3D zernike descriptors for content based shape retrieval

Abstract

Content based 3D shape retrieval for broad domains like the World Wide Web has recently gained considerable attention in Computer Graphics community. One of the main challenges in this context is the mapping of 3D objects into compact canonical representations referred to as descriptors, which serve as search keys during the retrieval process. The descriptors should have certain desirable properties like invariance under scaling, rotation and translation. Very importantly, they should possess descriptive power providing a basis for similarity measure between three-dimensional objects which is close to the human notion of resemblance.In this paper we advocate the usage of so-called 3D Zernike invariants as descriptors for content based 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under the above transformations. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with algorithms and computational details. Furthermore, we give a detailed discussion on influence of the algorithm parameters like type and resolution of the conversion into a volumetric function, number of utilized coefficients, etc. As is revealed by our study, the 3D Zernike descriptors are natural extensions of spherical harmonics based descriptors, which are reported to be among the most successful representations at present. We conduct a comparison of 3D Zernike descriptors against these regarding computational aspects and shape retrieval performance.

PANORAMA: A 3D Shape Descriptor Based on Panoramic Views for Unsupervised 3D Object Retrieval

“…Yu et al [28] used spherical functions to describe the topology and concavity of the surface of a 3D object and the amount of effort required to transform it to its bounding sphere. Generalizing from 2D to 3D, Novotni et al [29] presented the 3D Zernike descriptor, Daras et al [30] introduced the generalized radon transform, Ricard et al [31] developed the 3D ART descriptor by generalizing the 2D angular radial transform and Zaharia et al [32] proposed the C3DHTD descriptor by generalizing the 2D Hough Transform.…”

Autotagging to improve text search for 3D models

“…For the geometric similarity distance we used the Euclidean distances between Zernike descriptors [8], computed on a voxel grid of 128 voxels per side with a binary thickening kernel 4 voxels in diameter. For scaling, we used 7 point Gaussian numerical integration to find the center of mass of a uniform mass distribution on the surface of the object.…”

“…We start with a geometric shape similarity metric and find the neighbors of ω within some distance threshold τ (ω). We use Zernike descriptors [8] but in principal any reasonable shape distance should do. Note that τ is allowed to be a function of the model, which allows for adaptively defining the threshold based on the density of models in a given portion of the descriptor space.…”

Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation

“…A variation of this basic idea is the complex EGI proposed by Kang et al [8] where each EGI cell is described by a complex number which captures both rotation and translation information. Novotni et al [9] presented the 3D Zernike descriptor, generalizing the 2D Zernike descriptor. The descriptor is an extension of spherical harmonics descriptors because Zernike functions are spherical harmonic functions modulated by appropriate radial functions.…”