264 research outputs found
Centered Pyramids
Quadtree-like pyramids have the advantage of resulting in a multiresolution representation where each pyramid node has four unambiguous parents. Such a centered topology guarantees a clearly defined up-projection of labels. This concept has been successfully and extensively used in applications of contour detection, object recognition and segmentation. Unfortunately, the quadtree-like type of pyramid has poor approximation powers because of the employed piecewise-constant image model. This paper deals with the construction of improved centered image pyramids in terms of general approximation functions. The advantages of the centered topology such a symmetry, consistent boundary conditions and accurate up-projection of labels are combined with a more faithful image representation at coarser pyramid levels. We start by introducing a general framework for the design of least squares pyramids using the standard filtering and decimation tools. We give the most general explicit formulas for the computation of the filter coefficients by any (well behaving) approximation function in both the continuous and the discrete norm. We then define centered pyramids and provide the filter coefficients for odd spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications
The near shift-invariance of the dual-tree complex wavelet transform revisited
The dual-tree complex wavelet transform (DTCWT) is an enhancement of the
conventional discrete wavelet transform (DWT) due to a higher degree of
shift-invariance and a greater directional selectivity, finding its
applications in signal and image processing. This paper presents a quantitative
proof of the superiority of the DTCWT over the DWT in case of modulated
wavelets.Comment: 15 page
Framing pyramids
In 1983, Burt and Adelson introduced the Laplacian pyramid (LP) as a multiresolution representation for images. We study the LP using the frame theory, and this reveals that the usual reconstruction is suboptimal. We show that the LP with orthogonal filters is a tight frame, and thus, the optimal linear reconstruction using the dual frame operator has a simple structure that is sym- metric with the forward transform. In more general cases, we pro- pose an efficient filterbank (FB) for the reconstruction of the LP using projection that leads to a proved improvement over the usual method in the presence of noise. Setting up the LP as an oversam- pled FB, we offer a complete parameterization of all synthesis FBs that provide perfect reconstruction for the LP. Finally, we consider the situation where the LP scheme is iterated and derive the con- tinuous-domain frames associated with the LP
Directional multiresolution image representations
Efficient representation of visual information lies at the foundation of many image processing tasks, including compression, filtering, and feature extraction. Efficiency of a representation refers to the ability to capture significant information of an object of interest in a small description. For practical applications, this representation has to be realized by structured transforms and fast algorithms. Recently, it has become evident that commonly used separable transforms (such as wavelets) are not necessarily best suited for images. Thus, there is a strong motivation to search for more powerful schemes that can capture the intrinsic geometrical structure of pictorial information. This thesis focuses on the development of new "true" two-dimensional representations for images. The emphasis is on the discrete framework that can lead to algorithmic implementations. The first method constructs multiresolution, local and directional image expansions by using non-separable filter banks. This discrete transform is developed in connection with the continuous-space curvelet construction in harmonic analysis. As a result, the proposed transform provides an efficient representation for two-dimensional piecewise smooth signals that resemble images. The link between the developed filter banks and the continuous-space constructions is set up in a newly defined directional multiresolution analysis. The second method constructs a new family of block directional and orthonormal transforms based on the ridgelet idea, and thus offers an efficient representation for images that are smooth away from straight edges. Finally, directional multiresolution image representations are employed together with statistical modeling, leading to powerful texture models and successful image retrieval systems
A Novel Rate Control Algorithm for Onboard Predictive Coding of Multispectral and Hyperspectral Images
Predictive coding is attractive for compression onboard of spacecrafts thanks
to its low computational complexity, modest memory requirements and the ability
to accurately control quality on a pixel-by-pixel basis. Traditionally,
predictive compression focused on the lossless and near-lossless modes of
operation where the maximum error can be bounded but the rate of the compressed
image is variable. Rate control is considered a challenging problem for
predictive encoders due to the dependencies between quantization and prediction
in the feedback loop, and the lack of a signal representation that packs the
signal's energy into few coefficients. In this paper, we show that it is
possible to design a rate control scheme intended for onboard implementation.
