192,512 research outputs found
Geometric Structure Extraction and Reconstruction
Geometric structure extraction and reconstruction is a long-standing problem in research communities including computer graphics, computer vision, and machine learning. Within different communities, it can be interpreted as different subproblems such as skeleton extraction from the point cloud, surface reconstruction from multi-view images, or manifold learning from high dimensional data. All these subproblems are building blocks of many modern applications, such as scene reconstruction for AR/VR, object recognition for robotic vision and structural analysis for big data. Despite its importance, the extraction and reconstruction of a geometric structure from real-world data are ill-posed, where the main challenges lie in the incompleteness, noise, and inconsistency of the raw input data. To address these challenges, three studies are conducted in this thesis: i) a new point set representation for shape completion, ii) a structure-aware data consolidation method, and iii) a data-driven deep learning technique for multi-view consistency. In addition to theoretical contributions, the algorithms we proposed significantly improve the performance of several state-of-the-art geometric structure extraction and reconstruction approaches, validated by extensive experimental results
Quantum Diagonalization Method in the Tavis-Cummings Model
To obtain the explicit form of evolution operator in the Tavis-Cummings model
we must calculate the term explicitly which is very hard. In this paper we try to make the
quantum matrix diagonal to
calculate and, moreover, to know a deep structure of the model.
For the case of one, two and three atoms we give such a diagonalization which
is first nontrivial examples as far as we know, and reproduce the calculations
of given in quant-ph/0404034. We also give a hint to an
application to a noncommutative differential geometry.
However, a quantum diagonalization is not unique and is affected by some
ambiguity arising from the noncommutativity of operators in quantum physics.
Our method may open a new point of view in Mathematical Physics or Quantum
Physics.Comment: Latex files, 21 pages; minor changes. To appear in International
Journal of Geometric Methods in Modern Physic
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