Pre-organizing Shape Instances for Landmark-Based Shape Correspondence

Sparse deformation prediction using Markove Decision Processes (MDP) for Non-rigid registration of MR image

BACKGROUND AND OBJECTIVE

A framework of sparse deformation prediction using Markove Decision Processes is proposed for achieving a rapid and accurate registration by providing a suitable initial deformation.

METHODS

In the proposed framework, the tree is built based on the training set for each patch from the template image. The template patch is considered as the root. The node is the patch group in which multiple similar patches are extracted around a key point on the training image. Given the linkages between patch groups in the tree, MDP is introduced to select the optimal path with highest registration accuracy from each training patch to the template patch. The deformation between them is estimated along the selected path by patch-wise registration which can be realized by a non-learning-based method. Given the patches on a testing image, their best matching patches are fast chosen from the training patches and the corresponding deformations constitute a sparse deformation. A dense deformation for the entire test image is subsequently interpolated and used as an initial deformation for further registration.

RESULTS

With the non-learning-based registration as the baseline method, the proposed framework is evaluated using three datasets of inter-subject brain MR images with three learning-based methods. Experimental results of the non-learning-based method using the proposed framework reveal that the computation time is reduced by fivefold after using the proposed framework. And, with the same baseline method, the proposed framework demonstrates the higher accuracy than three learning-based methods which predicts the initial deformation at image scale. The mean Dice of three datasets for the tissues of the brain are 73.52%, 70.73% and 64.82%, respectively.

CONCLUSIONS

The proposed framework rapidly registers the inter-subject brains and achieves the high mean Dice for the tissues of the brain.

Automatic construction of statistical shape models using deformable simplex meshes with vector field convolution energy

BACKGROUND

In the active shape model framework, principal component analysis (PCA) based statistical shape models (SSMs) are widely employed to incorporate high-level a priori shape knowledge of the structure to be segmented to achieve robustness. A crucial component of building SSMs is to establish shape correspondence between all training shapes, which is a very challenging task, especially in three dimensions.

METHODS

We propose a novel mesh-to-volume registration based shape correspondence establishment method to improve the accuracy and reduce the computational cost. Specifically, we present a greedy algorithm based deformable simplex mesh that uses vector field convolution as the external energy. Furthermore, we develop an automatic shape initialization method by using a Gaussian mixture model based registration algorithm, to derive an initial shape that has high overlap with the object of interest, such that the deformable models can then evolve more locally. We apply the proposed deformable surface model to the application of femur statistical shape model construction to illustrate its accuracy and efficiency.

RESULTS

Extensive experiments on ten femur CT scans show that the quality of the constructed femur shape models via the proposed method is much better than that of the classical spherical harmonics (SPHARM) method. Moreover, the proposed method achieves much higher computational efficiency than the SPHARM method.

CONCLUSIONS

The experimental results suggest that our method can be employed for effective statistical shape model construction.

Predict brain MR image registration via sparse learning of appearance and transformation

We propose a new approach to register the subject image with the template by leveraging a set of intermediate images that are pre-aligned to the template. We argue that, if points in the subject and the intermediate images share similar local appearances, they may have common correspondence in the template. In this way, we learn the sparse representation of a certain subject point to reveal several similar candidate points in the intermediate images. Each selected intermediate candidate can bridge the correspondence from the subject point to the template space, thus predicting the transformation associated with the subject point at the confidence level that relates to the learned sparse coefficient. Following this strategy, we first predict transformations at selected key points, and retain multiple predictions on each key point, instead of allowing only a single correspondence. Then, by utilizing all key points and their predictions with varying confidences, we adaptively reconstruct the dense transformation field that warps the subject to the template. We further embed the prediction-reconstruction protocol above into a multi-resolution hierarchy. In the final, we refine our estimated transformation field via existing registration method in effective manners. We apply our method to registering brain MR images, and conclude that the proposed framework is competent to improve registration performances substantially.

Shape retrieval using hierarchical total Bregman soft clustering

In this paper, we consider the family of total Bregman divergences (tBDs) as an efficient and robust "distance" measure to quantify the dissimilarity between shapes. We use the tBD-based ℓ₁-norm center as the representative of a set of shapes, and call it the t-center. First, we briefly present and analyze the properties of the tBDs and t-centers following our previous work in. Then, we prove that for any tBD, there exists a distribution which belongs to the lifted exponential family (lEF) of statistical distributions. Further, we show that finding the maximum a posteriori (MAP) estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tBD to find the t-centers. This leads to a new clustering technique, namely, the total Bregman soft clustering algorithm. We evaluate the tBD, t-center, and the soft clustering algorithm on shape retrieval applications. Our shape retrieval framework is composed of three steps: 1) extraction of the shape boundary points, 2) affine alignment of the shapes and use of a Gaussian mixture model (GMM) to represent the aligned boundaries, and 3) comparison of the GMMs using tBD to find the best matches given a query shape. To further speed up the shape retrieval algorithm, we perform hierarchical clustering of the shapes using our total Bregman soft clustering algorithm. This enables us to compare the query with a small subset of shapes which are chosen to be the cluster t-centers. We evaluate our method on various public domain 2D and 3D databases, and demonstrate comparable or better results than state-of-the-art retrieval techniques.