A fast inverse consistent deformable image registration method based on symmetric optical flow computation.
ABSTRACT Deformable image registration is widely used in various radiation therapy applications including daily treatment planning adaptation to map planned tissue or dose to changing anatomy. In this work, a simple and efficient inverse consistency deformable registration method is proposed with aims of higher registration accuracy and faster convergence speed. Instead of registering image I to a second image J, the two images are symmetrically deformed toward one another in multiple passes, until both deformed images are matched and correct registration is therefore achieved. In each pass, a delta motion field is computed by minimizing a symmetric optical flow system cost function using modified optical flow algorithms. The images are then further deformed with the delta motion field in the positive and negative directions respectively, and then used for the next pass. The magnitude of the delta motion field is forced to be less than 0.4 voxel for every pass in order to guarantee smoothness and invertibility for the two overall motion fields that are accumulating the delta motion fields in both positive and negative directions, respectively. The final motion fields to register the original images I and J, in either direction, are calculated by inverting one overall motion field and combining the inversion result with the other overall motion field. The final motion fields are inversely consistent and this is ensured by the symmetric way that registration is carried out. The proposed method is demonstrated with phantom images, artificially deformed patient images and 4D-CT images. Our results suggest that the proposed method is able to improve the overall accuracy (reducing registration error by 30% or more, compared to the original and inversely inconsistent optical flow algorithms), reduce the inverse consistency error (by 95% or more) and increase the convergence rate (by 100% or more). The overall computation speed may slightly decrease, or increase in most cases because the new method converges faster. Compared to previously reported inverse consistency algorithms, the proposed method is simpler, easier to implement and more efficient.
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ABSTRACT: Image correlation is often required to utilize the complementary information in CT, MRI, and SPECT. A practical method for automatic image correlation in three-dimensions (3D) based on chamfer matching is described. The method starts with automatic extraction of contour points in one modality and automatic segmentation of the corresponding feature in the other modality. A distance transform is applied to the segmented volume and a cost function is defined that operates between the contour points and the distance transform. Matching is performed by iteratively optimizing the cost function for 3D translation, rotation, and scaling of the contour points. The complete matching process including segmentation requires no user interaction and takes about 100 s on an HP715/50 workstation. Perturbation tests on clinical data with cost functions based on mean, rms, and maximum distances in combination with two general purpose optimization procedures have been performed. The performance of the methods has been quantified in terms of accuracy, capture range, and reliability. The best results on clinical data are obtained with the cost function based on the mean distance and the simplex optimization method. The accuracy is 0.3 mm for CT-CT, 1.0 mm for CT-MRI, and 0.7 mm for CT-SPECT correlation of the head. The accuracy is usually at subpixel level but is limited by global geometric distortions, e.g., for CT-MRI correlation. Both for CT-CT and CT-MRI correlation the capture range is about 6 cm, which is higher than normal differences in patient setup found on the scanners (less than 4 cm). This means that the correlation procedure seldom fails (better than 98% reliability) and user interaction is unnecessary. For CT-SPECT matching the capture range is about 3 cm (80% reliability), and must be further improved. The method has already been introduced in clinical practice.Medical Physics 08/1994; 21(7):1163-78. · 2.91 Impact Factor
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ABSTRACT: A greyscale-based fully automatic deformable image registration algorithm, originally known as the 'demons' algorithm, was implemented for CT image-guided radiotherapy. We accelerated the algorithm by introducing an 'active force' along with an adaptive force strength adjustment during the iterative process. These improvements led to a 40% speed improvement over the original algorithm and a high tolerance of large organ deformations. We used three methods to evaluate the accuracy of the algorithm. First, we created a set of mathematical transformations for a series of patient's CT images. This provides a 'ground truth' solution for quantitatively validating the deformable image registration algorithm. Second, we used a physically deformable pelvic phantom, which can measure deformed objects under different conditions. The results of these two tests allowed us to quantify the accuracy of the deformable registration. Validation results showed that more than 96% of the voxels were within 2 mm of their intended shifts for a prostate and a head-and-neck patient case. The mean errors and standard deviations were 0.5 mm+/-1.5 mm and 0.2 mm+/-0.6 mm, respectively. Using the deformable pelvis phantom, the result showed a tracking accuracy of better than 1.5 mm for 23 seeds implanted in a phantom prostate that was deformed by inflation of a rectal balloon. Third, physician-drawn contours outlining the tumour volumes and certain anatomical structures in the original CT images were deformed along with the CT images acquired during subsequent treatments or during a different respiratory phase for a lung cancer case. Visual inspection of the positions and shapes of these deformed contours agreed well with human judgment. Together, these results suggest that the accelerated demons algorithm has significant potential for delineating and tracking doses in targets and critical structures during CT-guided radiotherapy.Physics in Medicine and Biology 07/2005; 50(12):2887-905. · 2.70 Impact Factor
