Computing segmentations directly from x-ray projection data via parametric deformable curves

Abstract

We describe an efficient algorithm that computes a segmented reconstruction directly from x-ray projection data. Our algorithm uses a parametric curve to define the segmentation. Unlike similar approaches which are based on level-sets, our method avoids a pixel or voxel grid; hence the number of unknowns is reduced to the set of points that define the curve, and attenuation coefficients of the segments. Our current implementation uses a simple closed curve and is capable of separating one object from the background. However, our basic algorithm can be applied to an arbitrary topology and multiple objects corresponding to different attenuation coefficients in the reconstruction. Through systematic tests we demonstrate a high robustness to the noise, and an excellent performance under a small number of projections.

DALM, Deformable Attenuation-Labeled Mesh for Tomographic Reconstruction and Segmentation

“…The proposed method is targeted at objects composed of homogeneous components. Our work extends the method by Dahl et al [2] that employs a deformable closed curve to outline one object in the reconstruction. Here, we replace one single The authors are with the Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Lyngby, Denmark (e-mail: jakoo@dtu.dk; abda@dtu.dk; vand@dtu.dk).…”

Shape from projections via differentiable forward projector for computed tomography

“…Gadelha et al (2019) used a deep convolutional neural network for 2D tomographic reconstruction, where the forward projection is based on the transformation of a regular grid and resampling. On the other hand, the work (Dahl et al, 2018) based on snakes (Kass et al, 1988) avoids a dense grid -it represents curves explicitly and proposes a direct forward projection of the curves. However, this method is limited to a single 2D curve, while the proposed method supports 3D objects.…”

“…However, this method is limited to a single 2D curve, while the proposed method supports 3D objects. Another difference is that (Dahl et al, 2018) evolves curves in the normal directions of curve points, while our deformation can displace the vertices in all directions.…”

A Data Consistent Variational Segmentation Approach Suitable for Real-time Tomography

“…Hence, the DART algorithm [5] alternates between an algebraic reconstruction step and a thresholding step, TVR-DART [44] is based on the same thresholding step augmented by a TV regularization under a variational approach. Other modern methods include levelset-based techniques using the Mumford-Shah functional [40,27,42,37,38] or parametric curve approaches [1,2], convex approaches [33], and graph-based approaches [20,32].…”