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### A benchmark set for the reconstruction of hv-convex discrete sets

Péter Balázs
2009 Discrete Applied Mathematics
of hv-convex discrete sets and its subclasses.  ...  By using this benchmark set the paper also collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kinds of discrete  ...  Preliminary version of the paper was presented at the 12th International Workshop on Combinatorial Image Analysis, Buffalo, NY, USA, April 2008 [1] .  ...

### Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections [chapter]

Péter Balázs
2009 Lecture Notes in Computer Science
The problem of reconstructing some special hv-convex discrete sets from their two orthogonal projections is considered.  ...  In this paper, we define an intermediate class -the class of hv-convex canonical discrete sets -and give a constructive proof that the above problem remains computationally tractable for this class, too  ...  ) ∈ F and |i l − i l+1 | + |j l − j l+1 | = 1 (|i l − i l+1 | + |j l − j l+1 | ≤ 2) for each l = 0, . . . , k − 1.  ...

### An Algorithm for Reconstructing Special Lattice Sets from Their Approximate X-Rays [chapter]

Sara Brunetti, Alain Daurat, Alberto Del Lungo
2000 Lecture Notes in Computer Science
We provide a polynomial-time algorithm for reconstructing Q-convex sets from their "approximate" X-rays. A Qconvex set is a special subset of Z 2 having some convexity properties.  ...  This algorithm can be used for reconstructing convex subsets of Z 2 from their exact X-rays in some sets of four prescribed lattice directions, or in any set of seven prescribed mutually nonparallel lattice  ...  In detail, given a pair of vectors V = (v 1 , . . . , v n ) and H = (h 1 , . . . , h m ), they want to reconstruct an hv-convex polyomino whose X-rays along vertical and horizontal directions are such  ...

### Community Based Network Reconstruction for an Evolutionary Algorithm Framework

Suma V
2021 Journal of Artificial Intelligence and Capsule Networks
It is based on multi-objective metaheuristic algorithm that is based on population and can be used as the base optimizer.  ...  Inferring complex and non-linear dynamic system using the data that is available plays an important role in many areas of work such as physical, social, biological and computer sciences.  ...  Using EA, the non-convex optimization problem can be overcome and eq (1) have proven to be the apt solution. Fig.1.  ...

### POCS-Based Iterative Reconstruction Algorithm of Missing Textures

Takahiro Ogawa, Miki Haseyama
2007 2007 IEEE International Conference on Image Processing
Experimental results show subjective and quantitative improvement of the proposed reconstruction technique over previously reported reconstruction techniques.  ...  Furthermore, by monitoring the errors converged by the POCS algorithm, selection of the optimal cluster for the target texture including missing intensities is realized in order to reconstruct it adaptively  ...  U k Ξ k HV k Λ k −1 . (6) Then, Eq. (4) can be rewritten as follows: D K k=1 M j=1 ||φ k j − Ξ k HV k Λ k −2 V k HΞ k φ k j || 2 . (7) Since the eigenvectors u k d (d = 1, 2, · · · , D) of U k in Eq. (  ...

### Generalized conic functions of hv-convex planar sets: continuity properties and relations to X-rays

Csaba Vincze, Ábris Nagy
2014 Aequationes Mathematicae
We show that the class of convex bodies that are determined by their coordinate X-rays coincides with the family of convex bodies K for which fK is a point of lower semi-continuity for Φ −1 . 1991 Mathematics  ...  In the paper we investigate the continuity properties of the mapping Φ which sends any non-empty compact connected hv-convex planar set K to the associated generalized conic function fK .  ...  Acknowledgements The authors would like to thank to the referee for the substantial contribution to the development of the final version of the paper. Cs  ...

### Multi-Objective Learning to Predict Pareto Fronts Using Hypervolume Maximization [article]

Timo M. Deist, Monika Grewal, Frank J.W.M. Dankers, Tanja Alderliesten, Peter A.N. Bosman
2021 arXiv   pre-print
We discuss and illustrate why training processes to approximate Pareto fronts need to optimize on fronts of individual training samples instead of on only the front of average losses.  ...  Intuitively, building machine learning solutions in such cases would entail providing multiple predictions that span and uniformly cover the Pareto front of all optimal trade-off solutions.  ...  Marco Virgolin from Chalmers University of Technology for his valuable contributions and discussions on concept and code.  ...

