Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional(2D and 3D) image not only in pattern recognition, image vision, but also in image processing and applications engine...Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional(2D and 3D) image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues: the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark(PSB) database for 3D image.展开更多
The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is ...The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is found that the flux of the enstrophy cascades to small scales and the direction cascade of the energy flux is upscaled. Moveover, the probability distribution function (PDF) of the enstrophy flux gives a clear evidence that the enstrophy cascades to smaller scales. Finally, the behavior of the cascade of the high-order Casimir invariants Zn is discussed. The flux of the fourth-order Casimir invariant Z4 cascades to small scales. The flux of Zn has a logarithmic relationship with the scale, that is,∏ 1^zn - l^ζn (n = 2,4,6).展开更多
For a vision measurement system consisted of laser-CCD scanning sensors, an algorithm is proposed to extract and recognize the target object contour. Firstly, the two-dimensional(2D) point cloud that is output by th...For a vision measurement system consisted of laser-CCD scanning sensors, an algorithm is proposed to extract and recognize the target object contour. Firstly, the two-dimensional(2D) point cloud that is output by the integrated laser sensor is transformed into a binary image. Secondly, the potential target object contours are segmented and extracted based on the connected domain labeling and adaptive corner detection. Then, the target object contour is recognized by improved Hu invariant moments and BP neural network classifier. Finally, we extract the point data of the target object contour through the reverse transformation from a binary image to a 2D point cloud. The experimental results show that the average recognition rate is 98.5% and the average recognition time is 0.18 s per frame. This algorithm realizes the real-time tracking of the target object in the complex background and the condition of multi-moving objects.展开更多
基金河北省自然科学基金(the Natural Science Foundation of Hebei Province of China under Grant No.A2006000941)河北省教育厅2006年科研计划(No.2006408)河北省科学技术研究与发展指导计划(No.072135142)。
文摘Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional(2D and 3D) image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues: the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark(PSB) database for 3D image.
基金supported by the National Natural Science Foundation of China(Grant No.91441104)the Ministry of Education in China via project(Grant No.IRT0844)the Shanghai Science and Technology Commission Project of leading Scientists and Excellent Academic Leaders(Grant No.11XD1402300)
文摘The Casimir invariants of the 2-D turbulence are investigated by the lattice Boltzmann method. A coarse-graining approach is used, that allows to resolve the flux of the Casimir invariant in scale and in space. It is found that the flux of the enstrophy cascades to small scales and the direction cascade of the energy flux is upscaled. Moveover, the probability distribution function (PDF) of the enstrophy flux gives a clear evidence that the enstrophy cascades to smaller scales. Finally, the behavior of the cascade of the high-order Casimir invariants Zn is discussed. The flux of the fourth-order Casimir invariant Z4 cascades to small scales. The flux of Zn has a logarithmic relationship with the scale, that is,∏ 1^zn - l^ζn (n = 2,4,6).
文摘For a vision measurement system consisted of laser-CCD scanning sensors, an algorithm is proposed to extract and recognize the target object contour. Firstly, the two-dimensional(2D) point cloud that is output by the integrated laser sensor is transformed into a binary image. Secondly, the potential target object contours are segmented and extracted based on the connected domain labeling and adaptive corner detection. Then, the target object contour is recognized by improved Hu invariant moments and BP neural network classifier. Finally, we extract the point data of the target object contour through the reverse transformation from a binary image to a 2D point cloud. The experimental results show that the average recognition rate is 98.5% and the average recognition time is 0.18 s per frame. This algorithm realizes the real-time tracking of the target object in the complex background and the condition of multi-moving objects.