Filtering in the diffeomorphism group and the registration of point sets

A Kalman Filtering Perspective for Multiatlas Segmentation

In multiatlas segmentation, one typically registers several atlases to the novel image, and their respective segmented label images are transformed and fused to form the final segmentation. In this work, we provide a new dynamical system perspective for multiatlas segmentation, inspired by the following fact: The transformation that aligns the current atlas to the novel image can be not only computed by direct registration but also inferred from the transformation that aligns the previous atlas to the image together with the transformation between the two atlases. This process is similar to the global positioning system on a vehicle, which gets position by inquiring from the satellite and by employing the previous location and velocity-neither answer in isolation being perfect. To solve this problem, a dynamical system scheme is crucial to combine the two pieces of information; for example, a Kalman filtering scheme is used. Accordingly, in this work, a Kalman multiatlas segmentation is proposed to stabilize the global/affine registration step. The contributions of this work are twofold. First, it provides a new dynamical systematic perspective for standard independent multiatlas registrations, and it is solved by Kalman filtering. Second, with very little extra computation, it can be combined with most existing multiatlas segmentation schemes for better registration/segmentation accuracy.

Elastic registration of prostate MR images based on estimation of deformation states

Magnetic resonance imaging (MRI) is being used increasingly for image-guided targeted biopsy and focal therapy of prostate cancer. In this paper, a combined rigid and deformable registration technique is proposed to register pre-treatment diagnostic 3T magnetic resonance (MR) images of the prostate, with the identified target tumor(s), to intra-treatment 1.5T MR images. The pre-treatment T2-weighted MR images were acquired with patients in a supine position using an endorectal coil in a 3T scanner, while the intra-treatment T2-weighted MR images were acquired in a 1.5T scanner before insertion of the needle with patients in the semi-lithotomy position. Both the rigid and deformable registration algorithms employ an intensity-based distance metric defined based on the modality independent neighborhood descriptors (MIND) between images. The optimization routine for estimating the rigid transformation parameters is initialized using four pairs of manually selected approximate corresponding points on the boundaries of the prostate. In this paper, the problem of deformable image registration is approached from the perspective of state estimation for dynamical systems. The registration algorithm employs a rather generic dynamic linear elastic model of the tissue deformation discretized by the finite element method (FEM). We use the model in a classical state estimation framework to estimate the deformation of the prostate based on the distance metric between pre- and intra-treatment images. Our deformable registration results using 17 sets of prostate MR images showed that the proposed method yielded a target registration error (TRE) of 1.87 ± 0.94 mm,2.03 ± 0.94 mm, and 1.70 ± 0.93 mm for the whole gland (WG), central gland (CG), and peripheral zone (PZ), respectively, using 76 manually-identified fiducial points. This was an improvement over the 2.67 ± 1.31 mm, 2.95 ± 1.43 mm, and 2.34 ± 1.11 mm, respectively for the WG, CG, and PZ after rigid registration alone. Dice similarity coefficients (DSC) in the WG, CG and PZ were 88.2 ± 5.3, 85.6 ± 7.6 and 68.7 ± 6.9 percent, respectively. Furthermore, the mean absolute distances (MAD) between surfaces was 1.26 ± 0.56 mm and 1.27 ± 0.55 mm in the WG and CG, after deformable registration. These results indicate that the proposed registration technique has sufficient accuracy for localizing prostate tumors in MRI-guided targeted biopsy or focal therapy of clinically localized prostate cancer.

A Framework for Joint Image-and-Shape Analysis

Techniques in medical image analysis are many times used for the comparison or regression on the intensities of images. In general, the domain of the image is a given Cartesian grids. Shape analysis, on the other hand, studies the similarities and differences among spatial objects of arbitrary geometry and topology. Usually, there is no function defined on the domain of shapes. Recently, there has been a growing needs for defining and analyzing functions defined on the shape space, and a coupled analysis on both the shapes and the functions defined on them. Following this direction, in this work we present a coupled analysis for both images and shapes. As a result, the statistically significant discrepancies in both the image intensities as well as on the underlying shapes are detected. The method is applied on both brain images for the schizophrenia and heart images for atrial fibrillation patients.

Joint segmentation of anatomical and functional images: applications in quantification of lesions from PET, PET-CT, MRI-PET, and MRI-PET-CT images

We present a novel method for the joint segmentation of anatomical and functional images. Our proposed methodology unifies the domains of anatomical and functional images, represents them in a product lattice, and performs simultaneous delineation of regions based on random walk image segmentation. Furthermore, we also propose a simple yet effective object/background seed localization method to make the proposed segmentation process fully automatic. Our study uses PET, PET-CT, MRI-PET, and fused MRI-PET-CT scans (77 studies in all) from 56 patients who had various lesions in different body regions. We validated the effectiveness of the proposed method on different PET phantoms as well as on clinical images with respect to the ground truth segmentation provided by clinicians. Experimental results indicate that the presented method is superior to threshold and Bayesian methods commonly used in PET image segmentation, is more accurate and robust compared to the other PET-CT segmentation methods recently published in the literature, and also it is general in the sense of simultaneously segmenting multiple scans in real-time with high accuracy needed in routine clinical use.