Cryo-electron tomography (Cryo-ET) is an imaging technique used to generate three-dimensional structures of cellular macromolecule complexes in their native environment. Due to developing cryo-electron microscopy technology, the image quality of three-dimensional reconstruction of cryo-electron tomography has greatly improved. However, cryo-ET images are characterized by low resolution, partial data loss and low signal-to-noise ratio (SNR). In order to tackle these challenges and improve resolution, a large number of subtomograms containing the same structure needs to be aligned and averaged. Existing methods for refining and aligning subtomograms are still highly time-consuming, requiring many computationally intensive processing steps (i.e. the rotations and translations of subtomograms in three-dimensional space). In this article, we propose a Stochastic Average Gradient (SAG) fine-grained alignment method for optimizing the sum of dissimilarity measure in real space. We introduce a Message Passing Interface (MPI) parallel programming model in order to explore further speedup. We compare our stochastic average gradient fine-grained alignment algorithm with two baseline methods, high-precision alignment and fast alignment. Our SAG fine-grained alignment algorithm is much faster than the two baseline methods. Results on simulated data of GroEL from the Protein Data Bank (PDB ID:1KP8) showed that our parallel SAG-based fine-grained alignment method could achieve close-to-optimal rigid transformations with higher precision than both high-precision alignment and fast alignment at a low SNR (SNR=0.003) with tilt angle range ±60 ∘ or ±40 ∘ . For the experimental subtomograms data structures of GroEL and GroEL/GroES complexes, our parallel SAG-based fine-grained alignment can achieve higher precision and fewer iterations to converge than the two baseline methods.

In this paper, we have proved the existence of projective moment invariants of images using finite combinations of weighted moments, with relative projective differential invariants as weight functions. We have given some instances constructed in that way, and analyzed possible issues could affect the performance. Some procedures are taken to estimate partial derivatives of discrete images, and a new method is designed to normalize the number of pixels for discrete images to minimize the changes before and after the projective transformation. We have carried out experiments using popular image databases and real images to test the performance. And the results show that the invariants proposed in this paper have better stability and discriminability than other previously used moment invariants in image retrieval and classification. Users can directly extract invariant features of images for a given planar object from different viewpoints without knowing the parameters of the 2D projective transformations. Therefore, the projective moment invariant could be potentially useful for planar object recognition, image description and classification.

Affine moment invariant (AMI) is a kind of hand-crafted image feature, which is invariant to affine transformations. This property is precisely what the standard convolution neural network (CNN) is difficult to achieve. In this letter, we present a kind of network architecture to introduce AMI into CNN, which is called AMI-Net. We achieved this by calculating AMI on the feature maps of the hidden layers. These AMIs will be concatenated with the standard CNN's FC layer to determine the network's final output. By calculating AMI on the feature maps, we can not only extend the dimension of AMIs, but also introduce affine transformation invariant into CNN. Two network architectures and training strategies of AMI-Net are illuminated, one is two-stage, and the other is end-to-end. To prove the effectiveness of the AMI-Net, several experiments have been conducted on common image datasets, MNIST, MNIST-rot, affNIST, SVHN, and CIFAR-10. By comparing with the corresponding standard CNN, respectively, we verify the validity of AMI-net.

Shape or color based moment invariants are conventional pattern sensitive features in the object recognition and image description. However, the existing moment invariants are not robust because they handle simplified cases, such as single impact of shape transformation, single color transformation, and a simple combination of them. In this paper, we propose a kind of shape-color moment invariants (SCMIs), taking complicated shape and color transformation into account. It is applicable to more complicated cases, such as changing viewpoints, different illuminations, different camera white balance modes, and different color spaces. The integral-based SCMI construction framework is extensible and general. We evaluate the technique through comprehensive experiments.

This paper proposes an extended 3-D shape retrieval feature, which is based on a new scheme. In our method, continuous principal component analysis is used to align 3-D models into a canonical position. We then represent 3-D polygonal mesh as a 3-D multi-layer closed curve. It can capture the more feature of the 3-D models. The feature of the 3-D model is extracted from the 3-D closed curve by the Fourier transform. And the experiments show it is more efficient.

In this paper, two evaluation factors are proposed to evaluate subdivision methods based on surface moments. Both factors are derived from moment invariants, and mainly used to measure shape stabilization. The experiment results show these factors are able to measure the distortion characteristic of 3-D models.

This paper presented necessary and sufficient condition of moment invariants under general linear transformation. Based on this condition, arbitrary order and dimensional moment invariant sets can be constructed. Due to their linear independence, previous invariants are special cases of them.

