دانلود رایگان مقاله محل تقاطع سه بعدی توصیف گر شکل (SID)

Abstract

This paper presents a novel 3D shape descriptor which explicitly captures the local geometry and encodes it using an efficient representation. Our method consists of multiple evolving fronts which are realized by a set of growing spheres on the surface. At the core of this method is a simple intersection operator between the spheres and the shape's surface. Intersection curves yield a discrete sampling of the surface at different positions and scales. Our key idea is to define a shape descriptor that captures the continuous local geometry of the surface in an efficient and consistent representation by intersecting the surface with multiple spheres and transforming the intersection curve to frequency domain. To evaluate our descriptor, we define shape similarity metric and perform shape matching on the SHREC11 non-rigid benchmark and other classes.

6. Limitations and conclusions

Limitations of our method include taking only a single intersection curve even if the sphere-to-surface intersection results in several curves. We limit the negative effect of this limitation by choosing this curve consistently by choosing a small enough initial sphere radius and r (see Section 4.1.1). As an evidence, in all of our experiments we did not encounter a jitter of the intersection curve, namely, a situation in which the chosen intersection curve “jumps” between several possible intersection curves. A further limitation is that feature matching false positives are possible, since we consider only the magnitudes and not the phases of the transformation of the intersection curve. However, we chose to use only the magnitudes since we aimed to minimize dimensionality of the descriptor and we observed empirically that the magnitude carry most of the important information. Additional limitation of our implementation is support for watertight triangular meshes only. We have presented a novel shape descriptor for efficient matching in large 3D databases and reported experimental analysis for its performance on various datasets. Our shape descriptor is highly distinctive, as it captures the entire (2π) relative curvature of the neighborhood of a point. It allows even a single feature to find a correct match with good probability in a large set of features. Our shape descriptor is compact as it represents the intersection of a sphere with a surface as 2 1D curves. The sphere intersection operation is simple and relies only on the point position, thus can be defined robustly everywhere on a surface. The use of a 2D image based representation allows efficient processing using image processing algorithms. Our experimental results show that our descriptor manages to capture the similarity among various dataset and is robust against various types of deformations.