A novel method is introduced for distinguishing counterfeit banknotes from genuine samples. The method is based on analyzing differences in the networks of paper fibers. The main tool is a curvelet-based algorithm for measuring the distribution of overall fiber orientation and quantifying its anisotropy. The use of a couple or more appropriate parameters makes it possible to distinguish forgeries from genuine samples as concentrated point clouds in a two- or three-dimensional parameter space. Furthermore, the techniques of making watermarks is investigated by comparing genuine and counterfeit €50 banknotes. In addition, the so-called wire markings are shown to differ significantly from each other in all of investigated banknotes.
A method based on the curvelet transform is introduced to estimate the orientation distribution from two-dimensional images of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform better than these traditional methods.
A method based on the curvelet transform is introduced for estimating from two-dimensional images the orientation distribution of small anisotropic particles. Orientation of fibers in paper is considered as a particular application of the method. Theoretical aspects of the suitability of this method are discussed and its efficiency is demonstrated with simulated and real images of fibrous systems. Comparison is made with two traditionally used methods of orientation analysis, and the new curvelet-based method is shown to perform clearly better than these traditional methods.
In this paper the new family of orthogonal compactly supported
M-band wavelets is presented. This family is similar to Coiflets
since scaling function and all wavelet functions have equal number
of vanishing moments. However, the center of these vanishing
moments can differ from zero. Equivalent moment conditions are
given also for scaling filter. Finally, estimate for asymptotic
convergence speed of wavelet sampling approximation of smooth functions is given.
In this paper we study a problem of signal compression how to choose a best mother wavelet from the set S of wavelets. The approach is following: First we calculate a discrete wavelet transform of signal by using one standard wavelet. Then we form coefficients mi for each scale i from the wavelet expansions coefficients. Coefficients mi are used for selecting best wavelet from the set S. Selection is classification problem and we have constructed classification algorithm that uses fuzzy similarity that is based on a continuous t-norm called Lukasiewicz algebra. We are using normal and cumulative forms of generalized Lukasiewicz algebra and we have also applied a genetic algorithm into the our classifier to choose appropriate weights in our classification tasks.
There are many advantages what we get by using t-norm called Lukasiewicz in classification: 1) Structure has a promising mathematical background 2) Mean of many fuzzy similarities is still a fuzzy similarity 3) Any pseudo-metric induces fuzzy similarity on a given non-empty set X with respect to the Lukasiewicz-conjunction.
Algorithm is efficient especially because we have to calculate wavelet transform only once and classification is simple and fast. Algorithm is also very flexible, cause we can implement any type metrics or mean measures into it. As our results we will present a new method to select best mother wavelet from a given set S. We will also show that proposed hybrid method can be used in this kind of analytical problems. The best way to form coefficients mi and choose metric or measure is depended of class of signals we are working with, which is still unclear.