warp using (Tiddeman et al., 2001)}
Φ = φ · Φ {Compose warp update with current
warp}
until N
new
< N
old
Φ = Upsample( Φ) {Interpolate warp to current
resolution}
return Φ
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
24
rent estimate of the warp and then the image deriva-
tives are calculated before matching. At the end of
each iteration through the set the warps are upsampled
to match the current resolution. The partial warps are
also normalised by calculating the average warp and
removing the average warp from each partial warp.
We do this for each partial warp by calculating the
average shift and current shift for each point and in-
terpolating between them.
Algorithm 3: Edge matching algorithm.
Require: Images A and B
Calculate {A
i
} = {A
x
,A
y
,A
xx
,A
xy
,A
yy
}
Calculate {B
i
} = {B
x
,B
y
,B
xx
,B
xy
,B
yy
}
Calculate edge maxima E
A
and E
B
edgeList = {}
for all pixels x do
if E
A
(x) then
p = bestMatch({A
i
},{B
i
},E
B
,x) {Algorithm
4}
if p 6= then
q =bestMatch({B
i
},{A
i
},E
B
, p)
if q = x then
edgeList = append(edgeList, {x, p})
end if
end if
end if
end for
return edgeList
2.3 Application to 3D Surfaces
The method described above for 2D images can be ex-
tended to texture mapped surfaces where the surface
can be parameterised to a 2D rectangle. The facial
surface data we use (3dMD, 2011) is supplied with
a texture map in two halves and the size of the im-
ages and the position of the join line varies with dif-
ferent captures. Also the data contains various holes,
occasionally disconnected regions and sometimes in-
correct texture coordinates. To cope with this kind of
data we flatten the texture map to a single texture im-
age using angle-based flattening (Floater, 2003), al-
though more sophisticated area preserving methods
may improve the results. We only use the largest con-
nected region of the mesh, which usually contains the
face, or extraneous regions can be deleted to ensure
the face region is selected. We also assume approxi-
mate rigid alignment of the 3D models.
In order to produce an average we need to repa-
rameterise all the meshes to have a standard structure.
In this work we just pick one surface to act as the tem-
plate for the mesh (number of vertices, connectivity
etc.). The reparameterisation of the mesh to 2D pro-
duces texture maps that have no relationship to each
other. In order to get the 2D coordinates into approxi-
mate alignment and to initialise the algorithm we use
a non-rigid iterative closest point matching of the 3D
surfaces. Rays are traced from the ”standard” surface
until they intersect the study surface (within a maxi-
mum range). These matches are interpolated using a
multi-level free-form deformation (MFFD), initially
with the minimum grid spacing set to a large size,
to give a smooth warp. The process is repeated with
the grid resolution increasing up to the maximum. At
the finest scale the texture coordinates at the ray in-
tersection points are used to drive the texture map of
the study surface into approximate alignment with the
standard mesh’s texture map.
Algorithm 4: Point matching algorithm.
Require: Image derivatives {A
i
},{B
i
}, edge image
E
B
, location x
minerror = , p =
for all pixels y
x
do
if E
B
(y) then
error =
i={x,y,xx,yy,xy}
(A
i
(x) B
i
(y))
2
if error < minerror then
minerror = error
p = y
end if
end if
end for
return p
When all surfaces have been approximately
aligned using the process described above, there are
still residual errors in the alignment of the textures.
We can use the algorithm described above for 2D im-
ages to improve the alignment of the surfaces. Appli-
cation of the algorithm to only the image data could
result in loss of good 3D alignment. In order to avoid
this we also use curvature information from the sur-
face. The surface is mapped to the 2D domain by
sampling the coordinates in the texture space. The
points of maximum concave and convex curvature in
the direction of the associated principal directions are
calculated. The curvature of a surface is independent
of the viewpoint, but is highly dependent on scaling
and regularisation of the surface. We adapt the 2D
algorithm to include the curvature maxima estimated
at the current matching scale. In addition to finding
matching points of the intensity images, bi-directional
matches are found in the curvature maxima, added to
the list of match points and interpolated. The process
is illustrated in Figure 3.
