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.     

The normalform of a space curve and its application to surface design

x )=0 with ∥▿h∥=1. The normalform function h is (unlike the latter cases) not differentiable at curve points. Despite of this disadvantage the normalform is a suitable tool for designing surfaces which can be treated as common implicit surfaces. Many examples (bisector surfaces, constant distance sum/product surfaces, metamorphoses, blending surfaces, smooth approximation surfaces) demonstrate applications of the normalform to surface design. Published online: 25 July 2001     

Geometric fusion for a hand-held 3D sensor

Abstract. This article presents a geometric fusion algorithm developed for the reconstruction of 3D surface models from hand-held sensor data. Hand-held systems allow full 3D movement of the sensor to capture the shape of complex objects. Techniques previously developed for reconstruction from conventional 2.5D range image data cannot be applied to hand-held sensor data. A geometric fusion algorithm is introduced to integrate the measured 3D points from a hand-held sensor into a single continuous surface. The new geometric fusion algorithm is based on the normal-volume representation of a triangle, which enables incremental transformation of an arbitrary mesh into an implicit volumetric field function. This system is demonstrated for reconstruction of surface models from both hand-held sensor data and conventional 2.5D range images. Received: 30 August 1999 / Accepted: 21 January 2000     

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     

Parametric G n blending of curves and surfaces

We introduce a simple blending method for parametric curves and surfaces that produces families of parametrically defined, G ⁿ –continuous blending curves and surfaces. The method depends essentially on the parameterizations of the curves/surfaces to be blended. Hence, the flexibility of the method relies on the existence of suitable parameter transformations of the given curves/surfaces. The feasibility of the blending method is shown by several examples. The shape of the blend curve/surface can be changed in a predictable way with the aid of two design parameters (thumb weight and balance).     

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)     

Volume-based three-dimensional metamorphosis using sphere-guided region correspondence

surface metamorphosis extends this paradigm by interpolating between discrete volume representations of the surfaces. The insensitivity of the established techniques to the surface topology enables morphing between completely different surfaces: however it can also lead to intermediate surfaces which have different topology from the originals. We present a method which improves on this situation by ensuring that no part of each surface remains disconnected during the morph. The morph is guided by region correspondence, derived automatically from a sphere representation of each surface: this can be combined with manual correspondence to retain user control over the morph. What emerges is a fast and flexible method for morphing surfaces, as demonstrated on several examples. Published online: 19 July 2001     

Reparameterization of piecewise rational Bezier curves and its applications

degree . Although the curve segments are C ¹ continuous in three dimensions, they may be C ⁰ continuous in four dimensions. In this case, the multiplicity of each interior knot cannot be reduced and the B-spline basis function becomes C ⁰ continuous. Using a surface generation method, such as skinning these kinds of rational B-spline curves to construct an interpolatory surface, may generate surfaces with C ⁰ continuity. This paper presents a reparameterization method for reducing the multiplicity of each interior knot to make the curve segments C ¹ continuous in four dimensions. The reparameterized rational B-spline curve has the same shape and degree as before and also has a standard form. Some applications in skinned surface and ruled surface generation based on the reparameterized curves are shown. Published online: 19 July 2001     

Automatic high-resolution optoelectronic photogrammetric 3D surface geometry acquisition system

A fast, high-resolution, automatic, non-contact 3D surface geometry measuring system using a photogrammetric optoelectronic technique based on lateral-photoeffect diode detectors has been developed. Designed for the acquisition of surface geometries such as machined surfaces, biological surfaces, and deformed parts, the system can be used in design, manufacturing, inspection, and range finding. A laser beam is focused and scanned onto the surface of the object to be measured. Two cameras in stereo positions capture the reflected light from the surface at 10 kHz. Photogrammetric triangulation quickly transforms the pair of 2D signals created by the camera detectors into 3D coordinates of the light spot. Because only one small spot on the object is illuminated at a time, the stereo correspondence problem is solved in real time. The resolution is determined by a 12-bit A/D converter and can be improved up to 25 60025 600 by oversampling. The irregular 3D data can be regularized for use with image-based algorithms. Received: 8 October 1996 / Accepted: 3 February 1997     

A volume-preserving approach for modeling and animating water flows generated by metaballs

This paper presents a volume-preserving approach for animating liquid flows modeled by metaballs. A volume of liquid can be adjusted to a previous volume by using the influence radius and the maximum density of metaballs as volume-controlling parameters. Recursive subdivision is used to efficiently calculate the volume of implicit surfaces. The criterion for subdivision is obtained by using the concept of interval analysis and the common property of metaball density functions. Providing a sequence of parameters, the volume-compensation region can be controlled according to the substance making up the object, resulting in local preservation of the volume. Set partition is used for determining isolated surfaces in order to apply local-volume preservation. Published online: 23 July 2002 Correspondence to: K. Kaneda     

Monotonic complements for independent data warehouses

Views over databases have regained attention in the context of data warehouses, which are seen as materialized views. In this setting, efficient view maintenance is an important issue, for which the notion of self-maintainability has been identified as desirable. In this paper, we extend the concept of self-maintainability to (query and update) independence within a formal framework, where independence with respect to arbitrary given sets of queries and updates over the sources can be guaranteed. To this end we establish an intuitively appealing connection between warehouse independence and view complements. Moreover, we study special kinds of complements, namely monotonic complements, and show how to compute minimal ones in the presence of keys and foreign keys in the underlying databases. Taking advantage of these complements, an algorithmic approach is proposed for the specification of independent warehouses with respect to given sets of queries and updates. Received: 21 November 2000 / Accepted: 1 May 2001 Published online: 6 September 2001     

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     

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     

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.     

