A 3D shape descriptor based on spherical harmonics through evolutionary optimization

In this paper, we propose a novel shape descriptor for 3D objects, called spatial geometric descriptor (SGD), to represent the spatial geometric information of a 3D model by mapping its furthest distance, normal and area distribution onto spherical grids in a sequence of concentric shells. Then these spherical distribution functions are transformed to spherical harmonic coefficients which not only save the storage space but also provide multi-resolution shape description for any 3D model by adopting different dimensions for the coefficients. The feature vector extraction time can be reduced by adopting a single scan scheme on the mesh surface for a given 3D model. The retrieval performance is evaluated on the public Princeton Shape Benchmark (PSB) dataset and the experimental results show that our method not only outperforms Light Field Descriptor which is regarded as the best shape descriptor so far but also maintains an advantage of fast feature vector extraction procedure.Keywords3D Model RetrievalShape DescriptorSpherical Harmonincs

In this paper, we consider 3D shape descriptors generated by using functions on a sphere. A set of rotation invariant descriptor vectors is extracted by using spherical harmonics. We first normalize the size of the models, then sample the data from the 3D model surface, and convert the 3D models into point cloud data. We define a unit spherical function for each point on the model surface, and apply spherical harmonics to each function to obtain rotation invariant descriptors. The major contribution of our work is that we can locate a set of rotation invariant descriptor vectors. Moreover, the method is stable to noise on the model surface. Experimental results show that the proposed method performs well in 3D model similarity matching.

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.

We propose a novel approach for 3D shape analysis of <i>heterochromatin foci</i> in 3D confocal light microscopy images of cell nuclei. The approach is based on a 3D parametric intensity model and uses a spherical harmonics (SH) expansion. The model parameters including the SH coefficients are automatically determined by least squares fitting of the model to the image intensities. Based on the obtained SH coefficients, a shape descriptor is determined, which enables distinguishing heterochromatin foci based on their 3D shape to characterize compaction states of heterochromatin. Our approach has been successfully applied to real static and dynamic 3D microscopy image data.

Determining the shape of agricultural materials using spherical harmonics

In this paper, we propose a method for indexing and retrieval of images based on shapes of objects. The concept of connectivity is introduced. 3D models are used to represent 2D images. 2D images are decomposed a priori using connectivity which is followed by 3D model construction. 3D model descriptors are obtained for 3D models and used to represent the underlying 2D shapes. We have used spherical harmonics descriptors as the 3D model descriptors. Difference between two images is computed as the Euclidean distance between their descriptors. Experiments are performed to test the effectiveness of spherical harmonics for retrieval of 2D images. The proposed method is compared with methods based on principal components analysis (PCA) and generic Fourier descriptors (GFD). It is found that the proposed method is effective. Item S8 within the MPEG-7 still images content set is used for performing experiments.

This paper introduces a novel 4D shape descriptor to match temporal surface sequences. A quantitative evaluation based on the receiver-operator characteristic (ROC) curve is presented to compare the performance of conventional 3D shape descriptors with and without using a time filter. Feature- based 3D shape descriptors including shape distribution (Osada et al., 2002 ), spin image (Johnson et al., 1999), shape histogram (Ankest et al., 1999) and spherical harmonics (Kazhdan et al., 2003) are considered. Evaluation shows that filtered descriptors outperform unfiltered descriptors and the best performing volume-sampling shape-histogram descriptor is extended to define a new 4D shape-flow descriptor. Shape-flow matching demonstrates improved performance in the context of matching time-varying sequences which is motivated by the requirement to connect similar sequences for animation production. Both simulated and real 3D human surface motion sequences are used for evaluation.

Fourier method for large-scale surface modeling and registration

This paper proposes novel descriptors that integrate information from multiple views of a 3D object, called Temporal Ensemble of Shape Functions (TESF) descriptors. The TESF descriptors are built by combining per-view Ensemble of Shape Functions (ESF) descriptors with Spatio-Temporal Appearance (STA) descriptors. ESF descriptors provide a compact representation of ten different shape functions per object view (obtained by virtually rendering the object from different viewpoints), and STA descriptors efficiently combine ESF descriptors of multiple object views. The proposed descriptors are evaluated on two publicly available datasets, the 3D-Net database and the Princeton Shape Benchmark. They provide a good performance on both datasets, similar to that of the Spherical Harmonic Descriptor (SHD), with the advantage that because of their view-based nature the TESF descriptors might prove useful for the problem of object classification from limited viewpoints. Such property is of special interest in robotics where the agent is able to move around the object to improve single-view results.

