Comment: Assessing Uncertainty in Backprojection

Comment on "Image reconstruction via the finite Hilbert transform of the derivative of the backprojection" [Med. Phys. 34, 2837-2843 (2007)].

A unified framework for exact cone-beam reconstruction formulas.

In this paper, we present concise proofs of several recently developed exact cone-beam reconstruction methods in the Tuy inversion framework, including both filtered-backprojection and backprojection-filtration formulas in the cases of standard spiral, nonstandard spiral, and more general scanning loci. While a similar proof of the Katsevich formula was previously reported, we present a new pro...

Probabilistic Analysis of Manipulation Tasks: A Conceptual Framework

This article addresses the problem of manipulation planning in the presence of uncertainty. We begin by reviewing the worst-case planning techniques introduced by Lozano-Pérez et al. (1984) and show that these methods are limited by an information gap inherent to worst-case analysis techniques. As the task uncertainty increases, these methods fail to produce useful information, even thou...

Accuracy Evaluation and Exploration of Measurement Uncertainty for Exact Helical Cone Beam Reconstruction Using Katsevich Filtered Backprojection in Comparison to Circular Feldkamp Reconstruction with Respect to Industrial CT Metrology

New requirements to scan long objects are fostering the use of helical scan trajectories. An exact filtered backprojection-based method has been suggested by Katsevich. In this paper, we investigate the applicability of this reconstruction strategy in industrial CT vs. conventional filtered backprojection type reconstructions. Hereby, we study the accuracy and the measurement uncertainty in ter...

Exploiting visual constraints in the synthesis of uncertainty-tolerant motion plans

The direciional backprojection i s one of the primary tools used b y fine-motion planning systems. Informally, a directional backprojection i s the set of configurations f rom which a commanded motion i s guaranteed to reach a goal configuration. It has been shown that, for force controlled motions, the topology of the directional backprojection only changes at a finite set of critical velocity...