Robust point correspondence applied to two and three-dimensional image registration

Accurate and robust correspondence calculations are very important in many medical and biological applications. Often, the correspondence calculation forms part of a rigid registration algorithm, but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time. In this paper, a new correspondence calculation algorithm, CSM (correspondence by sensitivity to movement), is described. A robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched. If the correspondence is reliable, a perturbation in the position of this point should not result in a large movement of the correspondence. A measure of reliability is also calculated. This correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2D elastic registration algorithm for warping serial sections and a 3D rigid registration algorithm for registering pre and postoperative facial range scans. These applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the CSM method. It is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondence

Distributed-memory large deformation diffeomorphic 3D image registration

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in medical image analysis. Our algorithm uses a partial differential equation constrained optimal control formulation. Finding the optimal deformation map requires the solution of a highly nonlinear problem that involves pseudo-differential operators, biharmonic operators, and pure advection operators both forward and back- ward in time. A key issue is the time to solution, which poses the demand for efficient optimization methods as well as an effective utilization of high performance computing resources. To address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov solver. Our algorithm integrates several components: a spectral discretization in space, a semi-Lagrangian formulation in time, analytic adjoints, different regularization functionals (including volume-preserving ones), a spectral preconditioner, a highly optimized distributed Fast Fourier Transform, and a cubic interpolation scheme for the semi-Lagrangian time-stepping. We demonstrate the scalability of our algorithm on images with resolution of up to $1024^3$ on the "Maverick" and "Stampede" systems at the Texas Advanced Computing Center (TACC). The critical problem in the medical imaging application domain is strong scaling, that is, solving registration problems of a moderate size of $256^3$---a typical resolution for medical images. We are able to solve the registration problem for images of this size in less than five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA; November 201

Breast Cancer: Modelling and Detection

This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection

3D Reconstruction: Novel Method for Finding of Corresponding Points using Pseudo Colors

This paper deals with the reconstruction of spatial coordinates of an arbitrary point in a scene using two images scanned by a 3D camera or two displaced cameras. Calculations are based on the perspective geom-etry. Accurate determination of corresponding points is a fundamental step in this process. The usually used methods can have a problem with points, which lie in areas without sufficient contrast. This paper describes our proposed method based on the use of the relationship between the selected points and area feature points. The proposed method finds correspondence using a set of feature points found by SURF. An algorithm is proposed and described for quick removal of false correspondences, which could ruin the correct reconstruction. The new method, which makes use of pseudo color image representation (pseudo coloring) has been proposed subsequently. By means of this method it is possible to significantly increase the color contrast of the surveyed image, and therefore add more information to find the correct correspondence. Reliability of the found correspondence can be verified by reconstruction of 3D position of selected points. Executed experiments confirm our assumption

Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling

We study 3D shape modeling from a single image and make contributions to it in three aspects. First, we present Pix3D, a large-scale benchmark of diverse image-shape pairs with pixel-level 2D-3D alignment. Pix3D has wide applications in shape-related tasks including reconstruction, retrieval, viewpoint estimation, etc. Building such a large-scale dataset, however, is highly challenging; existing datasets either contain only synthetic data, or lack precise alignment between 2D images and 3D shapes, or only have a small number of images. Second, we calibrate the evaluation criteria for 3D shape reconstruction through behavioral studies, and use them to objectively and systematically benchmark cutting-edge reconstruction algorithms on Pix3D. Third, we design a novel model that simultaneously performs 3D reconstruction and pose estimation; our multi-task learning approach achieves state-of-the-art performance on both tasks.Comment: CVPR 2018. The first two authors contributed equally to this work. Project page: http://pix3d.csail.mit.ed