Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curv...Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.展开更多
Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curva...Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.展开更多
In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are ...In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.展开更多
This paper proposes a novel double regular- ization control （DRC） method which is used for tablet packaging image segmentation. Since the intensities of tablet packaging images are inhomogenous, it is difficult to m...This paper proposes a novel double regular- ization control （DRC） method which is used for tablet packaging image segmentation. Since the intensities of tablet packaging images are inhomogenous, it is difficult to make image segmentation. Compared to methods based on level set, the proposed DRC method has some advantages for tablet packaging image segmentation. The local re- gional control term and the rectangle initialization contour are first employed in this method to quickly segment un- even grayscale images and accelerate the curve evolution rate. Gaussian filter operator and the convolution calcula- tion are then adopted to remove the effects of texture noises in image segmentation. The developed penalty energy function, as regularization term, increases the constrained conditions based on the gradient flow conditions. Since the potential function is embedded into the level set of evo- lution equations and the image contour evolutions are bi- laterally extended, the proposed method further improves the accuracy of image contours. Experimental studies show that the DRC method greatly improves the computational efficiency and numerical accuracy, and achieves better results for image contour segmentation compared to other level set methods.展开更多
基金Supported by Innovation Program of Shanghai Municipal Education Commission (10YZ160)Science and Technology Commission Foundation of Shanghai (071605123)Science Foundation for the Excellent Youth Scholars of Shanghai
文摘Lutwak, Yang, and Zhang posed the notion of Lp-curvature images and established several Lp analogs of the affne isoperimetric inequality. In this article, the notion of Lp-mixed curvature images is introduced, Lp-curvature images being a special case. The properties and Lp analogs of the affne isoperimetric inequality are established for Lp-mixed curvature images.
基金Supported by the National Natural Science Foundation of China(11161019)
文摘Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body.
基金Supported by the NNSF of China(11161024)Supported by the NSF of Jiangxi Province (2010GZC0115)
文摘In this paper, the concepts of the ith L;-mixed affine surface area and Lp-polar curvature images are introduced, some new inequalities connecting these new notions with Lρ-centroid bodies and ρ-Blaschke bodies are showed. Moreover, a Blaschke-Santalo type inequality for Lρ-mixed affine surface area is established. Our results also imply the similar to the inequalities for Marcus-Lopes, Bergstrom and Ky Fan.
基金the Science and Technology Commission of Shanghai Municipality(Grant No.14YF1408600)the Shanghai Municipal Commission of Economy and Informatization under Shanghai Industry University Research Collaboration(Grant No.CXY-2013-71)+2 种基金the Natural Science Foundation of Shandong Province(Grant No.ZR2012FM008)the Science and Technology Development Program of Shandong Province(Grant No.2013GNC11012)the National Natural Science Foundation of China(Grant No.61100115)
文摘This paper proposes a novel double regular- ization control （DRC） method which is used for tablet packaging image segmentation. Since the intensities of tablet packaging images are inhomogenous, it is difficult to make image segmentation. Compared to methods based on level set, the proposed DRC method has some advantages for tablet packaging image segmentation. The local re- gional control term and the rectangle initialization contour are first employed in this method to quickly segment un- even grayscale images and accelerate the curve evolution rate. Gaussian filter operator and the convolution calcula- tion are then adopted to remove the effects of texture noises in image segmentation. The developed penalty energy function, as regularization term, increases the constrained conditions based on the gradient flow conditions. Since the potential function is embedded into the level set of evo- lution equations and the image contour evolutions are bi- laterally extended, the proposed method further improves the accuracy of image contours. Experimental studies show that the DRC method greatly improves the computational efficiency and numerical accuracy, and achieves better results for image contour segmentation compared to other level set methods.
