ABSTRACT

Analyzing either high-frequency shape detail or any other 2D fields (scalar or vector) embedded over a 3D geometry is a complex task,
since detaching the detail from the overall shape can be tricky. An alternative approach is to move to the 2D space, resolving shape
reasoning to easier image processing techniques. In this paper we propose a novel framework for the analysis of 2D information
distributed over 3D geometry, based on a locally smooth parametrization technique that allows us to treat local 3D data in terms of
image content. The proposed approach has been implemented as a sketch-based system that allows to design with a few gestures
a set of (possibly overlapping) parameterizations of rectangular portions of the surface. We demonstrate that, due to the locality
of the parametrization, the distortion is under an acceptable threshold, while discontinuities can be avoided since the parametrized
geometry is always homeomorphic to a disk. We show the effectiveness of the proposed technique to solve specific Cultural Heritage
(CH) tasks: the analysis of chisel marks over the surface of a unfinished sculpture and the local comparison of multiple photographs
mapped over the surface of an artwork. We believe that our framework and the corresponding tool are the first steps toward a
computer-based shape reasoning system, able to support CH scholars with a medium they are more used to.



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IEEE Visualization 2011 paper

A demostrative Video




Application Domain

Chisel marks characterization
Our local flattening operator may been conceived as a new digital
tool to make measurements and comparisons in a radically new way
over the digital representation of the artworks



Some images presented in the paper


Pietà di Palestrina

		one pixel = 0.25 mm (right click to download full resolution version)
		one pixel = 0.25 mm (right click to download full resolution version)

San Matteo

		one pixel = 0.25 mm (right click to download full resolution version)
		one pixel = 0.25 mm (right click to download full resolution version)

Measurable evaluation of the restoration results
A second example of the capabilities of the proposed framework is
the visual comparison of the appearance of an artwork before and after
some critical events like a restoration

David




Correlate marks with curvature
The proposed framework allows to compare in a common parametric
space different shape characteristics, possibly also at different level of
scale. In this sense, another application is to compare the main surface
curvature direction, evaluated on a low resolution and smoothed representation,
with the orientation of the residual traces.

San Matteo