Abstract
Spherical harmonic (SH) has shown excellent advantages in terms of accuracy and efficiency in the retrieval of complete three-dimensional shapes. However, since the spherical function directly takes the shape centroid as the global reference point, the SH features depend heavily on the central position. In this context, the features become no longer reliable in the query of incomplete shapes that may cause erratic centroid. In this work, we propose a novel shape descriptor, namely spherical harmonic energy over the Gaussian sphere (SHE-GS), especially for the incomplete shape retrieval. Firstly, all unit normal vectors on the shape surface are mapped to points on a Gaussian sphere, which has the constant center. Secondly, kernel density estimation is used to establish a Gaussian Sphere Model (GSM) to describe the density change of these mapping points. Finally, the shape descriptor is generated by applying an SH transformation on the model. According to the way of GSM being regarded as a surface model or a volume model, we have separately designed two specific algorithm implementations. Experimental results, on two engineering shape sets containing artificially defective shapes, indicate that the proposed method outperforms other traditional methods also defined in the sphere space for incomplete shape retrieval. The superiority is verified for both similar objects in the same category or the single specific object of query.
Highlights
Stimulated by the needs of many industries, more and more 3D data collection techniques are emerging, such as laser scanning, stereo vision, structured light, mobile mapping, and GPS surveying
We propose a novel 3D shape descriptor for incomplete 3D shape retrieval, which we call spherical harmonic energy over the Gaussian sphere (SHE-GS)
Our descriptors express the shape feature by its normals distribution defined on the Gaussian sphere with a fixed center, and uses the energy of the feature contained in each spherical harmonic degree as the final descriptor
Summary
Stimulated by the needs of many industries, more and more 3D data collection techniques are emerging, such as laser scanning, stereo vision, structured light, mobile mapping, and GPS surveying. System is that, given a query shape, use a shape similarity matching algorithm to find the most similar 3D objects from a specific database. As descriptions become more and more detailed, these increasingly high-dimensional shape features bring a more significant computational burden to feature extraction, similarity matching, and database retrieval. Deep learning methods were introduced to reduce dimensionality recently [5]. In this development, most of the shape descriptors were designed for intact objects. Most of the shape descriptors were designed for intact objects Their applicability for incomplete shape retrieval has not been fully considered, whether for input query shapes or the target models stored in the database.
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