Search results for "Wavelet transform"
showing 10 items of 146 documents
Edge detection insensitive to changes of illumination in the image
2010
In this paper we present new edge detection algorithms which are motivated by recent developments on edge-adapted reconstruction techniques [F. Arandiga, A. Cohen, R. Donat, N. Dyn, B. Matei, Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques, Appl. Comput. Harmon. Anal. 24 (2) (2008) 225-250]. They are based on comparing local quantities rather than on filtering and thresholding. This comparison process is invariant under certain transformations that model light changes in the image, hence we obtain edge detection algorithms which are insensitive to changes in illumination.
A pre-processing technique based on the wavelet transform for linear autoassociators with applications to face recognition
1997
In order to improve the performance of a linear autoassociator (which is a neural network model), we explore the use of several preprocessing techniques. The gist of our approach is to store, in addition to the original pattern, one or several pre-processed (i.e. filtered) versions of the patterns to be stored in a neural network. First, we compare the performance of several pre-processing techniques (a plain vanilla version of the autoassociator as a control, a Sobel operator, a Canny-Deriche operator, and a multiscale Canny-Deriche operator) on an example of a pattern completion task using a noise degraded version of a face stored in an autoassociator. We found that the multiscale Canny-D…
Correlation of oscillatory behaviour in Matlab using wavelets
2014
Here we present a novel computational signal processing approach for comparing two signals of equal length and sampling rate, suitable for application across widely varying areas within the geosciences. By performing a continuous wavelet transform (CWT) followed by Spearman?s rank correlation coefficient analysis, a graphical depiction of links between periodicities present in the two signals is generated via two or three dimensional images. In comparison with alternate approaches, e.g., wavelet coherence, this technique is simpler to implement and provides far clearer visual identification of the inter-series relationships. In particular, we report on a Matlab? code which executes this tec…
Two-dimensional optical wavelet decomposition with white-light illumination by wavelength multiplexing
2001
We present a novel method for achieving in real time a two-dimensional optical wavelet decomposition with white-light illumination. The underlying idea of the suggested method is wavelength multiplexing. The information in the different wavelet components of an input object is transmitted simultaneously in different wavelengths and summed incoherently at the output plane. Experimental results show the utility of the new proposed method.
Optical illustration of a varied fractional Fourier-transform order and the Radon-Wigner display.
2010
Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon–Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensional input signal although the output signal contains two dimensions. The optical setup for obtaining the fractional Fourier transform was adapted to include only fixed free-space propagation distances and variable lenses. With a set of two multifacet composite holograms, the Radon–Wigner display has b…
WAVELET ANALYSIS OF THE MULTIFRACTAL CHARACTER OF THE GALAXY DISTRIBUTION
1993
We have determined generalized dimensions of the observed distribution of galaxies. Their different values indicate that this distribution may be described as a multifractal. In order to analyse this distribution further, we have applied local wavelet transforms. Wavelets provide us with an interesting tool to analyse the large-scale structure which can be mathematically quantified and intuitively visualized. Comparing the results of these transforms at different dilation factors helps to visualize more clearly the nearly singular nature of the distribution. This method also allows us to determine the range of the local density power laws
Inner functions and local shape of orthonormal wavelets
2011
Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.
Regularization operators for natural images based on nonlinear perception models.
2006
Image restoration requires some a priori knowledge of the solution. Some of the conventional regularization techniques are based on the estimation of the power spectrum density. Simple statistical models for spectral estimation just take into account second-order relations between the pixels of the image. However, natural images exhibit additional features, such as particular relationships between local Fourier or wavelet transform coefficients. Biological visual systems have evolved to capture these relations. We propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models. The results suggest that if the penalty operator take…
Multi-scale analysis of shell growth increments using wavelet transform
1999
Abstract Shell increments contain information related to the evolution of the environment in which the organism grew during its biomineralization. To extract the information from variations in shell topography, a new and promising technique is presented, involving multi-scale analysis of the shell topography using a B-spline wavelet transform. An accurate non-contact optical system, based on laser triangulation, is used to map the shell surface. The resulting range image is treated as a grey-level image by using a multi-resolution approach based on the generalization of the cascade algorithm. This method allows reconstruction of non-subsampled images that correspond to the projection onto t…
A Comparative Study and an Evaluation Framework of Multi/Hyperspectral Image Compression
2009
In this paper, we investigate different approaches for multi/hyperspectral image compression. In particular, we compare the classic multi-2D compression approach and two different implementations of 3D approach (full 3D and hybrid) with regards to variations in spatial and spectral dimensions. All approaches are combined with a weighted Principal Component Analysis (PCA) decorrelation stage to optimize performance. For consistent evaluation, we propose a larger comparison framework than the conventionally used PSNR, including eight metrics divided into three families. The results show the weaknesses and strengths of each approach.