GROUPWISE NON-RIGID IMAGE ALIGNMENT - Results of a Multiscale Iterative Best Edge Algorithm
25
Figure 3: The 3D alignment process showing the 3D models and associated texture maps, from left to right: the “standard”
model, an example subject model, the subject after reparameterising using non-rigid ICP and after additional groupwise
alignment. Estimated landmark locations are shown as green dots on the reparameterised 3D models. The non-rigid ICP fails
to position the landmarks correctly (especially around the mouth), whereas the groupwise alignment accurately places the
landmarks.
3 TESTING AND RESULTS
3.1 Average Construction
We have tested the 2D algorithm described above on
a set of 33 front-facing neutral expression male faces
from the IMM database (Nordstrøm et al., 2004),
the first 128 frames of the FGNET ”franck” dataset
(FGNET, 2004) and 434 of our own images contain-
ing approximately 13 images of individuals divided
into 4 age groups (child 10-12, teenager 13-19,
young adults 20-49, older adults 50+), 4 approxi-
mate ethnic groupings (white, black, Indian and Chi-
nese) and 2 gender groups. Figure 1 shows the mean
of these sets before and after application of our group-
wise alignment algorithm. Visual inspection of the
averages implies good alignment (on average), but
further tests were conducted to explore the quality of
the models constructed and the alignment speed. We
also tested the 3D algorithm on a set of 75 mixed age
and gender neutral 3D facial surfaces and 110 frames
from a 3D video sequence in the BU-4DFE set (Yin
et al., 2008). The results of blending using only pair-
wise shape alignment and using additional groupwise
alignment are shown in Figure 6.
3.2 Choice of Algorithm
We tested 3 versions of our algorithm using the speci-
ficity measure described in (Cootes et al., 2005):
(a) (b)
(c) (d)
Figure 4: Example faces generated from a combined shape-
appearance face model built from the IMM image set using
our algorithm. The models use (a) 5, (b) 10, (c) 15 and (d)
19 components of the combined face model.
1. Performing the alignment in the reference (aver-
age) frame using both 1st and 2nd derivative in-
formation to match edge points,
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
26
2. Performing the alignment in the target image
frame using first and second image derivatives and
3. Performing the alignment in the target frame
using only first derivative information (gradient
strength) to match edges.
In order to construct the combined appearance
model we manually delineated the mean image and
used the automatically generated warping functions
to map the points onto individual subjects. The shape
model was built from these points after removing vari-
ations due to rotation, translation and scaling. The
colour model was built from the images aligned using
the dense warping functions. The combined model
was then built using all the shape and colour PCA
weights from all images. The shape weights were
scaled by the square root of the ratio of the sum of
variances to balance their contribution to the model.
All the original images were rigid plus scale aligned
to the mean shape using the estimated points prior to
running the specificity tests as these parameters are
not constrained by the model.
The model was tested with 15 different numbers
of PCA parameters (from 5 to 19 inclusive). For each
set of parameters 1000 synthetic faces were gener-
ated. Example synthetic faces are shown in Figure
4. For each of these the difference from each original
face (average of absolute pixel differences) was cal-
culated, and the smallest added to the average error.
In previous work each pixel error was minimised over
a small neighbourhood by searching for the nearest
match, but in this work we just use the pixel at the
same location (i.e. the neighbourhood is just a single
pixel). The results of the specificity tests are shown
in Figure 5(a). These indicate that (as in previous
work) performing the alignment in the target image
reference frame leads to improved alignment, at the
expense of a small increase in algorithm complexity.
In addition, in this work the inclusion of 2nd deriva-
tive information in the edge matching also leads to an
improvement in the performance.
