25 research outputs found
State of the art in 2D content representation and compression
Livrable D1.3 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D3.1 du projet
Adapted generalized lifting schemes for scalable lossless image coding
International audienceStill image coding occasionally uses linear predictive coding together with multi-resolution decompositions, as may be found in several papers. Those related approaches do not take into account all the information available at the decoder in the prediction stage. In this paper, we introduce an adapted generalized lifting scheme in which the predictor is built upon two filters, leading to taking advantage of all this available information. With this structure included in a multi-resolution decomposition framework, we study two kinds of adaptation based on least squares estimation, according to different assumptions, which are either a global or a local second order stationarity of the image. The efficiency in lossless coding of these decompositions is shown on synthetic images and their performances are compared with those of well-known codecs (S+P, JPEG-LS, JPEG2000, CALIC) on actual images. Four images' families are distinguished: natural, MRI medical, satellite and textures associated with fingerprints. On natural and medical images, the performances of our codecs do not exceed those of classical codecs. Now for satellite images and textures, they present a slightly noticeable (about 0.05 to 0.08 bpp) coding gain compared to the others that permit a progressive coding in resolution, but with a greater coding time
Adaptive polyphase subband decomposition structures for image compression
Cataloged from PDF version of article.Subband decomposition techniques have been extensively used for data coding and analysis. In most filter
banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented
Multidimensional Wavelets and Computer Vision
This report deals with the construction and the mathematical analysis of multidimensional nonseparable wavelets and their efficient application in computer vision. In the first part, the fundamental principles and ideas of multidimensional wavelet filter design such as the question for the existence of good scaling matrices and sensible design criteria are presented and extended in various directions. Afterwards, the analytical properties of these wavelets are investigated in some detail. It will turn out that they are especially well-suited to represent (discretized) data as well as large classes of operators in a sparse form - a property that directly yields efficient numerical algorithms. The final part of this work is dedicated to the application of the developed methods to the typical computer vision problems of nonlinear image regularization and the computation of optical flow in image sequences. It is demonstrated how the wavelet framework leads to stable and reliable results for these problems of generally ill-posed nature. Furthermore, all the algorithms are of order O(n) leading to fast processing
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Adaptive lifting schemes with a global L1 minimization technique for image coding
International audienceMany existing works related to lossy-to-lossless image compression are based on the lifting concept. In this paper, we present a sparse op- timization technique based on recent convex algorithms and applied to the prediction filters of a two-dimensional non separable lifting structure. The idea consists of designing these filters, at each resolution level, by minimizing the sum of the â„“1-norm of the three detail subbands. Extending this optimization method in order to perform a global minimization over all resolution levels leads to a new opti- mization criterion taking into account linear dependencies between the generated coefficients. Simulations carried out on still images show the benefits which can be drawn from the proposed optimization techniques
Wavelet Theory
The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior
Riesz-Quincunx-UNet Variational Auto-Encoder for Satellite Image Denoising
Multiresolution deep learning approaches, such as the U-Net architecture,
have achieved high performance in classifying and segmenting images. However,
these approaches do not provide a latent image representation and cannot be
used to decompose, denoise, and reconstruct image data. The U-Net and other
convolutional neural network (CNNs) architectures commonly use pooling to
enlarge the receptive field, which usually results in irreversible information
loss. This study proposes to include a Riesz-Quincunx (RQ) wavelet transform,
which combines 1) higher-order Riesz wavelet transform and 2) orthogonal
Quincunx wavelets (which have both been used to reduce blur in medical images)
inside the U-net architecture, to reduce noise in satellite images and their
time-series. In the transformed feature space, we propose a variational
approach to understand how random perturbations of the features affect the
image to further reduce noise. Combining both approaches, we introduce a hybrid
RQUNet-VAE scheme for image and time series decomposition used to reduce noise
in satellite imagery. We present qualitative and quantitative experimental
results that demonstrate that our proposed RQUNet-VAE was more effective at
reducing noise in satellite imagery compared to other state-of-the-art methods.
We also apply our scheme to several applications for multi-band satellite
images, including: image denoising, image and time-series decomposition by
diffusion and image segmentation.Comment: Submitted to IEEE Transactions on Geoscience and Remote Sensing
(TGRS
Perfect Reconstruction Two-Channel Wavelet Filter-Banks for Graph Structured Data
In this work we propose the construction of two-channel wavelet filterbanks
for analyzing functions defined on the vertices of any arbitrary finite
weighted undirected graph. These graph based functions are referred to as
graph-signals as we build a framework in which many concepts from the classical
signal processing domain, such as Fourier decomposition, signal filtering and
downsampling can be extended to graph domain. Especially, we observe a spectral
folding phenomenon in bipartite graphs which occurs during downsampling of
these graphs and produces aliasing in graph signals. This property of bipartite
graphs, allows us to design critically sampled two-channel filterbanks, and we
propose quadrature mirror filters (referred to as graph-QMF) for bipartite
graph which cancel aliasing and lead to perfect reconstruction. For arbitrary
graphs we present a bipartite subgraph decomposition which produces an
edge-disjoint collection of bipartite subgraphs. Graph-QMFs are then
constructed on each bipartite subgraph leading to "multi-dimensional" separable
wavelet filterbanks on graphs. Our proposed filterbanks are critically sampled
and we state necessary and sufficient conditions for orthogonality, aliasing
cancellation and perfect reconstruction. The filterbanks are realized by
Chebychev polynomial approximations.Comment: 32 pages double spaced 12 Figures, to appear in IEEE Transactions of
Signal Processin