Efficient symmetric and inverse-consistent deformable registration through interleaved optimization

Abstract

Symmetry and inverse consistency are two important features for deformable image registration in medical imaging analysis. This work presents a novel registration method computing symmetric and inverse-consistent image alignment efficiently while preserving high accuracy and consistency of the mapping. This is achieved by optimizing a symmetric energy functional estimating forward and backward transformations constrained by the transformations being inverse to each other. In other words, this approach uses an interleaved optimization scheme borrowed from multiobjective optimization theory constrained by an inverse-consistency criterium. The new optimization scheme provides an efficient search in the space of diffeomorphisms while solving the symmetric registration problem. Moreover, it is not bound to any specific optimizer or energy functional other than to the requirement of being well-defined. In our experiments on clinical cardiac data, superior performance compared to standard, onedirectional registration is achieved. The resulting inverseconsistency and symmetry errors match previously reported values while being computed more efficiently. This general approach addresses a clinical need for consistent, highly accurate image alignment achieved in a practically accepted timeframe.

Simultaneous motion estimation and image reconstruction (SMEIR) for 4D cone‐beam CT

“…(13) is solved by an interleaved optimization scheme. 36 In the interleaved optimization scheme, optimization of f 1 and f 2 is performed alternately at each iteration. A nonlinear conjugate gradient algorithm with backtracking line search 23,33 is used for the optimization of f 1 and f 2 .…”

Automated Assessment of Left Ventricular Function and Mass Using Heart Deformation Analysis:

“…DIR algorithm has been applied to calculate myocardial strains or lung motion in previous studies (9, 10). Different from existing method for tracking cardiac motion by identifying edge-, or speckle-like characteristics of a structure, such as feature tracking (FT), HDA tool can automatically define and calculate deformation fields for the myocardial structures, including LV wall and blood-pool, over time frames through the entire cardiac cycle (2, 3, 11). With an operator-independent workflow, HDA tool is expected to serve as a robust tool that generates multiple indices for the comprehensive description of myocardial function, motion and morphological changes.…”

“…The HDA tool automatically detects anatomical landmarks in the heart as anchor points to initialize the automatic detection of the myocardial borders, including the mitral valve and apex point at the long-axis views, aortic valve anchor points and the right ventricle [RV] insertion/lateral points at the short-axis views. Using an existing DIR algorithm, elastic image registration was completed to calculate frame-to-frame motion deformation fields (2). A 2D displacement vector was then assigned to each pixel within specific deformation area.…”

“…Using a deformation image registration (DIR) algorithm, HDA is able to automatically track the shape of LV through the entire cardiac cycle by calculating deformation fields (forward and backward) of myocardium tissue among sequential cardiac time frames (2, 3). As such, global cardiac indices (LVEF, CO and LVM) as well as regional myocardial motion indices (displacement, velocity, strain and strain rate) can be extracted from cine images using a semi-automatic “one-stop-shop” analysis with minimal user interaction.…”

A Planning and Guidance Platform for Cardiac Resynchronization Therapy

“…A deformable registration algorithm [19] is used to compute the deformation fields between the first and any other frame in a slice by minimizing the local cross correlation between the two images. The algorithm uses an efficient scheme to update both the deformation and its inverse at each step of the gradient descent minimization in order to make the deformation field inverse consistent.…”