### An optimal algorithm for reconstructing images from binary measurements

Feng Yang, Yue M. Lu, Luciano Sbaiz, Martin Vetterli, Charles A. Bouman, Ilya Pollak, Patrick J. Wolfe
2010 Computational Imaging VIII
We prove that when the threshold T is "1", the negative loglikelihood function is a convex function. Therefore, optimal solution can be achieved using convex optimization.  ...  Numerical experiments with synthetic 1-D signals and images verify the effectiveness and quality of the proposed algorithm.  ...  Since the matrix A is a diagonal matrix, the multiplication of A and vector Hv is equal to the elementwise multiplication of the diagonal of A and Hv.  ...

### Solving Zero-Sum One-Sided Partially Observable Stochastic Games [article]

Karel Horák and Branislav Bošanský and Vojtěch Kovařík and Christopher Kiekintveld
2020 arXiv   pre-print
We provide a full picture for solving one-sided POSGs: we (1) give a theoretical analysis of one-sided POSGs and their value functions, (2) show that a variant of a value-iteration algorithm converges  ...  that our algorithm can solve one-sided POSGs of non-trivial sizes and analyze the scalability of our algorithm in three different domains: pursuit-evasion, patrolling, and search games.  ...  V Υ UB (b) = k+1 i=1 λ i y i + δ b − b 1 λ i and b represent an optimal solution of V Υ UB (b) ≥ |Υ| i=1 λ i · [HV Υ UB ](b i ) + δ b − b 1 ≥ [HV Υ UB ](b ) + δ b − b 1 HV Υ UB is convex, see Proposition  ...

### DISCRETE TOMOGRAPHIC RECONSTRUCTION OF BINARY IMAGES WITH DISJOINT COMPONENTS USING SHAPE INFORMATION

PÉTER BALÁZS
2008 International journal of shape modeling
Thus, a priori knowledge about the components of the image to be reconstructed can be incorporated into the reconstruction process.  ...  We present a general framework for reconstructing binary images with disjoint components from the horizontal and vertical projections.  ...  A preliminary version of this work was presented at the International Symposium on Visual Computing, Las Vegas, NV, 2008, Special Track on Discrete and Computational Geometry and their Applications in  ...

### Page 2191 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews
The main result of this paper is a sim- ple algorithm for reconstructing hv-convex polyominoes in time O(mn - min(m?, n?)).”  ...  (1-ICSI; Berkeley, CA) Reconstructing hy-convex polyominoes from orthogonal projections.  ...

### Rotation-invariance can further improve state-of-the-art blind deconvolution techniques

Fernando Cervantes, Bryan Usevitch, Vladik Kreinovich
2016 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC)
Therefore, even when the original reconstruction is optimal, the reconstruction of a rotated image will be different and, thus, not optimal.  ...  In this paper, we show how this can be done, and we show that this indeed improves the quality of blind deconvolution.  ...  ACKNOWLEDGMENT This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award "UTEP and Prudential  ...

### Page 584 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews
The sets considered are hv-convex polyominoes and hv-convex 8-connected sets.  ...  (H-SZEG-C; Szeged) ; Kuba, Attila (H-SZEG-C; Szeged) ; Dévényi, Csaba (H-SZEG-C; Szeged) ; Dei Lungo, Alberto (I-SIN; Siena) Comparison of algorithms for reconstructing hv-convex discrete sets.  ...

### Solving Partially Observable Stochastic Games with Public Observations

Karel Horák, Branislav Bošanský
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
Our results include: (1) theoretical analysis of PO-POSGs and their value functions showing convexity (concavity) in beliefs of maximizing (minimizing) player, (2) a novel algorithm for approximating the  ...  Solving POSGs in the most general setting is intractable.Therefore, the research has been focused on subclasses of POSGs that have a value of the game and admit designing (approximate) optimal algorithms  ...  The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory  ...

### Entropy Minimization for Convex Relaxation Approaches

Mohamed Souiai, Martin R. Oswald, Youngwook Kee, Junmo Kim, Marc Pollefeys, Daniel Cremers
2015 2015 IEEE International Conference on Computer Vision (ICCV)
We use difference of convex function (DC) programming as an efficient and provably convergent solver for the arising convex-concave minimization problem.  ...  We evaluate this approach on three prominent non-convex computer vision challenges: multi-label inpainting, image segmentation and spatio-temporal multi-view reconstruction.  ...  solving the following convex optimization problem: u k+1 = arg min u g(u) −hv k ,ui (3.2) In order to be able to solve problem (1.4) using DC programming we make the following identifications: g(u)=E(  ...
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