Double Your Views – Exploiting Symmetry in Transmission Imaging

Abstract

For a plane symmetric object we can find two views -mirrored at the plane of symmetry -that will yield the exact same image of that object. In consequence, having one image of a plane symmetric object and a calibrated camera, we can automatically have a second, virtual image of that object if the 3-D location of the symmetry plane is known. In this work, we show for the first time that the above concept naturally extends to transmission imaging and present an algorithm to estimate the 3-D symmetry plane from a set of projection domain images based on Grangeat's theorem. We then exploit symmetry to generate a virtual trajectory by mirroring views at the plane of symmetry. If the plane is not perpendicular to the acquired trajectory plane, the virtual and real trajectory will be oblique. The resulting X-shaped trajectory will be data-complete, allowing for the compensation of in-plane motion using epipolar consistency. We evaluate the proposed method on a synthetic symmetric phantom and, in a proof-of-concept study, apply it to a real scan of an anthropomorphic human head phantom.

Maximum Likelihood Estimation of Head Motion Using Epipolar Consistency

“…We use z-motion, because z-translations produce inconsistencies. In contrast, motions within the acquisition plane do not necessarily violate the consistency measure [3,4]. We show our results on three phantoms (cf.…”

“…This gives rise to a strong need for motion compensation algorithms [2]. In recent years, consistency conditions have been shown to be promising in this context [3,4]. Besides the compensation of motion, consistency measures are heavily used in cone-beam CT, as they provide a mathematical model constraining the imaging process.…”

“…The consistency measure can also be used to estimate missing data due to truncation for field of view reconstruction [8] and possibly to the closely related problem of overexposure correction [9]. The most widely use of Grangeat's consistency is the estimation of geometry information that is distorted either due to rigid patient motion or geometry jitter [3,4,10]. The reason for its wide applicability is the sensitivity of the consistency measure to a variety of image artifacts.…”

Motion gradients for epipolar consistency

“…3,4 Frysch et al proposed an optimization scheme utilizing Grangeat's theorem for head motion compensation based on the Nelder-Mead method 5 and Preuhs et al introduced symmetry priors for the estimation of head motion with Grangeat's consistency. 6 All methods utilize zero-order optimization, by successively evaluating the consistency with different motion configurations. In this work, we derive motion gradients for the estimation of motion parameters with Grangeat's theorem, enabling first-order optimization algorithms.…”

Abstract: Double Your Views: Exploiting Symmetry in Transmission Imaging

“…If the plane is not perpendicular to the acquired trajectory plane, the virtual and real trajectory will be oblique. The resulting X-shaped trajectory will be data-complete, allowing for the compensation of in-plane motion using epipolar consistency [1].…”