Statistical Atlas Construction

Spine vertebra atlas: 39.0% of shape variation is encoded in the first mode. The second and third modes encode 20.4% and 12.8% of shape variation.

ABSTRACT

The statistical atlas is a 3D medical image analysis tool towards more patient-oriented and more efficient diagnosis. The atlas includes information on geometry and their variation across populations. It can be used as a global constraint for the multi-image shape-from-shading method. As a key to build statistical atlases, 3D registration remains an important yet unsolved problem in the medical image field due to the geometrical complexity of anatomical shapes and computational complexity caused by the enormous size of volume data. We developed a two-level framework to efficiently solve 3D non-rigid registration and applied the method to the problem of building statistical atlases. Compared with a general multi-resolution framework, we employed an interpolation to propagate the matching instead of repeating the registration scheme in each resolution. The registration procedure is divided into two levels: a low-resolution solution to the correspondences and mapping of surface models using Chui and Rangarajan’s thin-plate spline (TPS) based algorithm, followed by an interpolation to achieve high-resolution matching. After that, principal component analysis (PCA) is used to build the statistical atlas. Experimental results demonstrate that out method significantly improves efficiency of registration without decreasing accuracy of atlases.

PUBLICATIONS

“Construction of Statistical Shape Atlases for Bone Structures based on Two-level Framework”

Chenyu Wu, Patricia Murtha, Branislav Jaramaz

To appear in International Journal of Medical Robotics and Computer Assisted Surgery, 2009

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“Femur Statistical Atlas Construction Based on Two-level 3D Non-rigid Registration”

Chenyu Wu, Patricia Murtha, Branislav Jaramaz

To appear in International Journal of Computer Aided Surgery, 2009

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“Build Spine Atlas from Sparse Data”

Chenyu Wu, Patricia Murtha, Branislav Jaramaz

9th Annual Meeting of the International Society for Computer Assisted Orthopaedic Surgery (CAOS’09), June, Boston, 2009

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“Two-level Method for 3D Non-rigid Registration: with an Application to Statistical Atlases Construction”

Chenyu Wu, Patricia E. Murtha, A. Mor, Branislav Jaramaz

2nd International Conference on Computer Vision Theory (VISAPP2007), Insticc Press, Volume 1, March 2007, Barcelona Spain

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“The influence of sex in the construction of a statistical atlas of the hemi-pelvis”

Patricia E Murtha, Chenyu Wu, Andrew B. Mor, Branislav Jaramaz

5th World Congress of Biomechanics, July 29-Aug. 4, 2006, Munich, Germany

“A Two-level Method for Building a Statistical Bony Atlas”

Chenyu Wu, Patricia E Murtha, Andrew B. Mor, Branislav Jaramaz

5th Annual Meeting of the Int. Society for Computer Assisted Orthopaedic Surgery (CAOS’05), June 19-22, 2005, Helsinki, Finland

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“Sex: Does it matter (in the construction of a statistical atlas of the hemi-pelvis)?”

Patricia E Murtha, Andrew B. Mor, Chenyu Wu, Branislav Jaramaz

5th Annual Meeting of the Int. Society for Computer Assisted Orthopaedic Surgery (CAOS’05), June 19-22, 2005, Helsinki, Finland

VDIEOS

	Femoral Head Atlas, Mode 1 (AVI)
	Femoral Head Atlas, Mode 2 (AVI)
	Condyles Atlas, Mode 1 (AVI)
	Condyles Atlas, Mode 2 (AVI)
	Femur Atlas, Mode 1 (AVI)
	Femur Atlas, Mode 2 (AVI)
	Spine Vertebra Atlas (AVI)

PICTURES (click on thumbnails to enlarge images)

	To build a femur statistical atlas given partial 3D surfaces, we developed a two-level approach inspired by Chui and Rangarajan’s thin-plate spline based algorithm and the previous multi-resolution work. Since Chui and Rangarajan’s algorithm is not efficient to handle more than 2000 3D points, we broke down registration into a two-level process to deal with both computational and geometrical complexity. We first applied Chui and Rangarajan’s algorithm to the simplified low-resolution surfaces. To improve the efficiency, instead of successively matching each resolution from coarse to fine, we directly propagated the correspondences from low resolution to high resolution by interpolation. A local refine procedure was introduced for both low-resolution and high resolution surfaces to improve matching. Finally we applied PCA to the aligned surfaces to construct the femur atlas.
	The registration can be further improved by minimizing the point-to-surface distances. xi is a vertex on the deformed surface X, whose corresponding vertex on the surface Y is yi . We check the neighboring triangles of yi , which are triangles sharing the same vertex yi , e.g. S1, S2 and S3. We examine the distance from xi to each neighboring triangle (the distance computed from the vertex i x to the plane where the triangle lies), i.e. d1, d2 and d3. If any of them is smaller than d0 = || xi −yi ||, we use the corresponding projected point to replace yi to achieve a better registration. For those cases where different vertices on the surface Χ correspond to the same surface point on Y, we assign this corresponding surface point to the vertex on Χ with the smallest distance and make it unavailable to other vertices on Χ.
	Given the particularity of the femur data, we need to do a pre-alignment to get rid of the effect caused by the missing shape. We use the bottom portion of the femur as an example. The surface Y has more femur shaft but less shaft remains on the surface X. If we simply align both centers as in previous work, experiments shows that the registration process will be very slow and may not converge in several cases. The reason is that a part of the surface Y (as bounded by blue in the left figure) has no counterpart on X. Therefore, in order to improve upon the process, we decided to estimate the pseudo center of Y instead of the true center. And then the pose of two surfaces are estimated and aligned.
	Our method needs 5 minutes or less to match any size of surfaces (with missing data) with less than 200,000 vertices. However, their method costs 5 minutes for 350 vertices, 10 minutes for 460 vertices, 20 minutes for 610 vertices, etc.
	By tuning the number N ref ^low, we compare the d Mean, d RMS. when N ref ^low ≥ 0.2% N ref ^high , d Mean will be less than 1mm, which is a practical number in the clinical applications.
	Compared with the femur, spine vertebrae have much more complicated shapes which makes it more difficult to segment the surface model from the 3D CT images using the marching cube algorithm. However it is very time consuming to manually label over ten thousand points to obtain the high-resolution surfaces. Without knowing any shape prior, a semi-automatic strategy is developed to combine surface segmentation and registration in the same procedure, and reduce manual work to a minimal. A high-resolution 3D surface of vertebra was first generated by triangulating 40682 points which were carefully labeled by hand. This step takes several hours but only need to be done once. We trimmed each spine CT images into small files with individual vertebra. We manually labeled about 250 surface points (of the same resolution as the simplified reference surface) for each DICOM file. It takes 10-15 minutes to label each vertebra, 8-9 points on each image slice: 12 slices from the coronal plane, 12 slides from the sagittal plane and 6 slices from the transverse plane (showed in the left figure). We applied the two-level registration algorithm on a high-resolution reference surface and a low-resolution 250 points data set. Instead of using the local refinement, a global RBF based interpolation using a bigger kernel is applied to further warp the high-resolution surface toward original labeled points.

Last Update: September 2009