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Debora Gil, & Petia Radeva. (2004). Shape Restoration via a Regularized Curvature Flow. Journal of Mathematical Imaging and Vision, 21(3), 205–223.
Abstract: Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.
In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.
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Ole Larsen, Petia Radeva, & Enric Marti. (1995). Bounds on the optimal elasticity parameters for a snake. Image Analysis and Processing, , 37–42.
Abstract: This paper develops a formalism by which an estimate for the upper and lower bounds for the elasticity parameters for a snake can be obtained. Objects different in size and shape give rise to different bounds. The bounds can be obtained based on an analysis of the shape of the object of interest. Experiments on synthetic images show a good correlation between the estimated behaviour of the snake and the one actually observed. Experiments on real X-ray images show that the parameters for optimal segmentation lie within the estimated bounds.
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Josep Llados, & Enric Marti. (1999). A graph-edit algorithm for hand-drawn graphical document recognition and their automatic introduction into CAD systems. Machine Graphics & Vision, 8, 195–211.
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Josep Llados, & Enric Marti. (1999). Graph-edit algorithms for hand-drawn graphical document recognition and their automatic introduction. Machine Graphics & Vision journal, special issue on Graph transformation, .
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Josep Llados, Enric Marti, & Juan J.Villanueva. (2001). Symbol recognition by error-tolerant subgraph matching between region adjacency graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10), 1137–1143.
Abstract: The recognition of symbols in graphic documents is an intensive research activity in the community of pattern recognition and document analysis. A key issue in the interpretation of maps, engineering drawings, diagrams, etc. is the recognition of domain dependent symbols according to a symbol database. In this work we first review the most outstanding symbol recognition methods from two different points of view: application domains and pattern recognition methods. In the second part of the paper, open and unaddressed problems involved in symbol recognition are described, analyzing their current state of art and discussing future research challenges. Thus, issues such as symbol representation, matching, segmentation, learning, scalability of recognition methods and performance evaluation are addressed in this work. Finally, we discuss the perspectives of symbol recognition concerning to new paradigms such as user interfaces in handheld computers or document database and WWW indexing by graphical content.
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