Deformable Registration Choices for Multi-Atlas Segmentation
Keyur Shah, James Shackleford, Nagarajan Kandasamy, and Gregory C. Sharp
CONTENTS
- 4.1 Introduction............................................................................................................................39
- 4.1.1 Deformable Registration.............................................................................................40
- 4.1.2 В-Spline Registration.................................................................................................41
- 4.1.3 Demons Algorithm.....................................................................................................41
- 4.2 Plastimatch MABS Implementation Details..........................................................................41
- 4.3 Evaluation Metrics..................................................................................................................42
- 4.4 Experimental steps.................................................................................................................42
- 4.5 Results.....................................................................................................................................45
- 4.6 Summary................................................................................................................................46
References........................................................................................................................................47
Registration is used for several purposes during multi-atlas segmentation. Atlases may be prealigned using rigid or deformable registration, and online registration may be performed during atlas selection. Furthermore, all atlas-based methods rely on deformable registration to map atlases onto the target image and the accuracy of the segmentation depends, to a large degree, on the deformable registration strategy undertaken. This chapter examines the influence of deformable registration parameter selection for two popular registration methods, the B-spline and demons algorithms. For B-spline methods, the effect of varying control point grid spacing, image subsampling rate, regularization method, and its corresponding weights are studied. The effect of Gaussian kernel width used to smooth the displacement field is explored for the demons algorithm. Experimental evaluation is performed on the Lung CT Segmentation Challenge (LCTSC) dataset.
Introduction
Deformable registration is one of the most important steps in the multi-atlas segmentation pipeline. One or more atlas images are registered to the image to be segmented, usually known as the query image, to create the segmentation. While it is widely acknowledged that deformable registration quality strongly influences the final segmentation quality, there is no consensus on the best registration techniques, such as the best objective function or transformation model. Various objective functions are used, most commonly: mean squared error (MSE) or sum of squared difference (SSD) of image intensity, mutual information (MI), normalized mutual information (NMI), and correlation coefficient (CC). Similarly, various transformation models have also been proposed, including: B-splines, thin plate splines (TPS), displacement fields, and velocity fields.
Several researchers have explored image registration approaches for atlas-based segmentation. Alven et al. presented a feature-based registration method which combines the information of the entire atlas set and efficiently finds robust correspondences and transformations between the target and all the images in the atlas set [1]. Bai et. al. compared, in their work, the performance of four different image registration algorithms: affine, B-spline, free-form deformation, and large deformation diffeomorphic metric mapping (LDDMM). Their experiments found that the LDDMM registration algorithm worked best for the mouse brain image segmentation task [2]. Datteri et al. used the adaptive bases algorithm (ABA) with an NMI objective function for registration. ABA models the deformation field as a linear combination of radial basis functions with finite support [3]. Doshi et al. used the Advanced Normalization Tools (ANTs) registration toolkit for atlas registration [4]. Heckemann et al. compare the image registration toolkit (IRTK) [5], based on B-splines and maximizing the NMI, with an algorithm they termed multi-atlas propagation with enhanced registration (MAPER), which optimizes both image intensity and tissue classification. They found that the MAPER approach provides superior results for a brain segmentation task [6]. Lotjonen et al. introduced a similarity metric based on intensity normalized images and compared it with NMI. They found a threefold reduction in the computation time with similar registration accuracy [7]. Sjoberg et al. compared a B-spline based method with a demons algorithm for registration strategy. No significant differences were reported [8]. Yeo et al. employed a generative model for the construction of a probabilistic atlas for joint registration and segmentation of images [9].
Previous works have largely considered the difference between registration methods. This chapter explores parameter choices for the B-spline and demons algorithm for atlas-based segmentation. The Plastimatch multi-atlas-based segmentation (MABS) platform is used [10]. Because the lung cancer segmentation challenge data uses CT, only the MSE similarity metric is considered. The following subsections describe the deformable registration problem, the transformation models, and the similarity metric.
Deformable Registration
The goal of deformable image registration is to align two or more images into the same reference frame. Given a fixed image F with voxel coordinates 0 = (x,y,z) and voxel intensities F(0) =/and moving image M with voxel coordinates ф = (x',уand voxel intensities М(ф) = m, the two images are said to be registered when the cost function
is minimized with respect to a similarity metric vg and regularization term S over the image overlap domain Q under the coordinate mapping T(0) = 0+ v. Here, v is the dense displacement field defined for every voxel OeQ, which maps from F to M.
