On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Context-free attentional operators: the generalized symmetry transform
International Journal of Computer Vision - Special issue on qualitative vision
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symmetry Detection by Generalized Complex (GC) Moments: A Close-Form Solution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast reflectional symmetry detection using orientation histograms
Real-Time Imaging - Special issue on real-time defect detection
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
A Reflective Symmetry Descriptor for 3D Models
Algorithmica
Sparse Image Coding Using a 3D Non-Negative Tensor Factorization
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Efficient MATLAB Computations with Sparse and Factored Tensors
SIAM Journal on Scientific Computing
Computing non-negative tensor factorizations
Optimization Methods & Software - Mathematical programming in data mining and machine learning
Shape symmetry analysis of breast tumors on ultrasound images
Computers in Biology and Medicine
Journal of Mathematical Imaging and Vision
Tensors in Image Processing and Computer Vision
Tensors in Image Processing and Computer Vision
Texture Synthesis with Grouplets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Online Learning for Matrix Factorization and Sparse Coding
The Journal of Machine Learning Research
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A signal processing approach to symmetry detection
IEEE Transactions on Image Processing
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Face recognition by independent component analysis
IEEE Transactions on Neural Networks
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This study explores an approach for analysing the mirror (reflective) symmetry of 3D shapes with tensor based sparse decomposition. The approach combines non-negative tensor decomposition and directional texture synthesis, with symmetry information about 3D shapes that is represented by 2D textures synthesised from sparse, decomposed images. This technique requires the center of mass of 3D objects to be at the origin of the coordinate system. The decomposition of 3D shapes and analysis of their symmetry are useful for image compression, pattern recognition, as well as there being an emerging interest in the medical community due to its potential to find morphological changes between healthy and pathological structures. This paper postulates that sparse texture synthesis can be used to describe the decomposed basis images acting as symmetry descriptors for a 3D shape. We apply the theory of non-negative tensor decomposition and sparse texture synthesis, deduce the new representation, and show some application examples.