Normalization and shape recognition of three-dimensional objects by 3D moments

Gálvez, Juan Manuel; Cantón, Manuel Alías

doi:10.1016/0031-3203(93)90120-l

Cited by 66 publications

(21 citation statements)

References 14 publications

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“…The basic idea of range image registration based on moments is to construct a coordinate frame which is rigidly attached to the object in each image [1], [3], [5]. After constructing the two frames, we know their relationship to the global coordinate system and thus we also know the rigid transformation between the two frames, which is also the rigid transformation of the object.…”

Section: Range Image Registrationmentioning

confidence: 99%

“…We will name the constructed frames the canonical frames. The canonical frame is constructed in two steps as follows [5] 1) In the first step, the global coordinate system is translated to the center of gravity of the object´ Ü Ý Þ µ to form coordinate system ¼ . Moments of individual superellipsoid parts (Ñ ÔÕÖ ) are transformed to the global coordinate system (Å ÔÕÖ ) and summed over the number of parts AE to compute the center of gravity.…”

Section: Range Image Registrationmentioning

confidence: 99%

“…A search for the most distant point on the object from the origin of the coordinate system along the principal axes was proposed in [5], and the use of third order moments in [3], to resolve the 4-way ambiguity. The presented approach is similar to [3], but with much simpler derivation.…”

Section: A Resolving 4-way Ambiguitymentioning

confidence: 99%

“…Initial two-dimensional moment invariants techniques were extended to three-dimensions [2]- [4] and three-dimensional moments were used for object-recognition [5].…”

mentioning

confidence: 99%

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Moments of superellipsoids and their application to range image registration

Jaklič

Solina

2003

IEEE Trans. Syst., Man, Cybern. B

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Abstract-Cartesian moments are frequently used global geometrical features in computer vision for object pose estimation and recognition. In the paper we derive a closed form expression for 3D Cartesian moment of order Ô ·Õ·Ö of a superellipsoid in its canonical coordinate system. We also show how 3D Cartesian moment of a globally deformed superellipsoid in general position and orientation can be computed as a linear combination of 3D Cartesian moments of the corresponding non-deformed superellipsoid in canonical coordinate system. Additionally, moments of objects that are compositions of superellipsoids can be computed as simple sums of moments of individual parts.To demonstrate practical application of the derived results we register pairs of range images based on moments of recovered compositions of superellipsoids. We use a standard technique to find centers of gravity and principal axes in pairs of range images while third-order moments are used to resolve the fourway ambiguity. Experimental results show expected improvement of recovered rigid transformation based on moments of recovered superellipsoids as compared to the registration based on moments of raw range image data. Beside object pose estimation the presented results can be directly used for object recognition with moments and/or moment invariants as object features.

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Section: Range Image Registrationmentioning

confidence: 99%

Section: Range Image Registrationmentioning

confidence: 99%

Section: A Resolving 4-way Ambiguitymentioning

confidence: 99%

“…Initial two-dimensional moment invariants techniques were extended to three-dimensions [2]- [4] and three-dimensional moments were used for object-recognition [5].…”

mentioning

confidence: 99%

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Moments of superellipsoids and their application to range image registration

Jaklič

Solina

2003

IEEE Trans. Syst., Man, Cybern. B

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“…Guo [3] used different approach with the same result. Galvez and Canton [4] used the normalization approach to 3D recognition. Cyganski and Orr [5] proposed a tensor method for derivation of rotation invariants from geometric moments.…”

Section: Introductionmentioning

confidence: 99%

Recognition of Symmetric 3D Bodies

Suk

Flusser

2014

Symmetry

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The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.

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