For a unimodal registration problem such as LCTSC, the MSE is an appropriate choice. The expression for MSE is given as:
where N is the number of voxels in £2.
Because deformable registration is an ill-posed problem, it is helpful to constrain the solution to the set of physically meaning transforms. Equation 4.1 achieves this through the use of a regularization penalty term, where the smoothness S(v) is used to drive T toward smoother displacement fields. For this study, the use of curvature and third order regularizers, which are commonly used regularizers in deformable registration, are considered using the implementation within Plastimatch [11, 12]. It is considered that choosing correct regularizer weights is more important than the choice of regularizer type.
B-Spline Registration
B-spline registration is a method of deformable image registration that uses B-spline functions to define a continuous displacement field that maps the voxels in one image to those in another image. B-spline interpolation yielding the x component of the vector field for a voxel located at 0 is
where px is the B-spline coefficient defining the x component of the displacement field for one of the 64 control points that influence the voxel. The |3,, p,„, and p„ terms represent the uniform cubic B-spline basis function in the x, y, and z directions, respectively and ux, n(, and u. represent the normalized voxel location relative to the control point locations [13].
Demons Algorithm
The demons algorithm uses gradient information of a static fixed image in order to generate the demons force that deforms the moving image. Unlike the B-spline deformation model which interpolates the displacement vector field based on the control point weights, the demons algorithm generates the displacement vector field at each voxel. There are many different variants of the demons algorithm, including diffeomorphic and symmetric forms [14-16]. This investigation considers only the classic demons algorithm [17]. The vector field at location в in the moving image is solved iteratively by updating a displacement field according to
where V/is the gradient of the fixed image at voxel в. At each iteration, an update to the displacement field is solved according to Equation 4.3. Between iterations, the displacement field is updated by smoothing.
Plastimatch MABS Implementation Details
The Plastimatch MABS implementation of atlas-based segmentation was used for this study. Plastimatch is an open source software for image computation with focus on high-performance volumetric registration of medical images. The MABS workflow is divided into a training phase, where registration and segmentation parameters can be optimized, and the segmentation phase which uses the optimized parameters to segment new cases. Both phases perform a sequence of operations: (1) data conversion (optional), (2) pre-alignment (optional), (3) atlas selection (optional), (4) image registration, and (5) voting. A configuration file describes the parameters used for each operation [10]. The configuration settings used in this study are briefly described.
Data Conversion: Digital Imaging and Communications in Medicine (DICOM) files from the clinical scanners are converted into a compressed raw' format to enable faster atlas file loading. In this study, the DICOM files were converted to the Nearly Raw Raster Data (NRRD) file format. Similarly, DICOM-RT Structure Set files containing the anatomical structures are rasterized into volumetric format using one file for each structure.
Pre-Alignment: The anatomical image within each atlas is pre-aligned to a randomly chosen reference image using rigid or affine transformation. The transformation is also applied to the structure images. In this study, the atlas images were pre-aligned to a reference image using the prealignment step.
Atlas Selection: A subset of atlases can be selected for a given atlas based on image similarity or displacement field metrics, such as NMI of the image intensities or mean-squared vector difference of the displacement field. Atlas selection can also be performed randomly or using a precomputed ranking. Once the atlases are ranked, a fixed number of atlases can be selected, or a variable number of atlases that meet a threshold criterion can be selected. The atlas selection step is optional; if not selected all the atlases in the database will be used. In this study, NMI was used as the metric and the five atlases with the highest NMI were selected. Chapter 3 explores atlas selection in more depth.
Image Registration: Each atlas from the selected set is registered to the query atlas using deformable image registration. Multiple registration strategies can be compared during the training phase, and the best strategy is selected using exhaustive search. Details of the image registration used in this study are found in the next section.
Voting: After the structures are warped into the reference of the query image, the final segmentations are generated through statistical algorithms. Plastimatch MABS supports Gaussian weighted (GW) and STAPLE as voting techniques. The voting parameters of either algorithm are specified in the configuration file and can be optimized during the training phase. In this study, Gaussian weighted voting was used, and voting parameters were optimized prior to investigating registration parameters.
