Finding axes of skewed symmetry
Computer Vision, Graphics, and Image Processing
On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Invariant Image Recognition by Zernike Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal Moment Features for Use With Parametric and Non-Parametric Classifiers
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting Symmetry in Grey Level Images: The Global Optimization Approach
International Journal of Computer Vision
On the Accuracy of Zernike Moments for Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Rotation Angle Estimator
IEEE Transactions on Pattern Analysis and Machine Intelligence
Evaluation of the symmetry plane in 3D MR brain images
Pattern Recognition Letters
Using phase information for symmetry detection
Pattern Recognition Letters
IEEE Transactions on Computers
On the recovery of a function on a circular domain
IEEE Transactions on Information Theory
Image restoration in X-ray microscopy: PSF determination and biological applications
IEEE Transactions on Image Processing
A signal processing approach to symmetry detection
IEEE Transactions on Image Processing
Accurate Computation of Zernike Moments in Polar Coordinates
IEEE Transactions on Image Processing
Testing for symmetries in multivariate inverse problems
Journal of Multivariate Analysis
Accurate calculation of Zernike moments
Information Sciences: an International Journal
Hi-index | 754.84 |
Statistical tests are introduced for checking whether an image function f (x, y) defined on the unit disc D = {(x, y) : x2 + y2 ≤ 1} is invariant under certain symmetry transformations of D, given that discrete and noisy data are observed. Invariance under reflections or under rotations by rational angles is considered, as well as rotational invariance. These symmetry relations can be naturally expressed as restrictions for the Zernike moments of f (x, y). Therefore, the test statistics are based on the L2 distance between Zernike series estimates of the image function itself and its version obtained after applying the symmetry transformation. The asymptotic distribution of the test statistics under both the hypothesis of symmetry as well as under fixed alternatives is derived. Furthermore, the quality of the asymptotic approximations via simulation studies is investigated. The usefulness of our theory is verified by examining an important problem in confocal microscopy, i.e., possible imprecise alignments in the optical path of the microscope are investigated. For optical systems with rotational symmetry, the theoretical point-spread function (PSF) is reflection symmetric with respect to two orthogonal axes, and rotationally invariant if the detector plane matches the optical plane of the microscope. The tests are used to investigate whether the required symmetries can indeed be detected in the empirical PSF.