GOGMA: Globally-Optimal Gaussian Mixture Alignment

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

Registration of prostate surfaces for image-guided robotic surgery via the da Vinci System

Organ-confined prostate cancer represents a commonly diagnosed cancer among men rendering an early diagnosis and screening a necessity. The prostate laparoscopic surgery using the da Vinci system is a minimally invasive, computer assisted and image-guided surgery application that provides surgeons with (i) navigational assistance by displaying targeting lesions of the intraoperative prostate anatomy onto aligned preoperative high-field magnetic resonance imaging (MRI) scans of the pelvis; and (ii) an effective clinical management of intra-abdominal cancers in real time. Such an image guidance system can improve both functional and oncological outcomes as well as augment the learning curve of the process increasing simultaneously the eligibility of patients for surgical resection. By segmenting MRI scans into 3D models of intraprostatic anatomy preoperatively, and overlaying them onto 3D stereoendoscopic images acquired intraoperatively using the da Vinci surgical system, a graphical representation of intraoperative anatomy can be provided for surgical navigation. The preoperative MRI surfaces are full 3D models and the stereoendoscopic images represent partial 3D views of the prostate due to occlusion. Hence achieving an accurate non-rigid image registration of full prostate surfaces onto occluded ones in real time becomes of critical importance, especially for use intraoperatively with the stereoendoscopic and MRI imaging modalities. This work exploits the registration accuracy that can be achieved from the application of selected state-of-the-art non-rigid registration algorithms and in doing so identifies the most accurate technique(s) for registration of full prostate surfaces onto occluded ones; a series of rigorous computational registration experiments is performed on synthetic target prostate data, which are aligned manually onto the MRI prostate models before registration is initiated. This effort extends to using real target prostate data leading to visually acceptable non-rigid registration results. A great deal of emphasis is placed on examining the capacity of the selected non-rigid algorithms to recover the deformation of the intraoperative prostate surfaces; the deformation of prostate can become pronounced during the surgical intervention due to surgical-induced anatomical deformities and pathological or other factors. The warping accuracy of the non-rigid registration algorithms is measured within the space of common overlap (established between the full MRI model and the target scene) and beyond. From the results of the registrations to occluded and deformed prostate surfaces (in the space beyond common overlap) it is concluded that the modified versions of the Kernel Correlation/Thin-plane Spline (KC/TPS) and Gaussian Mixture Model/Thin-plane Spline (GMM/TPS) methodologies can provide the clinical accuracy required for image-guided prostate surgery procedures (performed by the da Vinci system) as long as the size of the target scene is greater than ca. 30% of the full MRI surface. For the modified KC/TPS and GMM/TPS non-rigid registration techniques to be clinically acceptable when the measurement noise is also included in the simulations: (i) the size of the target model must be greater than ca. 38% of the full MRI surface; (ii) the standard deviation σ of the contributing Gaussian noise must be less than 0.345 for μ=0; and (iii) the observed deformation must not be characterized by excessively increased complexity. Otherwise the contribution of Gaussian noise must be explicitly parameterized in the objective cost functions of these non-rigid algorithms. The Expectation Maximization/Thin-plane Spline (EM/TPS) non-rigid registration algorithm cannot recover the prostate surface deformation accurately in full-model-to-occluded-model registrations due to the way that the correspondences are estimated. However, EM/TPS is more accurate than KC+TPS and GMM+TPS in recovering the deformation of the prostate surface in full-model-to-full-model registrations

Groupwise Multimodal Image Registration using Joint Total Variation

In medical imaging it is common practice to acquire a wide range of modalities (MRI, CT, PET, etc.), to highlight different structures or pathologies. As patient movement between scans or scanning session is unavoidable, registration is often an essential step before any subsequent image analysis. In this paper, we introduce a cost function based on joint total variation for such multimodal image registration. This cost function has the advantage of enabling principled, groupwise alignment of multiple images, whilst being insensitive to strong intensity non-uniformities. We evaluate our algorithm on rigidly aligning both simulated and real 3D brain scans. This validation shows robustness to strong intensity non-uniformities and low registration errors for CT/PET to MRI alignment. Our implementation is publicly available at https://github.com/brudfors/coregistration-njtv