On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
3-D Moment Forms: Their Construction and Application to Object Identification and Positioning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust Clustering with Applications in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
What's in a Set of Points? (Straight Line Fitting)
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Robust Estimation for Range Image Segmentation and Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Least Biased Fuzzy Clustering Method
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comments on: 'Robust Line Fitting in a Noisy Image by the Method of Moments'
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Efficient Method for the Computation of Legendre Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
A highly robust estimator for regression models
Pattern Recognition Letters
Exact Legendre moment computation for gray level images
Pattern Recognition
Lapped block image analysis via the method of legendre moments
EURASIP Journal on Applied Signal Processing
Refined translation and scale Legendre moment invariants
Pattern Recognition Letters
Fast and low-complexity method for exact computation of 3D Legendre moments
Pattern Recognition Letters
Skeletonization of noisy images via the method of legendre moments
ACIVS'05 Proceedings of the 7th international conference on Advanced Concepts for Intelligent Vision Systems
Moments and wavelets for classification of human gestures represented by spatio-temporal templates
AI'04 Proceedings of the 17th Australian joint conference on Advances in Artificial Intelligence
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The standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself. Here, we present a new statistical clustering method based on Legendre moment theory and maximum entropy principle for line fitting in a noisy image. We propose a new approach for estimating the underlying probability density function (p.d.f.) of the data set. The p.d.f. is expanded in terms of Legendre polynomials by means of the Legendre moments. The order of the expansion is selected according to the maximum entropy principle (M.E.P.). Then, the points corresponding to the maxima of the p.d.f. will be the true points of the line to be extracted by a chaining algorithm. This approach is directly generalized to multidimensional data. The proposed algorithm was successfully applied to real and simulated noisy line images, with comparison to some well-known methods.