Invariant Image Recognition by Zernike Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
State of the art in shape matching
Principles of visual information retrieval
ACM Transactions on Graphics (TOG)
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
3D Shape Histograms for Similarity Search and Classification in Spatial Databases
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
3D zernike descriptors for content based shape retrieval
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Rotation invariant spherical harmonic representation of 3D shape descriptors
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Shape Matching: Similarity Measures and Algorithms
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A new point matching algorithm for non-rigid registration
Computer Vision and Image Understanding - Special issue on nonrigid image registration
Three-Dimensional Model Based Face Recognition
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
A survey of content based 3D shape retrieval methods
Multimedia Tools and Applications
Fourier Descriptors for Plane Closed Curves
IEEE Transactions on Computers
Three-dimensional shape searching: state-of-the-art review and future trends
Computer-Aided Design
Efficient iris recognition by characterizing key local variations
IEEE Transactions on Image Processing
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Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for characterizing the unique and highly complex structures often encountered in the emerging field of nano and microscale self-assembly, or other disciplines involving complex structures such as computational biology. Computer science algorithms known as ''shape matching'' methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures. This pairwise matching operation, either implicitly or explicitly, lies at the heart of most standard structural characterization schemes for particle systems. By substituting more robust ''shape descriptors'' into these schemes we extend their applicability to structures formed from more complex building blocks. Here, we describe several structural characterization schemes and shape descriptors that can be used to obtain various types of structural information about particle systems. We demonstrate the application of shape matching algorithms to a variety of example problems, for topics including local and global structure identification and classification, automated phase diagram mapping, and the construction of spatial and temporal correlation functions. The methods are applicable to a wide range of systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.