Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy
Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this r...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ghasemzadeh, Hamzeh [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Multimedia tools and applications - Springer US, 1995, 77(2017), 6 vom: 06. Apr., Seite 6837-6861 |
|---|---|
| Übergeordnetes Werk: |
volume:77 ; year:2017 ; number:6 ; day:06 ; month:04 ; pages:6837-6861 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11042-017-4601-5 |
|---|
| Katalog-ID: |
OLC2035044790 |
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| 520 | |a Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. | ||
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10.1007/s11042-017-4601-5 doi (DE-627)OLC2035044790 (DE-He213)s11042-017-4601-5-p DE-627 ger DE-627 rakwb eng 070 004 VZ Ghasemzadeh, Hamzeh verfasserin aut Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2017 Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. Rectangular jigsaw puzzle Branch and bound (B&B) Minimum weight arborescence Edmond algorithm Performance criteria Mean opinion score (MOS) Arjmandi, Meisam K. aut Enthalten in Multimedia tools and applications Springer US, 1995 77(2017), 6 vom: 06. Apr., Seite 6837-6861 (DE-627)189064145 (DE-600)1287642-2 (DE-576)052842126 1380-7501 nnns volume:77 year:2017 number:6 day:06 month:04 pages:6837-6861 https://doi.org/10.1007/s11042-017-4601-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OLC-MKW GBV_ILN_70 AR 77 2017 6 06 04 6837-6861 |
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10.1007/s11042-017-4601-5 doi (DE-627)OLC2035044790 (DE-He213)s11042-017-4601-5-p DE-627 ger DE-627 rakwb eng 070 004 VZ Ghasemzadeh, Hamzeh verfasserin aut Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2017 Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. Rectangular jigsaw puzzle Branch and bound (B&B) Minimum weight arborescence Edmond algorithm Performance criteria Mean opinion score (MOS) Arjmandi, Meisam K. aut Enthalten in Multimedia tools and applications Springer US, 1995 77(2017), 6 vom: 06. Apr., Seite 6837-6861 (DE-627)189064145 (DE-600)1287642-2 (DE-576)052842126 1380-7501 nnns volume:77 year:2017 number:6 day:06 month:04 pages:6837-6861 https://doi.org/10.1007/s11042-017-4601-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OLC-MKW GBV_ILN_70 AR 77 2017 6 06 04 6837-6861 |
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10.1007/s11042-017-4601-5 doi (DE-627)OLC2035044790 (DE-He213)s11042-017-4601-5-p DE-627 ger DE-627 rakwb eng 070 004 VZ Ghasemzadeh, Hamzeh verfasserin aut Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2017 Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. Rectangular jigsaw puzzle Branch and bound (B&B) Minimum weight arborescence Edmond algorithm Performance criteria Mean opinion score (MOS) Arjmandi, Meisam K. aut Enthalten in Multimedia tools and applications Springer US, 1995 77(2017), 6 vom: 06. Apr., Seite 6837-6861 (DE-627)189064145 (DE-600)1287642-2 (DE-576)052842126 1380-7501 nnns volume:77 year:2017 number:6 day:06 month:04 pages:6837-6861 https://doi.org/10.1007/s11042-017-4601-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OLC-MKW GBV_ILN_70 AR 77 2017 6 06 04 6837-6861 |
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10.1007/s11042-017-4601-5 doi (DE-627)OLC2035044790 (DE-He213)s11042-017-4601-5-p DE-627 ger DE-627 rakwb eng 070 004 VZ Ghasemzadeh, Hamzeh verfasserin aut Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2017 Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. Rectangular jigsaw puzzle Branch and bound (B&B) Minimum weight arborescence Edmond algorithm Performance criteria Mean opinion score (MOS) Arjmandi, Meisam K. aut Enthalten in Multimedia tools and applications Springer US, 1995 77(2017), 6 vom: 06. Apr., Seite 6837-6861 (DE-627)189064145 (DE-600)1287642-2 (DE-576)052842126 1380-7501 nnns volume:77 year:2017 number:6 day:06 month:04 pages:6837-6861 https://doi.org/10.1007/s11042-017-4601-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-BUB SSG-OLC-MKW GBV_ILN_70 AR 77 2017 6 06 04 6837-6861 |
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Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy |
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Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy |
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Ghasemzadeh, Hamzeh |
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Multimedia tools and applications |
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Ghasemzadeh, Hamzeh Arjmandi, Meisam K. |
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10.1007/s11042-017-4601-5 |
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070 004 |
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optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy |
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Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy |
| abstract |
Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. © Springer Science+Business Media New York 2017 |
| abstractGer |
Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. © Springer Science+Business Media New York 2017 |
| abstract_unstemmed |
Abstract Automatic solution of rectangular jigsaw puzzles can be broken down into two separate steps of calculating pairwise compatibility metrics and jigsaw assembling algorithm. This work discriminates between two different sources of errors, each corresponding to one of these two steps. In this regard, type I error is defined as the imperfection of the used compatibility metric, and type II error is reserved to measure the imperfection of jigsaw assembling algorithm. Differentiating between these two types of error allows us to tweak and optimize different parts of the algorithm to achieve the best performance. Based upon these defined terms, this study argues that current jigsaw assembling algorithms mainly rely on either greedy methods or metaheuristic algorithms, which may impose a considerable amount of type II error to the final solution. This paper demonstrates that a powerful and perfect (i.e., type II error-free) jigsaw assembling algorithm is achievable by combining branch and bound technique with graph theory. This perfect jigsaw assembling algorithm is then utilized to measure the performances of various compatibility metrics and color models. The superiority of red-green-blue (RGB) color model and Mahalanobis gradient compatibility (MGC) metric in solving rectangular jigsaw puzzles is shown by providing conclusive evidence. Additionally, a mean opinion score (MOS) test is conducted to examine the accuracy of the existing metrics. According to the results from MOS test, we argue that the existing performance criteria are not concise and accurate; thus, a new accuracy metric is proposed on the basis of comparing different sub-blocks of solutions. Finally, the efficiency of jigsaw assembling algorithm is measured by proposing a new performance criterion. © Springer Science+Business Media New York 2017 |
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Optimum solution and evaluation of rectangular jigsaw puzzles based on branch and bound method and combinatorial accuracy |
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