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.
