Ana M. C. Ruedin

A statistical model for magnitudes and angles of wavelet frame coefficients and its application to texture retrieval

Abstract This paper presents a texture descriptor based on wavelet frame transforms. At each position in the image, and for each resolution level, we consider both vertical and horizontal wavelet detail coefficients as the components of a bivariate random vector. The magnitudes and angles of these vectors are computed. At each level the empirical histogram of magnitudes is modeled by a Generalized Gamma distribution, and the empirical histogram of angles is modeled by a different version of the von Mises distribution that accounts for histograms with 2 modes. Each texture is characterized by few parameters. A new distance is presented (based on the Kullback–Leibler divergence) that allows giving relative importance to each model and to each resolution level. This distance is later conveniently adapted to provide for rotation invariance, by establishing equivalence classes over distributions of angles. Through a broad set of experiments on three different image databases, we demonstrate that our new descriptor and distance measure can be successfully applied in the context of texture retrieval. We compare our system to several relevant methods in this field in terms of retrieval performance and number of parameters used by each method. We also include some classification tests. In all the tests, we obtain superior retrieval rates for a set of fewer parameters involved.

A new wavelet-based texture descriptor for image retrieval

This paper presents a novel texture descriptor based on the wavelet transform. First, we will consider vertical and horizontal coefficients at the same position as the components of a bivariate random vector. The magnitud and angle of these vectors are computed and its histograms are analyzed. This empirical magnitud histogram is modelled by using a gamma distribution (pdf). As a result, the feature extraction step consists of estimating the gamma parameters using the maxima likelihood estimator and computing the circular histograms of angles. The similarity measurement step is done by means of the well-known Kullback-Leibler divergence. Finally, retrieval experiments are done using the Brodatz texture collection obtaining a good performance of this new texture descriptor. We compare two wavelet transforms, with and without downsampling, and show the advantage of the second one, which is translation invariant, for the construction of our texture descriptor.

A Class-Conditioned Lossless Wavelet-Based Predictive Multispectral Image Compressor

We present a nonlinear lossless compressor designed for multispectral images consisting of few bands and having greater spatial than spectral correlation. Our compressor is based on a 2-D integer wavelet transform that reduces spatial correlation. Different models for the statistical dependences of wavelet detail coefficients are analyzed and tested to perform linear inter/intraband predictions. Band, class, scale, and orientation are used as conditioning contexts to calculate predictions, as well as to encode prediction errors with an adaptive arithmetic coder. A new mechanism is proposed for band ordering, based on wavelet fine detail coefficients. Our compressor CLWP outperforms state-of-the-art lossless compressors. It has random access capability and can be applied to compress volumetric data having similar characteristics.

Wavelet-Based Texture Retrieval Modeling the Magnitudes of Wavelet Detail Coefficients with a Generalized Gamma Distribution

This paper presents a texture descriptor based on the fine detail coefficients at three resolution levels of a traslation invariant undecimated wavelet transform. First, we consider vertical and horizontal wavelet detail coefficients at the same position as the components of a bivariate random vector, and the magnitude and angle of these vectors are computed. The magnitudes are modeled by a Generalized Gamma distribution. Their parameters, together with the circular histograms of angles, are used to characterize each texture image of the database. The Kullback-Leibler divergence is used as the similarity measurement. Retrieval experiments, in which we compare two wavelet transforms, are carried out on the Brodatz texture collection. Results reveal the good performance of this wavelet-based texture descriptor obtained via the Generalized Gamma distribution.

Construction of nonseparable multiwavelets for nonlinear image compression

A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. The matrix filter bank is viewed as the polyphase matrix of other filters, upon which the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with these wavelets is outlined: formulae for analysis and synthesis are given, the first steps are illustrated with images, and the decomposition of the original image into two input images is addressed. Compression is achieved in a nonlinear process. Experimental results show that (i) the constructed multiwavelets having lowpass properties perform better than other nonseparable multiwavelets, (ii) the energy compaction in the fine detail subbands is greater for the multiwavelets than for the one-dimensional wavelets tried.

Wavelet-Based Feature Extraction for Handwritten Numerals

We present a novel preprocessing technique for handwritten numerals recognition, that relies on the extraction of multiscale features to characterize the classes. These features are obtained by means of different continuous wavelet transforms, which behave as scale-dependent bandpass filters, and give information on local orientation of the strokes. First a shape-preserving, smooth and smaller version of the digit is extracted. Second, a complementary feature vector is constructed, that captures certain properties of the digits, such as orientation, gradients and curvature at different scales. The accuracy with which the selected features describe the original digits is assessed with a neural network classifier of the multilayer perceptron (MLP) type. The proposed method gives satisfactory results, regarding the dimensionality reduction as well as the recognition rates on the testing sets of CENPARMI and MNIST databases; the recognition rate being 92.60 % for the CENPARMI data-base and 98.22 % for the MNIST database.

Prediction of coefficients for lossless compression of multispectral images

We present a lossless compressor for multispectral Landsat images that exploits interband and intraband correlations. The compressor operates on blocks of 256 x 256 pixels, and performs two kinds of predictions. For bands 1, 2, 3, 4, 5, 6.2 and 7, the compressor performs an integer-to-integer wavelet transform, which is applied to each block separately. The wavelet coefficients that have not yet been encoded are predicted by means of a linear combination of already coded coefficients that belong to the same orientation and spatial location in the same band, and coefficients of the same location from other spectral bands. A fast block classification is performed in order to use the best weights for each landscape. The prediction errors or differences are finally coded with an entropy - based coder. For band 6.1, we do not use wavelet transforms, instead, a median edge detector is applied to predict a pixel, with the information of the neighbouring pixels and the equalized pixel from band 6.2. This technique exploits better the great similarity between histograms of bands 6.1 and 6.2. The prediction differences are finally coded with a context-based entropy coder. The two kinds of predictions used reduce both spatial and spectral correlations, increasing the compression rates. Our compressor has shown to be superior to the lossless compressors Winzip, LOCO-I, PNG and JPEG2000.

Lossless compression of hyperspectral images: Look-up tables with varying degrees of confidence

State-of-the-art algorithms LUT and LAIS-LUT, proposed for lossless compression of hyperspectral images, exploit high spectral correlations in these images, and use look-up tables to perform predictions. However, there are cases where their predictions are not accurate. In this work we also use look-up tables, but give these tables different degrees of confidence, based on the local variations of the scaling factor. Our results are highly satisfactory and outperform both LUT and LAIS-LUT methods.

Polyphase filter and polynomial reproduction conditions for the construction of smooth bidimensional multiwavelets

To construct a very smooth nonseparable multiscaling function, we impose polynomial approximation order 2 and add new conditions on the polyphase highpass filters. We work with a dilation matrix generating quincunx lattices, and fix the index set. Other imposed conditions are orthogonal filter bank and balancing. We construct a smooth, compactly supported multiscaling function and multiwavelet, and test the system on a noisy image with good results.

Dilation matrices for nonseparable bidimensional wavelets

For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all–important, since it governs the downsampling and upsampling steps, determines the cosets that give the positions of the filters, and defines the elementary set that gives a tesselation of the plane. We introduce nonseparable bidimensional wavelets, and give formulae for the analysis and synthesis of images. We analyze several dilation matrices, and show how the wavelet transform operates visually. We also show some distorsions produced by some of these matrices. We show that the requirement of their eigenvalues being greater than 1 in absolute value is not enough to guarantee their suitability for image processing applications, and discuss other conditions.