Estimating the Fundamental Matrix Without Point Correspondences With Application to Transmission Imaging

Tobias Würfl, Andre Aichert, Nicole Maaß, Frank Dennerlein, Andreas Maier

Abstract:

We present a general method to estimate the fundamental matrix from a pair of images under perspective projection without the need for image point correspondences. Our method is particularly well-suited for transmission imaging,
where state-of-the-art feature detection and matching approaches generally do not perform well. Estimation of the
fundamental matrix plays a central role in auto-calibration
methods for reflection imaging. Such methods are currently
not applicable to transmission imaging. Furthermore, our
method extends an existing technique proposed for reflection imaging which potentially avoids the outlier-prone feature matching step from an orthographic projection model
to a perspective model. Our method exploits the idea that
under a linear attenuation model line integrals along corresponding epipolar lines are equal if we compute their
derivatives in orthogonal direction to their common epipolar plane. We use the fundamental matrix to parametrize
this equality. Our method estimates the matrix by formulating a non-convex optimization problem, minimizing
an error in our measurement of this equality. We believe
this technique will enable the application of the large body
of work on image-based camera pose estimation to transmission imaging leading to more accurate and more general motion compensation and auto-calibration algorithms,
particularly in medical X-ray and Computed Tomography
imaging.