3.3 Accuracy
In order to compare our algorithm with manual anno-
tations we also used the warping function to project
a delineation of the mean image onto each image in
each set of face images. These automatically gen-
erated points were compared to the manually spec-
ified points by calculating the average distance of
each point from the manually specified location, di-
vided by the manually specified eye separation. For
the IMM and FGNET data we used the landmarkings
supplied with these data sets, for our own dataset we
used our own landmark data. The error was calcu-
4 6 8 10 12 14 16 18 20
40
41
42
43
44
45
46
47
48
49
50
Specificity comparison
target
reference
1st derivative
PCA Components
S
p
e
c
i
f
i
c
i
t
y
(a)
0 2 4 6 8 10 12 14
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Point Error Distribution
sci
imm
fgnet
Error (bin size = 0.5%)
P
r
o
b
a
b
i
l
i
t
y
(b)
0 50 100 150 200 250 300 350
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
Convergence comparison
IBE
Hand
SPSA
Iteration
E
r
r
o
r
m
e
t
r
i
c
(c)
Figure 5: (a) Specificity comparison demonstrates im-
proved performance for matching in the target image frame
vs reference image frame and for using both 1st and 2nd
derivative information vs only first derivative. (b) The dis-
tribution of errors from manually placed landmarks on the 3
image sets shown in figure 1. (c) Comparison of the conver-
gence speed between the stochastic optimisation algorithm
(SPSA) and our algorithm and hand delineation data on the
first 128 frames of the FGNET Franck sequence. (SPSA
and hand data taken from (Sidorov et al., 2009) Figure 6.)
lated as the average point distance as a percentage of
the eye manually specified eye separation (pupil cen-
tres on FGNET and our data, outer eye corners for
IMM). The results of this experiment are shown in
Figure 5(b) and indicate performance similar to pre-
vious work (e.g. (Cootes et al., 2010)). Unsurpris-
ingly, as the variation within each set increases the
alignment quality decreases.
GROUPWISE NON-RIGID IMAGE ALIGNMENT - Results of a Multiscale Iterative Best Edge Algorithm
27
(a)
(b)
(c)
(d)
Figure 6: Example output of our 3D algorithm. (a) and (c)
original blends after pairwise alignment with non-rigid ICP
(shape only), (b) and (d) after additional groupwise align-
ment on different images sets. (a-b) 75 3D captures of men,
women and children of varying age and ethnic origin. (c-d)
110 images from one of the BU 3D facial expression se-
quences.
0 2 4 6 8 10 12
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
3D Error Histogram
BU-IBE
BU-ICP
Error (bin size = 0.5%)
P
r
o
b
a
b
i
l
i
t
y
(a)
0 5 10 15 20 25
0
0.05
0.1
0.15
0.2
0.25
3D Error Histogram
EF-ICP
EF-IBE
Error (bin size = 0.5%)
P
r
o
b
a
b
i
l
i
t
y
(b)
Figure 7: Errors from hand landmarked data for the two
3D datasets shown in Figure 6. Errors are smaller for both
(a) the BU dataset and (b) our own data using the iterative
best edge algorithm (IBE) than using only pairwise iterative
closest point (ICP).
For the 3D surface data a similar experiment was
conducted. Landmarks specified in 2D on the average
texture map were projected onto each 3D surface us-
ing the estimated warping functions. These automati-
cally generated landmarks were compared with man-
ually specified 3D landmark locations, and the results
are measured as the average error over the points as a
percentage of the manually specified eye separation.
In both test sets the IBE algorithm demonstrates su-
perior alignment over pairwise shape only ICP align-
ment on both test data sets (Figure 7).
3.4 Speed
Direct comparison of convergence speed is extremely
difficult, with the risk that differences in the imple-
mentation or tuning effort can dominate the results.
Also, many papers don’t supply precise timings on
standard hardware and image data. With that health
warning in place, we provide results here that are
indicative of performance. We compare the con-
vergence speed (in terms of iteration counts) of our
algorithm to the SPSA based method described in
VISAPP 2011 - International Conference on Computer Vision Theory and Applications
28
(Sidorov et al., 2009). In the 10 iterations of our
algorithm we achieve a lower error than in approx.
300 iterations of the SPSA algorithm when using the
FGNET franck data (Figure 5(c)). Each iteration of
our algorithm is also fast as it only requires very lo-
cal searches and typically < 5 iterations of the edge
matching (in Algorithm 2) to converge at each scale.
4 CONCLUSIONS
In this paper we have developed a practical groupwise
alignment algorithm that demonstrates efficiency and
promising results. The algorithm uses a bottom up ap-
proach, combining many local estimates of the align-
ment using regularisation, rather then searching in a
large parameter space to optimise the alignment met-
ric. This makes the algorithm extremely efficient
and the results seem encouraging, but futher work is
needed to develop a rigorous theoretical underpinning
for the approach and to provide further comparisons
with alternative approaches.
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