The clinical value of the 3D reconstruction of a coronary artery is important for the diagnosis and intervention of cardiovascular diseases. This work proposes a method based on a deformable model for reconstructing coronary arteries from two monoplane angiographic images acquired from different angles. First, an external force back-projective composition model is developed to determine the external force, for which the force distributions in different views are back-projected to the 3D space and composited in the same coordinate system based on the perspective projection principle of x-ray imaging. The elasticity and bending forces are composited as an internal force to maintain the smoothness of the deformable curve. Second, the deformable curve evolves rapidly toward the true vascular centerlines in 3D space and angiographic images under the combination of internal and external forces. Third, densely matched correspondence among vessel centerlines is constructed using a curve alignment method. The bundle adjustment method is then utilized for the global optimization of the projection parameters and the 3D structures. The proposed method is validated on phantom data and routine angiographic images with consideration for space and re-projection image errors. Experimental results demonstrate the effectiveness and robustness of the proposed method for the reconstruction of coronary arteries from two monoplane angiographic images. The proposed method can achieve a mean space error of 0.564 mm and a mean re-projection error of 0.349 mm.
Three-dimensional (3-D) reconstruction of the coronary artery is important for the diagnosis and interventional treatment of cardiovascular diseases. In this paper, a novel mean composited external force back-projective composition model is proposed and integrated into the deformable model framework for the 3-D reconstruction of coronary arteries from multiple angiograms. The parametric snake evolves toward the real vascular centerline in 3-D space based on the integrated internal energy and composited external energy. In addition, a polynomial function is constructed to determine the diameter of the cross section of the vascular segments, which fully utilizes the back-projection information of multiple angiograms. The deformable and proposed methods are comparatively validated using phantom datasets and routine angiographic images with respect to space and reprojection Euclidean distance errors. The experimental results demonstrate the effectiveness and robustness of the proposed model, which can achieve a mean space error of 0.570 mm and a mean reprojection error of 0.351 mm. In addition, the influence of the angle difference to the reconstruction accuracy is discussed and validated on phantom datasets, which demonstrate that an angle difference of for any two angiograms is suitable for the 3-D reconstruction process.
The city is both a carrier and a subject of innovation. Based on the triple helix theory of industry–university research and the theory of spatial correlation, this study constructs a collaborative innovation framework both within the cities and between cities, and uses a network data envelopment analysis (DEA) model and spatial econometric model to measure and analyze the collaborative innovation efficiency in 75 innovative cities in China. The results show that collaborative innovation efficiency within cities is on the rise, and the efficiency of “research to production” is significantly higher than that of “learning to research.” Industrial structure and foreign factors have inhibited the efficiency improvements, and infrastructure and living standards have different promoting effects on different stages of efficiency. Between cities, capital flows have obvious spillover effects, which promote the efficiency of innovation networks, while the long‐term characteristics of institutional learning have a near‐term negative impact.
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