Alpha Shapes — a Survey

نویسنده

  • Herbert Edelsbrunner
چکیده

Alpha shapes have been conceived in 1981 as an attempt to define the shape of a finite set of point in the plane. Since then, connections to diverse areas in the sciences and engineering have developed, including to pattern recognition, digital shape sampling and processing, and structural molecular biology. This survey begins with a historical account and discusses geometric, algorithmic, topological, and combinatorial aspects of alpha shapes in this sequence.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Distributed Shape Analysis using Alpha and Delaunay-Čech shapes

Alpha shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for the shape of a given point set V . For a given point set V in 2 or 3 dimensions, we show that the knowledge of pairwise distances between pairs of points which are closer than a certain distance is sufficient to compute the alpha shape. We also show that the alpha shapes c...

متن کامل

Nuclear shapes from alpha-gamma-ray angular correlations.

The angular distribution of alpha particles with respect to the spin direction of the residual nuclei is used to probe the shapes of the emitting systems. Two compound systems have been studied: ' Yb and " Sn. Deformed emission shapes are required in order to understand the alpha-gamma correlations in the ' Yb system, but not for the " Sn compound system. These conclusions are identical to thos...

متن کامل

Topologically Correct Image Segmentation Using Alpha Shapes

Existing theories on shape digitization impose strong constraints on feasible shapes and require error-free measurements. We use Delaunay triangulation and α-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. Experiments on real and gen...

متن کامل

Shape-Similarity Comparison of 3D Models Using Alpha Shapes

As the number of in-house and public-domain 3D shape models increase, importance of shape-similarity based search and retrieval for 3D shapes models has increased rapidly. In this paper, we describe our preliminary findings in applying a multiresolution analysis technique to the task of shape similarity comparison of polygon soup models. We used the 3D alpha shapes algorithm to create a multire...

متن کامل

Conformal Alpha Shape-based Multi-scale Curvature Estimation from Point Clouds

Multi-scale geometrical and topological analyses of point clouds can reveal their rich structures. Because conformal alpha shapes of point clouds are hierarchical shapes under different mesh resolution or internal alpha values, their surface curvature estimations are one of the multi-scale geometrical analyses. We present a robust method for computing surface curvature of conformal alpha shapes...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009