Reconstruction and Simplification of Surfaces from Contours

doi:10.1006/gmod.2000.0530

Graphical Models

Volume 62, Issue 6, November 2000, Pages 429-443

https://doi.org/10.1006/gmod.2000.0530 Get rights and content

Abstract

In this paper we consider the problem of reconstructing triangular surfaces from given contours. An algorithm solving this problem must decide which contours of two successive slices should be connected by the surface (branching problem) and, given that, which vertices of the assigned contours should be connected for the triangular mesh (correspondence problem). We present a new approach that solves both tasks in an elegant way. The main idea is to employ discrete distance fields enhanced with correspondence information. This allows us not only to connect vertices from successive slices in a reasonable way but also to solve the branching problem by creating intermediate contours where adjacent contours differ too much. Last but not least we show how the 2D distance fields used in the reconstruction step can be converted to a 3D distance field that can be advantageously exploited for distance calculations during a subsequent simplification step.

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Citation Excerpt :
Depending on the initial input available, surface reconstruction methods can be roughly classified into three groups. The first group addresses the problem by obtaining a surface model exclusively from a set of given cross-sections [2,15,38,40,52,54]. This is a classical problem in medical science, biomedical engineering and CAD/CAM in which a volumetric object (such as a body inner organ, for instance) is typically defined by a sequence of 2D cross-sections or thin layers (acquired from computer tomography, magnetic resonance imaging, ultrasound imaging, etc.).
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Computerized girth determination for custom footwear manufacture
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To overcome this problem, a triangulation method, whereby the points are determined using the intersection of the required plane and triangles, was also proposed. Many different methods exist for triangulating a surface (Klein, Schilling, & Straβer, 2000). To reduce computational time, only the scanned points within 4 mm (four slices of data) from the 3D tape plane were used.
Good fitting footwear requires matching not just the linear dimensions of feet but their girths as well. Footwear fitters have been using manual measurements for a long time, but the development of computerized techniques and scanner technologies have now made automatic determination of different foot dimensions feasible. The resistance to using such computer measurements has been the lack of trust in the accuracy of the data. This paper proposes an approach to obtain the necessary girths of feet in order to customize footwear. The proposed approach attempts to simulate the manual measurement procedures, and its effectiveness is assessed through an experiment with 15 foot castings. The results show that the simulated measurements can be within 5 mm of the manual measurements if the measuring locations can be correctly identified. Linear regressions show that the differences between the manual measurements and the simulated measurements can be modeled with the addition of a systematic error term of less than 4 mm. The computerized acquisition of foot dimensions is a useful way forward for custom shoe manufacturers.
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A particular anatomic structure, the mushroom body, is labeled manually in every image of the volume data. The polyhedral model of the mushroom body can be obtained from the surface reconstruction algorithms [17,18]. The template fly brain can be selected arbitrarily.
High quality 3D visualization of anatomic structures is necessary for many applications. The anatomic structures first need to be segmented. A variety of segmentation algorithms have been developed for this purpose. For confocal microscopy images, the noise introduced during the specimen preparation process, such as the procedure of penetration or staining, may cause images to be of low contrast in some regions. This property will make segmentation difficult. Also, the segmented structures may have rugged surfaces in 3D visualization. In this paper, we present a hybrid method that is suitable for segmentation of confocal microscopy images. A rough segmentation result is obtained from the atlas-based segmentation via affine registration. The boundaries of the segmentation result are close to the object boundaries, and are regarded as the initial contours of the active contour models. After convergence of the snake algorithm, the resulting contours in regions of low contrast are locally refined by parametric bicubic surfaces to alleviate the problem of incorrect convergence. The proposed method increases the accuracy of the snake algorithm because of better initial contours. Besides, it can provide smoother segmented results in 3D visualization.
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Citation Excerpt :
The simplest solution to the correspondence problem is to assign the correspondences manually [3], but it is not convenient. For automation, some methods deal with this problem by matching contour segments [4–6], others by evaluating overlaps of areas enclosed by the contours [7,8], and still others by constructing the areas of difference [9–11]. These methods either restrict the input data to the case without branching or handle specific data set only.
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This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in $R^{3}$ and employs multi-level partition of unity (MPU) implicit models to create a surface that approximately fits to the 3D points. Since MPU implicit models additionally require surface normal information at each point, an algorithm that estimates normals from the contour data is also described. Contour data frequently contains noise from the scanning and delineation process. MPU implicit models provide a superior approach to the problem of contour-based surface reconstruction, especially in the presence of noise, because they are based on adaptive implicit functions that locally approximate the points within a controllable error bound. We demonstrate the effectiveness of our technique with a number of example datasets, providing images and error statistics generated from our results.

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Regular ArticleReconstruction and Simplification of Surfaces from Contours

Abstract

Comput. Vision Image Understand.

Comput. Vision Graph. Image Process.

Graph. Models Image Process.

Conversion of complex contour line definitions into polygonal element mosaics

Comput. Graph.

A comparison of mesh simplification algorithms

Comput. Graph.

Simplification envelopes

Comput. Graph.

Optimal surface resconstruction from planar contours

Comm. Assoc. Comput. Mach.

Shape-based interpolation

IEEE Comput. Graph. Appl.

A new approach to the construction of surfaces from contour data

Comput. Graph. Forum

Approximating complex surfaces by triangulation of contour lines

IBM J. Res. Dev.

Regular Article
Reconstruction and Simplification of Surfaces from Contours