Praktische Verfahren der Gleichungsauflösung .

Mises, R. V.; Pollaczek-Geiringer, H.

doi:10.1002/zamm.19290090206

Cited by 179 publications

(83 citation statements)

References 2 publications

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“…I nstead we calculate the minimum and maximum eigenvalues with the power iteration method [28], and then find the eigenvectors with eigenvalues closest to a number of values regularly selected between the minimum and maximum eigenvalues, with the inverse power iteration method [29]. In this work, we empirically select this number as 300.…”

Section: The Proposed Segmentation Methodsmentioning

confidence: 99%

Quantum mechanics in computer vision: Automatic object extraction

Aytekin

Kıranyaz

Gabbouj

2013

2013 IEEE International Conference on Image Processing

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An automatic object extraction method is proposed exploiting the rich mathematical structure of quantum mechanics. First, a novel segmentation method based on the solutions of Schrödinger's equation is proposed. This powerful segmentation method allows us to model complex objects and inherent structures of edge, shape, and texture information along with the grey-level intensity uniformity, all in a single equation. Due to the large amount of segments extracted with the proposed method, the selection of the object segment is performed by maximizing a regularization energy function based on a recently proposed sub-segment analysis indicating the object boundaries. The results of the proposed automatic object extraction method exhibit such a promising accuracy that pushes the frontier in this field to the borders of the input-driven processing only -without the use of "object knowledge" aided by long-term human memory and intelligence.

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Section: The Proposed Segmentation Methodsmentioning

confidence: 99%

Quantum mechanics in computer vision: Automatic object extraction

Aytekin

Kıranyaz

Gabbouj

2013

2013 IEEE International Conference on Image Processing

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“…We used the power method, also known as power iteration or Von Mises iteration [21]. The algorithm does not compute a matrix decomposition, so it is quite efficient for large sparse matrices.…”

Section: B the Control Parametermentioning

confidence: 99%

Control of accuracy in the Wang-Landau algorithm

2017

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The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model.

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“…Interestingly, the eigenvector of interest can also be computed by means of the power iteration method [28], whose computational burden can be easily and conveniently distributed over the network (other linear algebra algorithms that can be formulated in a distributed way are considered in [26]). However, even considering the complete eigenvalue decomposition, its computational complexity is polynomial (approximately O(m 3 )).…”

Section: Tree Distributed Reconstructionmentioning

confidence: 99%

Affinity-based distributed algorithm for 3D reconstruction in large scale Visual Sensor Networks

Masiero¹,

Cenedese

2014

2014 American Control Conference

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In recent years, Visual Sensor Networks have emerged as an interesting category of distributed sensor-actor systems to retrieve data from the observed scene and produce information. Indeed, the request for accurate 3D scene reconstruction in several applications is leading to the development of very large systems and more specifically to large scale motion capture systems. When dealing with such huge amount of data from a large number of cameras it becomes very hard to make real time reconstruction on a single machine.Within this context, a distributed approach for reconstruction on large scale camera networks is proposed. The approach is based on geometric triangulation performed in a distributed fashion on the computational grid formed by the camera network organized into a tree structure. Since the computational performance of the algorithm strongly depends on the order in which cameras are paired, to optimize the reconstruction a pairing strategy is designed that relies on an affinity score among cameras. This score is computed from a probabilistic perspective by studying the variance of the 3D target reconstruction error and resorting to a normalized cut graph partitioning.The scaling laws and the results obtained in simulation suggest that the proposed strategy allows to obtain a significant reduction of the computational time.

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Praktische Verfahren der Gleichungsauflösung .

Cited by 179 publications

References 2 publications

Quantum mechanics in computer vision: Automatic object extraction

Quantum mechanics in computer vision: Automatic object extraction

Control of accuracy in the Wang-Landau algorithm

Affinity-based distributed algorithm for 3D reconstruction in large scale Visual Sensor Networks

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