In particular, we study the case for graphs of periodic functions. In this article, we prove some results on the uniqueness of the circular area signature. However, in contrast to differential invariants of curves, it is currently unknown whether integral signatures offer unique representations of curves. Integral invariants are preferred over their differential counter-parts due to their robustness with respect to noise. The representation of curves by integral invariant signatures is an important step in shape recognition and classification. Index Terms-surface characterization, interactive inspection, Cultural Heritage, mesh parameterization, image processing. For this very difficult task, 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. 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 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. 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. 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. An alternative approach is to move to the 2D space, resolving shape reasoning to easier image processing techniques. 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.
POSTVIEW PRINCIPAL CURVATURE PATCH
A graphical example of residual marks detection and characterization: the user interactively selects a portion of the surface to be studied the system produces a parameterized image patch then, high frequencies encoding residual marks are evaluated and stored in an image finally, image based processing helps the user to identify and classify the different chisel marks. Our focal mesh estimation also provides a novel discrete shape operator that simultaneously estimates the principal curvatures and principal directions.įig. We develop both CPU and GPU-based algorithms to efficiently approximate these two slits and, hence, the focal meshes. We show neighboring normal triplets are constrained to pass simultaneously through two slits, which are parallel to the specified parametrization planes and rule the focal surfaces. Our approach locally parameterizes the surface normals about a point by their intersections with a pair of parallel planes. We provide algorithms to robustly approximate the focal surfaces of a triangle mesh with known or estimated normals. For instance, the normal of each focal surface indicates a principal direction of the corresponding point on the original surface. Focal surfaces have many useful properties. In this article, we develop a focal-surfacebased differential geometry interpretation for discrete mesh surfaces. These focal surfaces are swept by the loci of the principal curvatures’ radii. The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces.
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