A bin picking system based on depth from defocus

It is generally accepted that to develop versatile bin-picking systems capable of grasping and manipulation operations, accurate 3-D information is required. To accomplish this goal, we have developed a fast and precise range sensor based on active depth from defocus (DFD). This sensor is used in conjunction with a three-component vision system, which is able to recognize and evaluate the attitude of 3-D objects. The first component performs scene segmentation using an edge-based approach. Since edges are used to detect the object boundaries, a key issue consists of improving the quality of edge detection. The second component attempts to recognize the object placed on the top of the object pile using a model-driven approach in which the segmented surfaces are compared with those stored in the model database. Finally, the attitude of the recognized object is evaluated using an eigenimage approach augmented with range data analysis. The full bin-picking system will be outlined, and a number of experimental results will be examined. Received: 2 December 2000 / Accepted: 9 September 2001 Correspondence to: O. Ghita     

Wood inspection with non-supervised clustering

Abstract. The appearance of sawn timber has huge natural variations that the human inspector easily compensates for mentally when determining the types of defects and the grade of each board. However, for automatic wood inspection systems these variations are a major source for complication. This makes it difficult to use textbook methodologies for visual inspection. These methodologies generally aim at systems that are trained in a supervised manner with samples of defects and good material, but selecting and labeling the samples is an error-prone process that limits the accuracy that can be achieved. We present a non-supervised clustering-based approach for detecting and recognizing defects in lumber boards. A key idea is to employ a self-organizing map (SOM) for discriminating between sound wood and defects. Human involvement needed for training is minimal. The approach has been tested with color images of lumber boards, and the achieved false detection and error escape rates are low. The approach also provides a self-intuitive visual user interface. Received: 16 December 2000 / Accepted: 8 December 2001 Correspondence to: O. Silvén     

Machine tool condition monitoring using workpiece surface texture analysis

Tool wear affects the surface roughness dramatically. There is a very close correspondence between the geometrical features imposed on the tool by wear and micro-fracture and the geometry imparted by the tool on to the workpiece surface. Since a machined surface is the negative replica of the shape of the cutting tool, and reflects the volumetric changes in cutting-edge shape, it is more suitable to analyze the machined surface than look at a certain portion of the cutting tool. This paper discusses our work that analyzes images of workpiece surfaces that have been subjected to machining operations and investigates the correlation between tool wear and quantities characterizing machined surfaces. Our results clearly indicate that tool condition monitoring (the distinction between a sharp, semi-dull, or a dull tool) can be successfully accomplished by analyzing surface image data. Received: 9 June 1998 / Accepted: 6 October 1999     

Detecting and reconstructing subdivision connectivity

inverse subdivision algorithms , with linear time and space complexity, to detect and reconstruct uniform Loop, Catmull–Clark, and Doo–Sabin subdivision structure in irregular triangular, quadrilateral, and polygonal meshes. We consider two main applications for these algorithms. The first one is to enable interactive modeling systems that support uniform subdivision surfaces to use popular interchange file formats which do not preserve the subdivision structure, such as VRML, without loss of information. The second application is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Our Loop inverse subdivision algorithm is based on global connectivity properties of the covering mesh, a concept motivated by the covering surface from Algebraic Topology. Although the same approach can be used for other subdivision schemes, such as Catmull–Clark, we present a Catmull–Clark inverse subdivision algorithm based on a much simpler graph-coloring algorithm and a Doo–Sabin inverse subdivision algorithm based on properties of the dual mesh. Straightforward extensions of these approaches to other popular uniform subdivision schemes are also discussed. Published online: 3 July 2002     

The normal of a fractal surface

  We have discovered a class of fractal functions that are differentiable. Fractal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fractal interpolation function remains a fractal interpolation function, and this new fractal interpolation function is differentiable. Tensor products of pairs of these fractal functions form fractal surfaces with a well-defined tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirrors.     

Robust online detection of pipeline corrosion from range data

We present the Finite-Window Robust Sequential Estimator for the detection and analysis of corrosion in range images of gas pipelines. This statistically robust, real-time technique estimates the pipeline surface range function in the presence of noise, surface deviations, and changes in the underlying model. Deviations from the robust surface fit, corresponding to statistical outliers, represent potential areas of corrosion. Because the algorithm estimates surface parameters over a finite, sliding window of data, it can track moderately high-order surfaces using lower order models. The system is consistent, objective, and non-destructive and can be used with the pipeline in service. Received: 7 September 1999 / Accepted: 2 November 2000