Three dimensional moment invariants under rigid transformation

1993 ◽  
pp. 518-522 ◽  
Author(s):  
Xuan Guo
Keyword(s):  
Three Dimensional ◽  
Moment Invariants ◽  
Rigid Transformation

scholarly journals V4PCS: Volumetric 4PCS Algorithm for Global Registration

2017 ◽  
Author(s):  
Jida Huang ◽  
Tsz-Ho Kwok ◽  
Chi Zhou
Keyword(s):  
Mass Customization ◽  
Process Development ◽  
Three Dimensional ◽  
Rigid Transformation ◽  
New Paradigm ◽  
Shape Registration ◽  
Related Data ◽  
Global Registration ◽  
Information Reuse ◽  
Customized Products

With the advances in hardware and process development, additive manufacturing is realizing a new paradigm: mass customization. There are massive human-related data in mass customization, but there are also many similarities in mass-customized products. Therefore, reusing information can facilitate mass customization and create unprecedented opportunities in advancing the theory, method, and practice of design for mass-customized products. To enable information reuse, different models have to be aligned so that their similarity can be identified. This alignment is commonly known as the global registration that finds an optimal rigid transformation to align two three-dimensional shapes (scene and model) without any assumptions on their initial positions. The Super 4-Points Congruent Sets (S4PCS) is a popular algorithm used for this shape registration. While S4PCS performs the registration using a set of 4 coplanar points, we find that incorporating the volumetric information of the models can improve the robustness and the efficiency of the algorithm, which are particularly important for mass customization. In this paper, we propose a novel algorithm, Volumetric 4PCS (V4PCS), to extend the 4 coplanar points to non-coplanar ones for global registration, and theoretically demonstrate the computational complexity is significantly reduced. Several typical human-centered applications such as tooth aligner and hearing aid are investigated and compared with S4PCS. The experimental results show that the proposed V4PCS can achieve a maximum of 20 times speedup and can successfully compute the valid transformation with very limited number of sample points.

scholarly journals Simultaneous Robot–World and Hand–Eye Calibration without a Calibration Object

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3949 ◽  
Author(s):  
Wei Li ◽  
Mingli Dong ◽  
Naiguang Lu ◽  
Xiaoping Lou ◽  
Peng Sun
Keyword(s):  
Three Dimensional ◽  
Real Data ◽  
Medical Robotics ◽  
Calibration Method ◽  
Bundle Adjustment ◽  
Data Sets ◽  
Rigid Transformation ◽  
Validation Experiment ◽  
Dimensional Reconstruction ◽  
Sparse Bundle Adjustment

An extended robot–world and hand–eye calibration method is proposed in this paper to evaluate the transformation relationship between the camera and robot device. This approach could be performed for mobile or medical robotics applications, where precise, expensive, or unsterile calibration objects, or enough movement space, cannot be made available at the work site. Firstly, a mathematical model is established to formulate the robot-gripper-to-camera rigid transformation and robot-base-to-world rigid transformation using the Kronecker product. Subsequently, a sparse bundle adjustment is introduced for the optimization of robot–world and hand–eye calibration, as well as reconstruction results. Finally, a validation experiment including two kinds of real data sets is designed to demonstrate the effectiveness and accuracy of the proposed approach. The translation relative error of rigid transformation is less than 8/10,000 by a Denso robot in a movement range of 1.3 m × 1.3 m × 1.2 m. The distance measurement mean error after three-dimensional reconstruction is 0.13 mm.

Three-Dimensional Moment Invariants

1980 ◽  
Vol PAMI-2 (2) ◽  
pp. 127-136 ◽  
Author(s):  
Firooz A. Sadjadi ◽  
Ernest L. Hall
Keyword(s):  
Three Dimensional ◽  
Moment Invariants

scholarly journals V4PCS: Volumetric 4PCS Algorithm for Global Registration

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Jida Huang ◽  
Tsz-Ho Kwok ◽  
Chi Zhou
Keyword(s):  
Mass Customization ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Data Driven ◽  
Rigid Transformation ◽  
Shape Registration ◽  
Related Data ◽  
Global Registration ◽  
Information Reuse ◽  
3D Shapes