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ABSTRACT: A method for determining differences in patient position between projection radiographs such as those routinely used in radiation therapy has been developed. Determination of a transformation relating two radiographs permits registration of simulation and portal images and the transfer of information between them. The algorithm is based on spatially registering segments of open curves or points seen on both images, and does not require identification of corresponding curve endpoints. The method as implemented is both fast and accurate. After user definition of the curves or points to be registered, the optimal transformation is calculated in approximately 1 s. Calculational experiments indicate that corresponding points on open curves are registered to better than 2 mm, even when random errors (FWHM 1 mm) in digitization are included. Experiments on the registration of clinical portal and simulation images (pixel size = 0.5 by 0.5 mm) indicate an accuracy on the order of 2 mm or less in translation and 2 deg or less in rotation. Analysis of portal and simulation radiographs of the brain, thorax, and pelvis indicates this algorithm to be robust and clinically applicable. The rapid and accurate registration of portal and simulation images is potentially important in the application of real time portal imaging devices in radiation therapy.Medical Physics 01/1992; 19(2):329-34. · 2.91 Impact Factor
A fast inverse consistent deformable image registration method based on symmetric optical
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2008 Phys. Med. Biol. 53 6143
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PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 53 (2008) 6143–6165
A fast inverse consistent deformable image registration
method based on symmetric optical flow computation
Deshan Yang1, Hua Li, Daniel A Low, Joseph O Deasy
and Issam El Naqa
Department of Radiation Oncology, School of Medicine, Washington University in St. Louis,
4921 Parkview Place, LL, St. Louis, MO 63110, USA
Received 10 June 2008, in final form 16 September 2008
Published 14 October 2008
Online at stacks.iop.org/PMB/53/6143
Deformable image registration is widely used in various radiation therapy
applications including daily treatment planning adaptation to map planned
tissue or dose to changing anatomy. In this work, a simple and efficient inverse
consistency deformable registration method is proposed with aims of higher
I to a second image J, the two images are symmetrically deformed toward one
by minimizing a symmetric optical flow system cost function using modified
optical flow algorithms. The images are then further deformed with the delta
motion field in the positive and negative directions respectively, and then used
for the next pass. The magnitude of the delta motion field is forced to be less
than 0.4 voxel for every pass in order to guarantee smoothness and invertibility
for the two overall motion fields that are accumulating the delta motion fields
in both positive and negative directions, respectively. The final motion fields
to register the original images I and J, in either direction, are calculated by
inverting one overall motion field and combining the inversion result with the
other overall motion field. The final motion fields are inversely consistent
and this is ensured by the symmetric way that registration is carried out. The
proposed method is demonstrated with phantom images, artificially deformed
patient images and 4D-CT images. Our results suggest that the proposed
method is able to improve the overall accuracy (reducing registration error by
30% or more, compared to the original and inversely inconsistent optical flow
the convergence rate (by 100% or more). The overall computation speed may
slightly decrease, or increase in most cases because the new method converges
1Author to whom any correspondence should be addressed.
0031-9155/08/216143+23$30.00© 2008 Institute of Physics and Engineering in MedicinePrinted in the UK 6143
6144 D Yang et al
faster. Compared to previously reported inverse consistency algorithms, the
proposed method is simpler, easier to implement and more efficient.
(Some figures in this article are in colour only in the electronic version)
It has been witnessed in the recent years that anatomical image information (kVCT, daily
fMRI, etc) were increasingly adopted into patient radiation treatment management. Image
registration is a procedure to transform different image datasets into a common coordinate
system so that corresponding points of the images are matched and the complementary
information from the different images can be analyzed for different diagnostic and therapeutic
purposes. Kessler provided a comprehensive review of image registration for radiation
therapy (Kessler 2006). Image registration algorithms can be generally grouped into rigid
registration and deformable (non-rigid) registration according to the type of transformation
with limited number of free parameters (up to 12), deformable registration uses much larger
number of free parameters (up to three times the total number of voxels in an image) in order
to describe non-rigid tissue deformation in 3D space.
Deformable image registration can be computed based on features extracted from the
images, e.g. points (Kessler et al 1991), lines (Balter et al 1992) and surfaces (van Herk
and Kooy 1994) or based on metrics directly derived from the image intensity values,
e.g. mean square error (MSE) (Thirion 1998) for images from the same modality, mutual
information (MI) (Viola and Wells 1995) and cross-correlation (Kim and Fessler 2004) for
images from different modalities. Mean-squared-error (MSE) based CT to CT deformable
image registration is especially important for radiation therapy applications, including patient
response monitoring, treatment adaptation, dose tracking and patient motion modeling, etc
(Lu et al 2004, Wang et al 2005, Sarrut et al 2007). This paper focuses on such algorithms.
Regardless of the image registration algorithm, registration accuracy is always one of the
images, registration results often cannot be validated on a voxel-by-voxel basis because there
is no such ground truth available. While landmark matching and structure volume matching
are often used for results validation, they are not voxel by voxel based and the overall accuracy
of such a validation is quite limited because landmarks or structures can only cover limited
regions of the entire image.