In particular, we propose a general framework to select quantizers in each
spatial and spectral region of an image so as to achieve the desired target
rate while minimizing distortion. The rate control algorithm allows to achieve
lossy, near-lossless compression, and any in-between type of compression, e.g.,
lossy compression with a near-lossless constraint. While this framework is
independent of the specific predictor used, in order to show its performance,
in this paper we tailor it to the predictor adopted by the CCSDS-123 lossless
compression standard, obtaining an extension that allows to perform lossless,
near-lossless and lossy compression in a single package. We show that the rate
controller has excellent performance in terms of accuracy in the output rate,
rate-distortion characteristics and is extremely competitive with respect to
state-of-the-art transform coding
Scalable video compression
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1992.Includes bibliographical references (leaves 85-88).by Joseph Bruce Stampleman.M.S
Diffusion, methods and applications
Tesis doctoral inédita leída en la Universidad Autónoma de Madrid, Escuela Politécnica Superior, Departamento de Ingeniería Informática. Fecha de lectura: junio de 2014Big Data, an important problem nowadays, can be understood in terms of a very large number of
patterns, a very large pattern dimension or, often, both. In this thesis, we will concentrate on the
high dimensionality issue, applying manifold learning techniques for visualizing and analyzing
such patterns.
The core technique will be Di usion Maps (DM) and its Anisotropic Di usion (AD) version,
introduced by Ronald R. Coifman and his school at Yale University, and of which we will give
a complete, systematic, compact and self-contained treatment. This will be done after a brief
survey of previous manifold learning methods.
The algorithmic contributions of the thesis will be centered in two computational challenges of
di usion methods: the potential high cost of the similarity matrix eigenanalysis that is needed
to define the di usion embedding coordinates, and the di culty of computing this embedding
over new patterns not available for the initial eigenanalysis. With respect to the first issue, we
will show how the AD set up can be used to skip it when looking for local models. In this case,
local patterns will be selected through a k-Nearest Neighbors search using a properly defined
local Mahalanobis distance, that enables neighbors to be found over the latent variable space
underlying the AD model while we can work directly with the observable patterns and, thus,
avoiding the potentially costly similarity matrix eigenanalysis.
The second proposed algorithm, that we will call Auto-adaptative Laplacian Pyramids (ALP),
focuses in the out-of-sample embedding extension and consists in a modification of the classical
Laplacian Pyramids (LP) method. In this new algorithm the LP iterations will be combined with
an estimate of the Leave One Out CV error, something that makes possible to directly define
during training a criterion to estimate the optimal stopping point of this iterative algorithm.
This thesis will also present several application contributions to important problems in renewable
energy and medical imaging. More precisely, we will show how DM is a good method
for dimensionality reduction of meteorological weather predictions, providing tools to visualize
and describe these data, as well as to cluster them in order to define local models.
In turn, we will apply our AD-based localized search method first to find the location in the
human body of CT scan images and then to predict wind energy ramps on both individual farms
and over the whole of Spain. We will see that, in both cases, our results improve on the current
state of the art methods.
Finally, we will compare our ALP proposal with the well-known Nyström method as well as
with LP on two large dimensional problems, the time compression of meteorological data and
the analysis of meteorological variables relevant in daily radiation forecasts. In both cases we
will show that ALP compares favorably with the other approaches for out-of-sample extension
problemsBig Data es un problema importante hoy en día, que puede ser entendido en términos de un
amplio número de patrones, una alta dimensión o, como sucede normalmente, de ambos. Esta
tesis se va a centrar en problemas de alta dimensión, aplicando técnicas de aprendizaje de
subvariedades para visualizar y analizar dichos patrones.
La técnica central será Di usion Maps (DM) y su versión anisotrópica, Anisotropic Di usion
(AD), introducida por Ronald R. Coifman y su escuela en la Universidad de Yale, la cual va a
ser tratada de manera completa, sistemática, compacta y auto-contenida. Esto se llevará a cabo
tras un breve repaso de métodos previos de aprendizaje de subvariedades.
Las contribuciones algorítmicas de esta tesis estarán centradas en dos de los grandes retos en
métodos de difusión: el potencial alto coste que tiene el análisis de autovalores de la matriz de
similitud, necesaria para definir las coordenadas embebidas; y la dificultad para calcular este
mismo embedding sobre nuevos datos que no eran accesibles cuando se realizó el análisis de
autovalores inicial. Respecto al primer tema, se mostrará cómo la aproximación AD se puede
utilizar para evitar el cálculo del embedding cuando estamos interesados en definir modelos locales.
En este caso, se seleccionarán patrones cercanos por medio de una búsqueda de vecinos
próximos (k-NN), usando como distancia una medida de Mahalanobis local que permita encontrar
vecinos sobre las variables latentes existentes bajo el modelo de AD. Todo esto se llevará
a cabo trabajando directamente sobre los patrones observables y, por tanto, evitando el costoso
cálculo que supone el cálculo de autovalores de la matriz de similitud.
