Abstract. Let [Formula: see text] be a set of [Formula: see text] points in [Formula: see text], and suppose that the distance between each pair of points is revealed independently with probability [Formula: see text]. We study when this information is sufficient to reconstruct large subsets of [Formula: see text], up to isometry. Strong results for [Formula: see text] have been obtained by Girão et al. In this paper, we investigate higher dimensions, and show that if [Formula: see text], then we can reconstruct almost all of [Formula: see text] up to isometry, with high probability. We do this by relating it to a polluted graph bootstrap percolation result, for which we adapt the methods of Balogh, Bollobás, and Morris.

We present an algorithm of time complexity O(knk+2) deciding whether a graph G on n vertices is k-copwin. The fastest algorithm thus far had time complexity O(n2k+2).

This paper presents a new image-based visual servoing approach to control a robotic system equipped with an ultrasound (US) imaging device. The presented method allows an automatic positioning of the probe with respect to an object of interest. Moments-based image features are computed from three orthogonal US images to servo in-plane and out-of-plane motions of the system. An efficient segmentation method, based on graph-cut strategy, is proposed to extract the object contour in each image plane. Simulation results demonstrate that this approach improves upon techniques based on a single 2-D US image in terms of probe positioning. Our method was also validated from robotic experiments performed on a US phantom with the use of a motorized 3-D probe that provides the three US images.

UNLABELLED: The goal of this article is to quantify the influence of truncation artifacts in the magnetic resonance (MR)-based attenuation map (MRMap) on reconstructed positron emission tomography (PET) image volumes and to propose a new method for minimizing this influence. METHODS: PET data sets of 20 patients investigated in a Philips Ingenuity PET/MR were reconstructed with and without applying two different methods for truncation compensation (TC1 vendor-provided, TC2 newly developed). In this patient group, the extent of truncation artifacts and quality of the truncation compensation (TC) was assessed visually in the MRMaps. In three additional patients MRMaps generated by algorithm TC2 could be compared to the ground truth of transmission-based attenuation maps obtained with a Siemens ECAT HR(+) scanner. The influence of truncation on regional SUVs in lesions, other hot structures (bladder, kidney, myocardium) and the arms was assessed in suitable volume of interests (VOI). RESULTS: Truncation compensated MRMaps exhibited residual artifacts in the arms in 16 patients for algorithm TC1 and to a lesser extent in eight patients for algorithm TC2. Compared to the transmission-based attenuation maps algorithm TC2 slightly overestimated the size of the truncated arms by 0.3 cm in the radial direction. Without truncation compensation, VOIs located in the trunk showed an average SUVmax underestimation of less than 5.4% relative to the results obtained with TC2. Inside the patients' arms underestimations up to 46.5% were found. CONCLUSION: In the trunk, standardized uptake values (SUV) underestimations due to truncation artifacts in the MRMap are rather small. Inside the arms, severe SUV underestimations can occur. Therefore, reliable TC is mandatory and can be achieved by applying the newly developed algorithm TC2 which has yielded promising results so far. Implementation of the proposed method is straightforward and should be easily adaptable to other PET/MR systems.