Inverse consistency, which means that the registration results are consistent from
registering the images in the forward direction (from image 1 to image 2) or in the reverse
direction (from image 2 to image 1), is often considered as one of the more feasible ways
for measuring image registration accuracy (Christensen et al 2006) for any registration
algorithms. This is based on the fact that results by an accurate registration algorithm must
be inversely consistent. Therefore, inverse consistency is always desirable for any deformable
registration algorithm in addition to its accuracy. For image-guided and adaptive radiation
therapy (ART) applications, such inverse consistency is not only desirable but also practically
useful. Information such as treatment planning contours, etc is defined on the treatment
planning CT, while daily doses, contours, etc are referenced to the daily images. Inverse
consistency registrations can provide voxel mapping in both directions so that information can
be consistently mapped from one image to the other image.
A fast inverse consistent deformable image registration method 6145
Table 1. Notations used in this paper.
I ◦ V
The moving image, or the first image
The fixed image, or the second image
The difference image, Id= J − I
The image domain
Coordinates of image positions in ?
The ‘pull-back’ displacement motion vector fields
The delta motion field
=I(x−V(x)), the image I deformed by V
=V1(x−V2(x)) + V2(x), the composition of two motion fields
The inverted vector field of V
(ART). For example, registration needs to be computed quickly and accurately between the
treatment fractionations. In the future, such a computation may need to be completed online
while a patient is on the treatment table. Computation speed is also demanded by 4D-CT
based respiratory motion estimation because of the large amount of 4D image data.
Because of these reasons, we propose a new and efficient inversely consistent deformable
registration method in this paper. The new method uses a simplified system cost function
and solves registration in a symmetric way.
intensity gradients) from both images are symmetrically used in the computation, both
asymmetrical inverse-inconsistency algorithms. Because the system cost function is simpler,
the overall computation speed is improved compared to other inverse consistency algorithms.
Because image information (intensity and
1.1. Optical flow deformable image registration and inverse consistency
1.1.1. Optical flow.
modality deformable image registration. They are based on image intensity and gradient
information. For two images I and J to be registered, let I be the moving image and J be the
fixed image, a displacement motion vector field V registers I to J so that
Optical flow algorithms are among the most used algorithms for single
J = I ◦ V ≡ I(x − V(x)),
where ◦ is the composition operator, V is the motion field and x is the spatial coordinate. The
motion field V is the displacement vector field instead of the transformation vector field. V
is often referred to as the deformation field or the optical flow field. Description of notations
used in this paper is in table 1.
V normally cannot be resolved by only using equation (1) because the system is
underdetermined. Other constraints, such as global smoothness, are often enforced in order
to successfully compute V. With the additional global smoothness constraints, the system cost
function could be written as
where R is the smoothness constraint (also known as regularization constraint) function,
? is the image domain and α is a constant. Many optical flow algorithms use R(V) =
tr((∇V)T(∇V)), where tr( ) is the matrix trace operator. If |V| is small, equation (2) could
((J − I ◦ V)2+ α2R(V))d?,
6146D Yang et al
Figure 1. Illustration of asymmetric registration and inverse consistency error. Point A (in
image I) and B (in image J) are matching points. V is computed by registering I to J. U is computed
by registering image J to image I. (a) After imperfect asymmetric registrations, point A moves to
point A?and point B moves to point B?. (b) Using U, A?will be moved to A??. Similarly, B??is
B?moved by using V. The distance from A to A??, and from B to B??, are the inverse consistency
be expressed using a Taylor expansion of the first-order terms in the following differential
where Id= J − I, ∇ is the gradient operator, · is the vector inner product operator.
V could be solved by minimizing E1with many numerical methods, either iteratively or
techniques, region-based matching, energy-based methods and phase-based techniques. This
paper uses the Horn–Schunck (HS) algorithm (Horn and Schunck 1981) and the demons
where the differential form of the system cost equation is solved using the image intensity and
gradient. Such differential optical flow algorithms are often referred to as small-motion-model
algorithms because they only work if |V| is sufficiently small so that the Taylor expansion
series can be applied.
((Id+ ∇I · V)2+ α2R(V))d?,
1.1.2. Registration in the inverse direction.
to image I in the backward direction, the second motion field U needs to be computed so
Traditionally, if image J needs to be registered
I = J ◦ U.
A similar system equation could be written as
Even if V has already been computed, U has to be computed independently because there
is unfortunately no direct dependence among the solutions of V and U. This is illustrated in
((I − J + ∇J · U)2+ α2R(U))d?.
1.1.3. Inverse consistency.
consistent so that registration could start with either image and the results are consistent.
Inverse consistency could be written as
It is desirable for many applications that V and U are inversely
V ◦ U = 0 = U ◦ V,
where the composition operator ◦ between two motion fields is defined in table 1.