Joining polyhedral objects using implicitly defined surfaces

Published online: 2 October 2001     

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

Published online: 19 July 2001     

Minimal area for surface reconstruction from cross sections

Surface reconstruction from cross-sectional data is important in a variety of applications. It is usually possible to generate a surface in many ways, but only reasonable ones are acceptable. A surface of minimal area has been considered as one of the most natural optimal criteria for the original tiling method of surface reconstruction from cross sections. In the paper, we consider minimal surfaces for continuous generalization of the tiling approach and in the general situation of reconstruction from cross sections. We show that in these cases the minimal area criterion leads to defective surfaces and is thus unacceptable. Published online: 23 July 2002 Correspondence to: D. Berzin     

Model-based interpretation of stereo imagery of textured surfaces

We present a scheme for reliable and accurate surface reconstruction from stereoscopic images containing only fine texture and no stable high-level features. Partial shape information is used to improve surface computation: first by fitting an approximate, global, parametric model, and then by refining this model via local correspondence processes. This scheme eliminates the window size selection problem in existing area-based stereo correspondence schemes. These ideas are integrated in a practical vision system that is being used by environmental scientists to study wind erosion of bulk material such as coal ore being transported in open rail cars. Received: 14 August 1995 / Accepted: 27 May 1997     

Robust and efficient surface reconstruction from contours

We propose a new approach for surface recovery from planar sectional contours. The surface is reconstructed based on the so-called “equal importance criterion,” which suggests that every point in the region contributes equally to the reconstruction process. The problem is then formulated in terms of a partial differential equation, and the solution is efficiently calculated from distance transformation. To make the algorithm valid for different application purposes, both the isosurface and the primitive representations of the object surface are derived. The isosurface is constructed by means of a partial differential equation, which can be solved iteratively. The traditional distance interpolating method, which was used by several researchers for surface reconstruction, is an approximate solution of the equation. The primitive representations are approximated by Voronoi diagram transformation of the surface space. Isosurfaces have the advantage that subsequent geometric analysis of the object can be easily carried out while primitive representation is easy to visualize. The proposed technique allows for surface recovery at any desired resolution, thus avoiding the inherent problems of correspondence, tiling, and branching.     

Automatic reconstruction of 3D human arm motion from a monocular image sequence

A model-based approach to reconstruction of 3D human arm motion from a monocular image sequence taken under orthographic projection is presented. The reconstruction is divided into two stages. First, a 2D shape model is used to track the arm silhouettes and second-order curves are used to model the arm based on an iteratively reweighted least square method. As a result, 2D stick figures are extracted. In the second stage, the stick figures are backprojected into the scene. 3D postures are reconstructed using the constraints of a 3D kinematic model of the human arm. The motion of the arm is then derived as a transition between the arm postures. Applications of these results are foreseen in the analysis of human motion patterns. Received: 26 January 1996 / Accepted: 17 July 1997     

Taxonomy of interpolation constraints on recursive subdivision surfaces

Published online: 14 May 2002     

Merging polyhedral shapes with scattered features

1. initial embeddings of the polyhedra on unit spheres are computed, 2. the embeddings are deformed so that user-defined features (vertices) coincide on the spheres, and 3. an overlay of the subdivisions is computed and the aligned vertices are fused in the merged model.     

Defect detection in textured surfaces using color ring-projection correlation

In this paper, we present a correlation scheme that incorporates a color ring-projection representation for the automatic inspection of defects in textured surfaces. The proposed color ring projection transforms a 2-D color image into a 1-D color pattern as a function of radius. For a search window of width W, data dimensionality is reduced from in the 2-D image to O(W) in the 1-D ring-projection space. The complexity of computing a correlation function is significantly reduced accordingly. Since the color ring-projection representation is invariant to rotation, the proposed method can be applied for both isotropic and oriented textures at arbitrary orientations. Experiments on regular textured surfaces have shown the efficacy of the proposed method. Received: 30 March 2000 / Accepted: 24 July 2001 Correspondence to: D.-M. Tsai (e-mail: iedmtsai@saturn.yzu.edu.tw)     

Multipass hierarchical stereo matching for generation of digital terrain models from aerial images

This paper presents a new multi-pass hierarchical stereo-matching approach for generation of digital terrain models (DTMs) from two overlapping aerial images. Our method consists of multiple passes which compute stereo matches with a coarse-to-fine and sparse-to-dense paradigm. An image pyramid is generated and used in the hierarchical stereo matching. Within each pass, the DTM is refined by using the image pyramid from the coarse to the fine level. At the coarsest level of the first pass, a global stereo-matching technique, the intra-/inter-scanline matching method, is used to generate a good initial DTM for the subsequent stereo matching. Thereafter, hierarchical block matching is applied to image locations where features are detected to refine the DTM incrementally. In the first pass, only the feature points near salient edge segments are considered in block matching. In the second pass, all the feature points are considered, and the DTM obtained from the first pass is used as the initial condition for local searching. For the passes after the second pass, 3D interactive manual editing can be incorporated into the automatic DTM refinement process whenever necessary. Experimental results have shown that our method can successfully provide accurate DTM from aerial images. The success of our approach and system has also been demonstrated with a flight simulation software. Received: 4 November 1996 / Accepted: 20 October 1997     

