Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an...Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.展开更多
In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions fo...In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
A new approach is proposed for automatically creating B-rep models of a three-dimensional planar object from a line drawing depicting the object under orthographically axonometric projection. A new line parameterizati...A new approach is proposed for automatically creating B-rep models of a three-dimensional planar object from a line drawing depicting the object under orthographically axonometric projection. A new line parameterization that satisfies the uniqueness, boundedness and uniformness for representing lines in 2D and 3D space is given. According to the location relation between lines and planes of object depicted by the line drawing, some constraints about object’s 3D information are produced and a linear system based on those constraints is established. 3D information of a planar body can be obtained by solving the linear system. It is proved that, during the processing, there existed at least four degrees of freedom. It is more convenient to use information about lines and planes instead of points and planes for computer vision and intelligent CAD systems to interpret line drawings of planar objects.展开更多
文摘Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.
文摘In this paper, we shall be interested in characterization of efficient solutions for special classes of problems. These classes consider roughly B-invexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
基金Supported by Open Foundation of Research Center of Measuring Technologies and Control Engineering, Nanchang Institute of Aeronautical Technology (2003-013) amd Natural Science Foundation of Jiangxi Province (0311018) Shaanxi Province (2002E224) in China.
文摘A new approach is proposed for automatically creating B-rep models of a three-dimensional planar object from a line drawing depicting the object under orthographically axonometric projection. A new line parameterization that satisfies the uniqueness, boundedness and uniformness for representing lines in 2D and 3D space is given. According to the location relation between lines and planes of object depicted by the line drawing, some constraints about object’s 3D information are produced and a linear system based on those constraints is established. 3D information of a planar body can be obtained by solving the linear system. It is proved that, during the processing, there existed at least four degrees of freedom. It is more convenient to use information about lines and planes instead of points and planes for computer vision and intelligent CAD systems to interpret line drawings of planar objects.
