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Surface curvature maps and Michelangelo’s David (2005)

by J Rugis
Venue:Otago University
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A comparative study on 2d curvature estimators

by Simon Hermann, Reinhard Klette , 2006
"... Abstract. Curvature is a frequently used property in two-dimensional (2D) shape analysis, directly or for derived features such as corners or convex and concave arcs. This paper presents curvature estimators which follow approaches in differential geometry. Digital-straight segment approximation (as ..."
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Abstract. Curvature is a frequently used property in two-dimensional (2D) shape analysis, directly or for derived features such as corners or convex and concave arcs. This paper presents curvature estimators which follow approaches in differential geometry. Digital-straight segment approximation (as known from digital geometry) is used in those estimators. Results of multigrid experiments are evaluated leading to a comparative performance analysis of several curvature estimators. 1
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...differential geometry (for example in [2, 9]) or heuristics (as many of the methods reviewed in [13]). Curvature estimation is also of importance for characterizing surfaces in 3D space. For example, =-=[18]-=- defines and uses curvature maps for rectifying scanned patches (e.g., of Michelangelo’s David). A review on curvature methods is given in two chapters of [10]. The next section presents curvature est...

Feature Analysis of Digital Curves

by Simon Hermann , 2006
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Extracting Surface Curvature from Noisy Scan Data

by J. Rugis
"... In general, the noise that is present in real-world 3D surface scan data prevents accurate curvature calculation. In this paper we show how curvature can be extracted from noisy data by applying filtering after a noisy curvature calculation. To this end, we extend the standard Gaussian filter (as us ..."
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In general, the noise that is present in real-world 3D surface scan data prevents accurate curvature calculation. In this paper we show how curvature can be extracted from noisy data by applying filtering after a noisy curvature calculation. To this end, we extend the standard Gaussian filter (as used in 2D image processing) by taking adjacent point distances along the scanned surface into account. A brief comparison is made between this new 2.5D Gaussian filter and a standard 2D Gaussian filter using data from the Digital Michelangelo Project.
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...e, in the case of adjacency point counts other than six. 3 Curvature maps For 2D visualization purposes it is useful to convert the mean curvature values at surface scan points intoa(2D)curvature map =-=[9]-=-. If the 3D point data has been acquired in a 3D orthogonal grid, then the curvature mapping is straightforward (defined by orthogonal cuts parallel to coordinate planes, see [10]). For data that has ...

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