With the advances in three-dimensional (3D) scanning and sensing technologies, massive human-related data are now available and create many applications in data-driven design. Similarity identification is one of the basic problems in data-driven design and can facilitate many engineering applications and product paradigm such as quality control and mass customization. Therefore, reusing information can create unprecedented opportunities in advancing the theory, method, and practice of product design. To enable information reuse, different models must be aligned so that their similarity can be identified. This alignment is commonly known as the global registration that finds an optimal rigid transformation to align two 3D shapes (scene and model) without any assumptions on their initial positions. The Super 4-Points Congruent Sets (S4PCS) is a popular algorithm used for this shape registration. While S4PCS performs the registration using a set of four coplanar points, we find that incorporating the volumetric information of the models can improve the robustness and the efficiency of the algorithm, which are particularly important for mass customization. In this paper, we propose a novel algorithm, Volumetric 4PCS (V4PCS), to extend the four coplanar points to noncoplanar ones for global registration, and theoretically demonstrate the computational complexity is significantly reduced. Experimental tests are conducted on several models such as tooth aligner and hearing aid to compare with S4PCS. The experimental results show that the proposed V4PCS can achieve a maximum of 20 times speedup and can successfully compute the valid transformation with very limited number of sample points. An application of the proposed method in mass customization is also investigated.

Three-dimensional moment invariants for automated target recognition

1996 ◽  
Author(s):  
Tayib I. Samu ◽  
Firooz A. Sadjadi ◽  
Ernest L. Hall
Keyword(s):  
Target Recognition ◽  
Three Dimensional ◽  
Moment Invariants

Ambiguous Pictorial Depth Cues and Perceptions of Nonrigid Motion in the Three-Loop Figure

Perception ◽  
1994 ◽  
Vol 23 (9) ◽  
pp. 1049-1062
Author(s):  
Jack Broerse ◽  
Rongxin Li ◽  
Roderick Ashton
Keyword(s):  
Three Dimensional ◽  
Nonrigid Motion ◽  
Rigid Transformation ◽  
Shape Constancy ◽  
Depth Cues ◽  
Pictorial Depth ◽  
Rigidity Constraint ◽  
Invariance Hypothesis ◽  
Special Instance ◽  
Classical Size

The three-loop figure is a two-dimensional (2-D) pattern that generates (mis)perceptions of nonrigid three-dimensional (3-D) structure when rotated about its centre. Such observations have been described as counterexamples to the principle whereby a moving object is presumed to be rigid, provided that a rigid interpretation is possible (ie the ‘rigidity constraint’). In the present investigation we demonstrated that stationary three-loop figures exhibit many of the classic properties of multistable/ambiguous figures, with any one of several possible 3-D configurations being reported at any one instant. Further investigation revealed that perceived nonrigidity during rotation was markedly reduced (and rigidity enhanced) when the figure was modified with static pictorial depth cues (eg shading, interposition). These cues had no effect on the overall proportion of time that observers reported 3-D organisations in stationary versions of the figure, but significantly reduced the frequency of perceptual reorganisation, and increased the duration for reporting a particular organisation. Since each of the perceived 3-D structures in a stationary ambiguous 2-D figure has a unique kinetic counterpart (ie rigid transformation), we attribute the nonrigid structure perceived when the figure rotates to the integration of these otherwise inconsistent kinetic components; and have further illustrated this with modified versions of a Penrose impossible triangle. Under kinetic versions of the classical size/distance invariance hypothesis, the rigidity constraint may be considered to represent a special instance of size/shape constancy, in which case counterexamples involving (mis)perceptions of nonrigid structure are comparable to other well-known exceptions to such principles of minimum object change (eg classical illusions).

Three dimensional radial Tchebichef moment invariants for volumetric image recognition

2017 ◽  
Vol 27 (4) ◽  
pp. 810-824 ◽  
Author(s):  
M. El Mallahi ◽  
A. Zouhri ◽  
J. El-Mekkaoui ◽  
H. Qjidaa
Keyword(s):  
Image Recognition ◽  
Three Dimensional ◽  
Moment Invariants ◽  
Tchebichef Moment
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