We present a novel image registration method based on B-spline free-form deformation that simultaneously optimizes particle correspondence and image similarity metrics. Different from previous B-spline based registration methods optimized w.r.t. the control points, the deformation in our method is estimated from a set of dense unstructured pair of points, which we refer as

The study of brain changes in rodent models of neuropathology and drug exposure has been of increasing interest to the neuroscience community. In contrary to human studies, rodent models have several advantages, such as a well controlled environments and access to genetic modifications as well as shorter lifespan. Magnetic Resonance Imaging (MRI) has emerged as an important modality to study such rodent brain morphological changes. Non-rigid registration is a crucial tool to process such MRIs providing structural segmentations and enabling the analysis of group differences.

Several methods have been proposed for the study of rodent brains. Among those atlas-based registration methods are popularly used. However, a single atlas-based method has a disadvantage of the introduction of bias that might cause poor segmentation and dilute the difference between groups [

Motivated by a particle correspondence algorithm [

Unbiased Group-wise Registration with Implicit Mean: Instead of choosing a specific template, a common reference frame is estimated from dynamic particles distributed inside ROIs,

As our work is in an early stage, we demonstrate preliminary results of rodent brain structure segmentation with comparison to two different registration methods for humans: the spline-based FFD available in Slicer and to SyN available in ANTS. We show that our group-wise algorithm performs better in different sizes as well as produces statistically indifferent results with the comparing methods otherwise.

We propose a group-wise image registration method guided by dynamic particles. The structure of our method is similar to the surface-based particle correspondence algorithm [

The main goal of our method is to drive each particle toward a corresponding position that satisfies two conditions in the mean space: 1) overlapping of particles and 2) local intensity similarity. The particles are governed by two forces: a positional coherence force and a force from local intensity similarity.

To describe the motion of particles, we define the particle system ^{1}, ^{2}, …, ^{N}}. For each subject _{P} (_{i}) and a local intensity similarity metric _{I}(_{i}). The final dense deformation field ^{j} to ^{j} and

By the transform _{j}, a particle _{i} should move to the direction where the variance of _{i} is minimized as depicted in _{i} and

Since the number of particles is much smaller than the number of voxels, we sample a local patch near by a particle

Given covariance matrices of Σ and Λ that follows _{P} and _{I} analytically [_{P}_{I}

From the particle perspective, the negative gradient direction,

Corresponding particles across subjects are attracted together to be overlapped at a locally similar position. Without an appropriate repulsion force, the particles would degenerate to a single point. Moreover, since we sample local intensity values nearby a particle, a repulsion force is required to uniformly sample a given image domain. In order for that, we extend the surface-based particle correspondence algorithm [

Given a bounded region of interest Ω in a volume _{i} = (_{S} is the differential entropy
_{i} is i.i.d, _{S}(_{i}). From the definition,

A key step to compute

For the optimization, we employ a standard gradient descent optimization via Euler scheme, _{j} for each particle [

An improved FFD B-spline is proposed by [_{j} directly from the set of corresponding particles interpolating B-spline deformation in Least Squares sense. [

Since the registration is performed by iterative particle optimization, the initial particle placement is important to achieve good registration results. Assuming that a basic preprocessing such as the rigid or affine registration is performed, we compute the initial particle placement as following:

Compute the intersection Ω_{M} of a set of given ROIs Ω_{1}, Ω_{2}, …, Ω_{N}

Choose random particle samples _{M}

Uniformly distribute the sampled particles _{M}

Transfer _{i} inside Ω_{i}

The data set acquired post mortem, at 3 age groups across adolescence (postnatal days 28 through 80). MR images of each animal using a Bruker BioSpec 9.4T horizontal bore MRI system (Bruker, Billerica, MA). Images were acquired using a 4-channel phase-array surface coil with the rat in supine position. 3D MDEFT sequence was used for T1-weighted image acquisition with the following parameters: TE=6.7 ms, TR=4000 ms, NEX=4; matrix size of 320×210, and the voxel size of 0.1mm isotropic, and acquisition time was 6 hours. To improve signal-to-noise-ratio (SNR), two images were acquired immediately following each other for each animal, and these two were averaged together following rigid registration. Total imaging time was 12 hours.

For the preliminary results of our method, we compared the results of our method with two popularly used non-rigid registration methods using cross correlation as a similarity metric: the non-rigid FFD B-spline image registration method packaged in Slicer3, and the SyN image registration method implemented in ANTS [

From the results, the proposed method showed higher Dice coefficients than other two methods. Our method showed better performance in Dice coefficients than the FFD B-spline implementation and ANTS tool in the manually segmented regions.

We proposed a novel image registration method that is guided by dynamic particles. Having correspondences each other, those particles are driven to locally similar positions in the mean space. By computing an implicit mean rather than an explicit image, our method was efficiently performed group-wise image registration in a linear time with respect to the number of subjects. Our method can be immediately applied to for example the multi-atlas joint registration/segmentation, the detection of outliers in a large data study, the inclusion of statistical shape information during registration, etc. Since the proposed method stays at a very early stage of research, future work will include thorough validation for its accuracy and robustness as well as comparison to other group-wise registration method [

The following grants are acknowledged for financial support: P01 DA022446, P30 HD03110, R41 NS059095, U01 AA020022, A020023, A020024, AA06059, AA019969, U54 EB005149.

Schematic diagram of (a) overlapping particles and local intensity similarity in correspondence across subjects. Colored in blue, green, and red, each particle has correspondence across subjects and attracts together minimizing _{P}

Overall algorithm flow. The registration process is finished when the system stabilizes, and images are registered with the estimated _{j}

Visual comparison of segmentation results. From left to right, the moving, fixed, result of proposed method, B-spline, and ANTS respectively in the first three rows. The bottom row shows sagittal slices of the fixed image, the result of the proposed image, and the moving image. The intensity scale was inverted during the acquisition but corrected in the experiments.

Overall Dice coefficients and its standard deviation of Thalamus and Cerebellum, by the proposed group-wise method, Symmetric Diffeomorphic Mapping in ANTS, and FFD B-spline registration.

Methods | Thalamus | Cerebellum |
---|---|---|

The proposed method | 86% (±8%) | 87.8% (±6%) |

ANTS | 81% (± 6%) | 84% (± 14%) |

B-spline | 81% (± 6%) | 79% (± 11%) |