With the development of computer techniques, 3D model has been used more and more widely and content-based 3D model retrieval has been a hotspot in the area of multimedia information retrieval. How to extract 3D models' feature effectively is still a difficulty. Projection based 3D model feature extraction is an important kind in feature extraction, because of its robustness against noise, simplification and its simplicity of feature extraction. Based on the theory of principle plane, a feature extraction method based on the projection of principle plane is proposed and applied to 3D model retrieval. The experiments show that the method performs well.

3D face data have been increased recently with the development of 3D data acquisition technology. 3D face has extensive applications. A proper coordinate system defined on faces is sometimes necessary. However, building a canonical coordinate system for all the 3D faces presenting the physiological vertical direction of human face is still an open question. In this paper, we propose a new 3D face canonical coordinate system based on the physiological structure of human face. Once locating the nose tip and finding the symmetry plane, we use the circular points on the face around the cheekbones to decide the front view, as the direction of the average normal of them is almost vertical to the center axis of human head. The experiment shows that our method is robust to rough data and provides a uniform description for all the 3D face models with different positions and expressions.

We convert watertight polygonal models to volumetric models by using voxelization methods. Then we use invariant feature descriptors such as volume moment invariants and shape histogram for shape retrieval. The experiment result reveals that 3D models represented by voxels are highly robust to noise and perturbations.

3D face scans often contain too much noise and other irregularities in them. Geometric processing techniques such as smoothing and hole filling are employed to preprocess this kind of data. Each face model is then segmented to get a series of partial surfaces and curves. We use surface moment invariants and curve moment invariants as shape descriptors for the shape retrieval of them.

In this paper, volume models are obtained from closed surface models by an accurate voxelization method which can handle the hidden cavities. This kind of 3D binary images is then converted to gray-level images by a fast Euclidean distance transform (EDT). Moment invariants (Mis) which are invariant shape descriptors under similarity transformations, are then computed based on the gray images. Applications in shape analysis area such as principal axis determination, skeleton and medial axis extraction, and shape retrieval can be carried out base on EDT and Mis.

Structure alignment could help to find shape similarities between proteins and guide structure classification and fold recognition. Common substructure detection and extraction are especially important, for which could guide the biologist to discover binding site or active site. We represent each segment of alpha-carbon backbone by using dihedral angles and curve moment invariants. Then, local and global structure alignment could be performed by iterative closest point algorithm. Maximum common substructures between a pair of proteins or within a protein could be found. Active sites also could be detected by the proposed algorithm.

Analysis of transforming matrices between Bezier basis functions and geometrically continuous basis functions is presented. It is shown that G/sup 2/ transforming matrix has some relationship with G/sup 1/ transforming matrix. Based on this relationship a method of calculating G/sup 1/ basis functions is introduced, the degree of which is higher than quadratic. These basis functions are expressed explicitly via matrices decomposition. Equations for constructing G/sup 2/ splines can be presented independently of geometric shape parameters' values.

This correspondence addresses the problem of rotation, scale, and translation invariant recognition of images. Object shape comparability is a challenging problem in the field of pattern recognition and computer vision. The method based on the geometric moment invariants is the typical method in these applications. This paper introduces curve structure moment invariants based on the geometric moment invariants from transforming the density in geometric moments into a new density. The difference in the shapes is increased by using the curve structure moment invariants. Therefore, this method can be used in object shape analysis. To support our new theory, an algorithm for object shape analysis is designed and experiments based on square transform are conducted. Experiments give an encouraging high recognition rate by using the curve structure moment invariants.

Plenty of structured data existing on the grid need to be managed by databases, but there is little work available on grid-enabled databases. Two problems lie in current research: the first is the deficiency of a uniform management and access method to various kinds of databases; the second is that query efficiency decreases rapidly with the increase of the amount of data records. Metadata plays a critical role in grid databases integration, so a layered metadata model is put forward which comprises information of data storage, data properties and relations between data objects. Through the metadata model, the distributed, heterogeneous data resources can be accessed uniformly and efficiently. At last an example of hospital information database system proves the validity and feasibility of our model.

The theory of 1D generalized multiresolution analysis (GMRA) with quasi-real dilation is put forward. In this paper we will focus on the 2D extension of the optimal m-band wavelets and its applications in planar image processing. Given a class of image, we will present optimal m-band wavelets for them only by a part of samples. The efficiency and superiority of the algorithm can been seen from the processing result of datasets of the human body slices.