A survey of methods for recovering quadrics in triangle meshes

Petitjean, Sylvain

doi:10.1145/508352.508354

Cited by 187 publications

(113 citation statements)

References 109 publications

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“…The remaining quadric types all exist in simpler sub-spaces with fewer degrees of freedom [17]. The key to efficiently fitting these quadric types is to express the quadric with fewer parameters, such that only quadrics of the specified type can be generated, and then apply the standard algebraic fitting procedures of Sec.…”

Section: Fitting Methods For Lower-dimensional Quadric Typesmentioning

confidence: 99%

“…For example, for planes and spheres we can simply drop and combine terms from the standard implicit quadric function to arrive at a plane-or sphere-specific function (e.g. For most other lower-dimensional quadrics, the required low-dimensional space is more complicated: For example, there is no known linear least-squares method to fit circular cones and cylinders to a point cloud using just point positions [17]. However, there are linear least-squares methods for fitting such shapes to point clouds with normals [15].…”

Section: Fitting Methods For Lower-dimensional Quadric Typesmentioning

confidence: 99%

“…Efficient fitting of quadric surfaces to unstructured point clouds or triangle meshes is an important component of many reverse engineering systems [17,24]. Users may want a given surface to be fit by a specific quadric type: For example, they may want the quadric to be a cone, ellipsoid, or a rotationally-symmetric subtype (spheroid, circular cone, etc).…”

Section: Introductionmentioning

confidence: 99%

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Type-Constrained Direct Fitting of Quadric Surfaces

Andrews¹,

Séquin²

2013

Computer-Aided Design and Applications

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We present a catalog of type-specific, direct quadric fitting methods: Given a selection of a point cloud or triangle mesh, and a desired quadric type (e.g. cone, ellipsoid, paraboloid, etc), our methods recover a best-fit surface of the given type to the given data. Type-specific quadric fitting methods are scattered throughout the literature; here we present a thorough, practical collection in one place. We add new methods to handle neglected quadric types, such as non-circular cones and general rotationally symmetric quadrics. We improve upon existing methods for ellipsoid-and hyperboloid-specific fitting. Our catalog handles a wide range of quadric types with just two high-level fitting strategies, making it simpler to understand and implement.

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Section: Fitting Methods For Lower-dimensional Quadric Typesmentioning

confidence: 99%

Section: Fitting Methods For Lower-dimensional Quadric Typesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Type-Constrained Direct Fitting of Quadric Surfaces

Andrews¹,

Séquin²

2013

Computer-Aided Design and Applications

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“…The idea of local surface (with or without cropping) has been widely used for the extraction of local reference frame and subsequent invariant features. The reader is referred to the survey of Petitjean [29] for details. Many existing methods fit a local surface to the data points and derive the reference frame from the fitted surface.…”

Section: Keypoint Detection In Full 3d Modelsmentioning

confidence: 99%

On the Repeatability and Quality of Keypoints for Local Feature-based 3D Object Retrieval from Cluttered Scenes

2009

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3D object recognition from local features is robust to occlusions and clutter. However, local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features. We present an algorithm for the detection of such keypoints on 3D models and partial views of objects. The keypoints are highly repeatable between partial views of an object and its complete 3D model. We also propose a quality measure to rank the keypoints and select the best ones for extracting local features. Keypoints are identified at locations where a unique local 3D coordinate basis can be derived from the underlying surface in order to extract invariant features. We also propose an automatic scale selection technique for extracting multi-scale and scale invariant features to match objects at different unknown scales. Features are projected to a PCA subspace and matched to find correspondences between a database and query object. Each pair of matching features gives a transformation that aligns the query and database object. These transformations are clustered and the biggest cluster is used to identify the query object. Experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multi-scale features have a recognition rate of over 95% for up to 80% occluded objects.

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“…This strategy is well-suited to industrial sites since most parts of them are composed of primitive shapes ( [12,20,21]). However, such methods rarely extract complete pipe-runs with accurate connectivity.…”

Section: Introductionmentioning

confidence: 99%

Pipe-Run Extraction and Reconstruction from Point Clouds

Qiu

Zhou

Neumann

2014

Computer Vision – ECCV 2014

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Abstract. This paper presents automatic methods to extract and reconstruct industrial site pipe-runs from large-scale point clouds. We observe three key characteristics in this modeling problem, namely, primitives, similarities, and joints. While primitives capture the dominant cylindric shapes, similarities reveal the inter-primitive relations intrinsic to industrial structures because of human design and construction. Statistical analysis over point normals discovers primitive similarities from raw data to guide primitive fitting, increasing robustness to data noise and incompleteness. Finally, joints are automatically detected to close gaps and propagate connectivity information. The resulting model is more than a collection of 3D triangles, as it contains semantic labels for pipes as well as their connectivity.

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A survey of methods for recovering quadrics in triangle meshes

Cited by 187 publications

References 109 publications

Type-Constrained Direct Fitting of Quadric Surfaces

Type-Constrained Direct Fitting of Quadric Surfaces

On the Repeatability and Quality of Keypoints for Local Feature-based 3D Object Retrieval from Cluttered Scenes

Pipe-Run Extraction and Reconstruction from Point Clouds

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