3D Feature Space Research Articles

A History-Independent Modelling-Oriented Approach to Solve Geometric Constraints Between Features in 3D Space

History-independent modelling systems are more flexible than history-based ones. They let designers manipulate the model in a more associative, rather than prescribed, way. In this paper, an approach based on 2D geometric constraint solving and a topological entity naming mechanism (TENM) is presented to solve the geometric constraints between features in 3D space. Firstly, in order to break the unidirectional dependency between features in a history-based modelling system, a data structure named feature constraint graph(FCG) is adopted to represent the geometric constraints between features in 3D space. Then a solving sequence is obtained using degree-of-freedom (DOF) based graph analysis. And finally, during the evaluation of the solving sequence, the dimensions in 3D space are mapped to 2D space, the dimensions in 3D space are satisfied indirectly by solving the corresponding 2D geometric constraint system. An example is given to illustrate the process of our approach.

In vivo validation of tissue segmentation based on a 3D feature map using both a hamster brain tumor model and stereotactically guided biopsy of brain tumors in man.

The purpose of this study was to validate our MR tissue segmentation technique using a hamster brain tumor model and malignant brain tumors in man. We used a multispectral tissue segmentation analysis. Three sets of MRI data were included: proton density, T2-weighted fast spin echo, and T1-weighted spin echo, as inputs. Three image preprocessing steps included correcting image nonuniformity, application of an anisotropic diffusion type filter, and data point selection by a qualified observer. We used the k-Nearest Neighbor segmentation algorithm, which does not require prior knowledge of the sample distribution. This choice allowed us to optimize the different tissue clusters present in three-dimensional (3D) feature space. In vivo validation of the technique was performed in hamsters harboring tumors induced with JC virus-transformed HJC-15 cells, as compared to three control animals. Human brain tumors obtained by stereotactically guided biopsy in six patients were also included in the study. Finally, brain tumors were removed from two patients who underwent conventional craniotomy using segmentation-derived images as a guide. In the hamsters, 10 tissues were correctly identified by segmentation and were confirmed histologically (P < .02). In the patients, there was also a strong correlation between our segmentation results and the tissue obtained by stereotactic biopsy (P < .01). In one of the two patients who underwent open craniotomy, segmentation images were useful in revealing tumor spread into vital areas of the brain (motor area). In conclusion, the results of segmentation correlate well with the tissues in vivo and thus warrant further clinical utilization and evaluation.

Motion and structure from feature correspondences: a review

We present a review of algorithms and their performance for determining three-dimensional (3D) motion and structure of rigid objects when their corresponding features are known at different times or are viewed by different cameras. Three categories of problems are considered, depending upon whether the features are two (2D) or three-dimensional (3D) and the type of correspondence: a) 3D to 3D (i.e., locations of corresponding features in 3D space are known at two different times), b) 2D to 3D (i.e., locations of features in 3D space and their projection on the camera plane are known, and c) 2D to 2D (i.e., projections of features on the camera plane are known at two different times). Features considered include points, straight lines, curved lines, and corners. Emphasis is on problem formulation, efficient algorithms for solution, existence and uniqueness of solutions, and sensitivity of solutions to noise in the observed data. Algorithms described have been used in a variety of applications. Some of these are: a) positioning and navigating 3D objects in a 3D world, b) camera calibration, i.e., determining location and orientation of a camera by observing 3D features whose location is known, c) estimating motion and structure of moving objects relative to a camera. We mention some of the mathematical techniques borrowed from algebraic geometry, projective geometry, and homotopy theory that are required to solve these problems, list unsolved problems, and give some directions for future research.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

High level 3D structures from a single view

Abstract This paper is concerned with the interpretation of a 3D scene from a single view. The persepctive transformation is interpreted in the image to infer local configurations of features in 3D space. A local configuration is a set of 3D symbolic structures described in this paper. This high-level representation is concise, and makes geometric properties implicit.