Epi-NAF: Enhancing Neural Attenuation Fields for Limited-Angle CT with Epipolar Consistency Conditions

TL;DR

A novel loss term based on consistency conditions between corresponding epipolar lines in X-ray projection images, aimed at regularizing neural attenuation field optimization, results in both qualitative and quantitative improvements in reconstruction compared to baseline methods.

Abstract

Neural field methods, initially successful in the inverse rendering domain, have recently been extended to CT reconstruction, marking a paradigm shift from traditional techniques. While these approaches deliver state-of-the-art results in sparse-view CT reconstruction, they struggle in limited-angle settings, where input projections are captured over a restricted angle range. We present a novel loss term based on consistency conditions between corresponding epipolar lines in X-ray projection images, aimed at regularizing neural attenuation field optimization. By enforcing these consistency conditions, our approach, Epi-NAF, propagates supervision from input views within the limited-angle range to predicted projections over the full cone-beam CT range. This loss results in both qualitative and quantitative improvements in reconstruction compared to baseline methods.

Figures (3)

• Figure 1: Epipolar consistency in X-ray imaging.$P_0$ and $P_1$ are two X-ray projection images, where $\boldsymbol{c}_0$ and $\boldsymbol{c}_1$ are the corresponding X-ray source locations. We consider the cosine-weighted projection images, $\Tilde{P_0}$ and $\Tilde{P_1}$, obtained by multiplying the intensity value of each pixel by $cos(\beta)$, where $\beta$ is the angle between the pixel, the source location and the image origin $O$. The source locations, along with a point in the body $p$ define an epipolar plane, which intersects the projection images at $l_0$, $l_1$. The two corresponding epipolar lines are defined by the angle $\alpha$ and the distance to the origin $t$.
• Figure 2: Epi-NAF Method Overview. On the left part of the figure, we mark the limited-angle region of the provided projections in green, and the unseen projections region in red. Epi-NAF comprises two loss terms: (1) $\mathcal{L}_{\text{recon}}$, based on the $L_2$ difference between the predicted and ground-truth intensity values (green pixels), and (2) our novel $\mathcal{L}_{\text{ECC}}$, which enforces consistency in the derivatives in the $t$ direction of line integrals along corresponding epipolar lines (blue pixels). Crucially, projection $(iii)$ receives direct supervision from the input, which is propagated to projections $(i)$ and $(ii)$ via the ECC loss. This propagation of supervision from limited input angles to unseen projections enhances the overall reconstruction quality.
• Figure 3: Qualitative comparison between our method (bottom row) and the vanilla NAF (middle row) in the 90° angle setting, alongside ground-truth slices of abdomen and chest CT scans (top row). We recommend the reader to zoom in electronically for a clearer view of the details.