Geometric techniques for 3D tracking of ultrasound sensor,tumor segmentation in ultrasound images,and 3D reconstruction

This paper presents different methods, some based on geometric algebra, for ultrasound probe tracking in endoscopic images, 3D allocation of the ultrasound probe, ultrasound image segmentation (to extract objects like tumors), and 3D reconstruction of the surface defined by a set of points. The tracking of the ultrasound probe in endoscopic images is done with a particle filter and an auxiliary method based on thresholding in the HSV space. The 3D pose of the ultrasound probe is calculated using conformal geometric algebra (to locate each slide in 3D space). Each slide (ultrasound image) is segmented using two methods: the level-set method and the morphological operators approach in order to obtain the object we are interested in. The points on the object of interest are obtained from the segmented ultrasound images, and then a 3D object is obtained by refining the convex hull. To do that, a peeling process with an adaptive radius is applied, all of this in the geometric algebra framework. Results for points from ultrasound images, as well as for points from objects from the AimatShape Project, are presented (A.I.M.A.T.S.H.A.P.E. – Advanced an Innovative Models And Tools for the development of Semantic-based systems for Handling, Acquiring, and Processing knowledge Embedded in multidimensional digital objects).     

A 2-point algorithm for 3D reconstruction of horizontal lines from a single omni-directional image

Reconstruction of 3D scenes with abundant straight line features has many applications in computer vision and robot navigation. Most approaches to this problem involve stereo techniques, in which a solution to the correspondence problem between at least two different images is required. In contrast, 3D reconstruction of straight horizontal lines from a single 2D omni-directional image is studied in this paper. The authors show that, for symmetric non-central catadioptric systems, a 3D horizontal line can be estimated using only two points extracted from a single image of the line. One of the two points is the symmetry point of the image curve of horizontal line, and the other is a generic point on the image curve. This paper improves on several prior works, including horizontal line detection in omni-directional image and line reconstruction from four viewing rays, but is simpler than those methods while being more robust. We evaluate how the precision of feature point extraction can affect line reconstruction accuracy, and discuss preliminary experimental results.     

Parameterization for reconstruction of 3D freeform objects from laser-scanned data based on a PDE method

Published online: 19 July 2001