Optimized triangle mesh reconstruction from unstructured points

A variety of approaches have been proposed for polygon mesh reconstruction from a set of unstructured sample points. Suffering from severe aliases at sharp features and having a large number of unnecessary faces, most resulting meshes need to be optimized using input sample points in a postprocess. In this paper, we propose a fast algorithm to reconstruct high-quality meshes from sample data. The core of our proposed algorithm is a new mesh evaluation criterion which takes full advantage of the relation between the sample points and the reconstructed mesh. Based on our proposed evaluation criterion, we develop necessary operations to efficiently incorporate the functions of data preprocessing, isosurface polygonization, mesh optimization and mesh simplification into one simple algorithm, which can generate high-quality meshes from unstructured point clouds with time and space efficiency. Published online: 28 January 2003 Correspondence to: Y.-J. Liu     

Efficient CAD-based triangulation of unordered 3D data

Abstract. The paper proposes a new method for efficient triangulation of large, unordered sets of 3D points using a CAD model comprising NURBS entities. It is primarily aimed at engineering applications involving analysis and visualisation of measured data, such as inspection, where a model of the object in question is available. Registration of the data to the model is the necessary first step, enabling the triangulation to be efficiently performed in 2D, on the projections of the measured points onto the model entities. The derived connectivity is then applied to the original 3D data. Improvement of the generated 3D mesh is often necessary, involving mesh smoothing, constraint-based elimination of redundant triangles and merging of mesh patches. Examples involving random measurements on aerospace and automotive free-form components are presented. Received: 30 August 1999 / Accepted: 10 January 2000     

Optimistic parallel Delaunay triangulation

The paper describes a new parallel algorithm of Delaunay triangulation based on randomized incremental insertion. The algorithm is practical, simple and can be modified also for constrained triangulation or tetrahedralization. It was developed for architectures with a lower degree of parallelism, such as several-processor workstations, and tested on up to 8 processors. Published online: November 20, 2002 This work was supported by the Ministry of Education of The Czech Republic, project MSM 235 200 005     

Smooth multiple B-spline surface fitting with Catmull%ndash;Clark subdivision surfaces for extraordinary corner patches

This paper presents an algorithm for simultaneously fitting smoothly connected multiple surfaces from unorganized measured data. A hybrid mathematical model of B-spline surfaces and Catmull–Clark subdivision surfaces is introduced to represent objects with general quadrilateral topology. The interconnected multiple surfaces are G ² continuous across all surface boundaries except at a finite number of extraordinary corner points where G ¹ continuity is obtained. The algorithm is purely a linear least-squares fitting procedure without any constraint for maintaining the required geometric continuity. In case of general uniform knots for all surfaces, the final fitted multiple surfaces can also be exported as a set of Catmull–Clark subdivision surfaces with global C ² continuity and local C ¹ continuity at extraordinary corner points. Published online: 14 May 2002 Correspondence to: W. Ma     

Using vanishing points for camera calibration and coarse 3D reconstruction from a single image

In this paper, we show how to calibrate a camera and to recover the geometry and the photometry (textures) of objects from a single image. The aim of this work is to make it possible walkthrough and augment reality in a 3D model reconstructed from a single image. The calibration step does not need any calibration target and makes only four assumptions: (1) the single image contains at least two vanishing points, (2) the length (in 3D space) of one line segment (for determining the translation vector) in the image is known, (3) the principle point is the center of the image, and (4) the aspect ratio is fixed by the user. Each vanishing point is determined from a set of parallel lines. These vanishing points help determine a 3D world coordinate system R _o. After having computed the focal length, the rotation matrix and the translation vector are evaluated in turn for describing the rigid motion between R _o and the camera coordinate system R _c. Next, the reconstruction step consists in placing, rotating, scaling, and translating a rectangular 3D box that must fit at best with the potential objects within the scene as seen through the single image. With each face of a rectangular box, a texture that may contain holes due to invisible parts of certain objects is assigned. We show how the textures are extracted and how these holes are located and filled. Our method has been applied to various real images (pictures scanned from books, photographs) and synthetic images.     

The perceptive workbench: Computer-vision-based gesture tracking,object tracking,and 3D reconstruction for augmented desks

Abstract. The Perceptive Workbench endeavors to create a spontaneous and unimpeded interface between the physical and virtual worlds. Its vision-based methods for interaction constitute an alternative to wired input devices and tethered tracking. Objects are recognized and tracked when placed on the display surface. By using multiple infrared light sources, the object's 3-D shape can be captured and inserted into the virtual interface. This ability permits spontaneity, since either preloaded objects or those objects selected at run-time by the user can become physical icons. Integrated into the same vision-based interface is the ability to identify 3-D hand position, pointing direction, and sweeping arm gestures. Such gestures can enhance selection, manipulation, and navigation tasks. The Perceptive Workbench has been used for a variety of applications, including augmented reality gaming and terrain navigation. This paper focuses on the techniques used in implementing the Perceptive Workbench and the system's performance.     

Evaluation of piecewise smooth subdivision surfaces

Published online: 23 July 2002