In this paper, an engineering drawing retrieval method based on spherical harmonics is proposed. Firstly, the sample points are uniformly generated by computing the interaction points between the rays and the engineering drawing. Secondly, the sampled points are transformed from the 2D space into the 3D space to get the spherical harmonics shape descriptors. Finally, the Euclidean distance is adopted to compute the distance between the two feature vectors, which can give the similarity coefficient for two compared engineering drawings. Experimental results show that the proposed method is good at retrieving engineering drawings and the retrieval performance can meet the requirement of the practical retrieval.

Macroscopic mechanical properties of granular materials are closely related to particle morphology. For practical reasons, the morphological features are commonly examined from projected two-dimensional (2D) images of the three-dimensional (3D) particles. This brings forward the need for quantifying the correlations between the 2D and 3D particle descriptors. This paper addresses these correlations for irregular granular particles. Three-dimensional images of sand particles were acquired through microfocus X-ray computed tomography, based on which 3D surfaces of the particles were reconstructed using spherical harmonic analyses. The 3D particle size and shape descriptors were subsequently evaluated. All-around projection and random projection of the particles onto 2D planes were undertaken numerically to obtain the projected 2D images and thus the corresponding 2D size and shape descriptors. The results indicate that there are close correlations between 3D and 2D size descriptors averaged from the all-around projections. 2D and 3D shape descriptors can be approximately fitted with a linear relationship. The mean value of 2D descriptors of the tested sands obtained from a series of independent random-projection tests is essentially identical to that from the all-around projections; except that the data from the random-projection tests show a larger scatter. In light of the relationships among the descriptors, a novel and promising approach to predict the cumulative distribution of 3D descriptors from that of 2D descriptors evaluated from a random-projection test is proposed.

We present an approach for robust shape retrieval from data-bases containing articulated 3D shapes. We represent each shape by the eigenvectors of an appropriately defined affinity matrix, obtaining a spectral embedding. Retrieval is then performed on these embeddings using global shape descriptors. Transformation into the spectral domain normalizes the shapes against articulation (bending), rigid-body transformations, and uniform scaling. Experimentally, we show absolute improvement in retrieval performance when conventional shape descriptors are used in the spectral domain on the McGill database of articulated 3D shapes. We also propose a simple eigenvalue-based descriptor, which is easily computed and performs comparably against the best known shape descriptors applied to the original shapes.

The use of 3D polygonal data and volumetric data has attracted attention in recent years, because of advancement in 3D printing technology. The amount of online 3D data is increasing, and systematic searches and classifications are required for 3D model databases. It is important to extract shape descriptors from such 3D data. This paper describes a shape descriptor extraction method for volumetric data, and proposes descriptors called Neighboring Voxel Patters (NVP). These shape descriptors are computed based on voxel patterns in target volumetric data. The technique uses small local 3 x 3 x 3 voxel regions to compute all the possible voxel pattern combinations, and classifies these voxel patterns into a small number of groups. NVP descriptors are computed easily from volumetric data. Although the descriptors are small in size, these descriptors efficiently classify 3D models that are represented by volumetric data. Preliminary experiments are conducted with voxelized 3D model benchmark data. Various sizes of volumetric data are analyzed for similarity retrieval experiments, and the web-based similarity retrieval system is implemented.

In recent years, the demand for a content-based 3D model retrieval system becomes an important issue. In this study, a novel feature, derivative elevation descriptor (DED), is proposed to extract the exterior information of 3D model. The derivative elevation descriptor (DED) is combined with the elevation descriptor (ED) to retrieval 3D models based on the exterior shape information. Moreover, to derive better retrieval results, we will combine the exterior features with an interior feature 3D-ART by a novel relevance feedback approach. The experiments are conducted on the Princeton Shape Benchmark (PSB) database. Experiment results show that our proposed method is superior to others.

3D shape descriptor for object recognition based on Kinect-like depth image