El segundo algoritmo propuesto, que llamaremos Auto-adaptative Laplacian Pyramids (ALP),
se centra en la extensión del embedding para datos fuera de la muestra, y se trata de una modificación
del método denominado Laplacian Pyramids (LP). En este nuevo algoritmo, las iteraciones
de LP se combinarán con una estimación del error de Leave One Out CV, permitiendo definir
directamente durante el periodo de entrenamiento, un criterio para estimar el criterio de parada
óptimo para este método iterativo.
En esta tesis se presentarán también una serie de contribuciones de aplicación de estas técnicas
a importantes problemas en energías renovables e imágenes médicas. Más concretamente, se
muestra como DM es un buen método para reducir la dimensión de predicciones del tiempo
meteorológico, sirviendo por tanto de herramienta de visualización y descripción, así como de
clasificación de los datos con vistas a definir modelos locales sobre cada grupo descrito.
Posteriormente, se aplicará nuestro método de búsqueda localizada basado en AD tanto a la
búsqueda de la correspondiente posición de tomografías en el cuerpo humano, como para la
detección de rampas de energía eólica en parques individuales o de manera global en España.
En ambos casos se verá como los resultados obtenidos mejoran los métodos del estado del arte
actual.
Finalmente se comparará el algoritmo de ALP propuesto frente al conocido método de Nyström
y al método de LP, en dos problemas de alta dimensión: el problema de compresión temporal
de datos meteorológicos y el análisis de variables meteorológicas relevantes para la predicción
de la radiación diaria. En ambos casos se mostrará cómo ALP es comparativamente mejor que
otras aproximaciones existentes para resolver el problema de extensión del embedding a puntos
fuera de la muestr
Speckle Noise Reduction in Medical Ultrasound Images
Ultrasound imaging is an incontestable vital tool for diagnosis, it provides
in non-invasive manner the internal structure of the body to detect eventually
diseases or abnormalities tissues. Unfortunately, the presence of speckle noise
in these images affects edges and fine details which limit the contrast
resolution and make diagnostic more difficult. In this paper, we propose a
denoising approach which combines logarithmic transformation and a non linear
diffusion tensor. Since speckle noise is multiplicative and nonwhite process,
the logarithmic transformation is a reasonable choice to convert
signaldependent or pure multiplicative noise to an additive one. The key idea
from using diffusion tensor is to adapt the flow diffusion towards the local
orientation by applying anisotropic diffusion along the coherent structure
direction of interesting features in the image. To illustrate the effective
performance of our algorithm, we present some experimental results on
synthetically and real echographic images
Distortion-constraint compression of three-dimensional CLSM images using image pyramid and vector quantization
The confocal microscopy imaging techniques, which allow optical sectioning, have
been successfully exploited in biomedical studies. Biomedical scientists can benefit
from more realistic visualization and much more accurate diagnosis by processing and
analysing on a three-dimensional image data. The lack of efficient image compression
standards makes such large volumetric image data slow to transfer over limited
bandwidth networks. It also imposes large storage space requirements and high cost in
archiving and maintenance.
Conventional two-dimensional image coders do not take into account inter-frame
correlations in three-dimensional image data. The standard multi-frame coders, like
video coders, although they have good performance in capturing motion information,
are not efficiently designed for coding multiple frames representing a stack of optical
planes of a real object. Therefore a real three-dimensional image compression
approach should be investigated.
Moreover the reconstructed image quality is a very important concern in compressing
medical images, because it could be directly related to the diagnosis accuracy. Most of
the state-of-the-arts methods are based on transform coding, for instance JPEG is based on discrete-cosine-transform CDCT) and JPEG2000 is based on discrete-
wavelet-transform (DWT). However in DCT and DWT methods, the control
of the reconstructed image quality is inconvenient, involving considerable costs in
computation, since they are fundamentally rate-parameterized methods rather than
distortion-parameterized methods. Therefore it is very desirable to develop a
transform-based distortion-parameterized compression method, which is expected to
have high coding performance and also able to conveniently and accurately control
the final distortion according to the user specified quality requirement.
This thesis describes our work in developing a distortion-constraint three-dimensional
image compression approach, using vector quantization techniques combined with
image pyramid structures. We are expecting our method to have:
1. High coding performance in compressing three-dimensional microscopic
image data, compared to the state-of-the-art three-dimensional image coders
and other standardized two-dimensional image coders and video coders.
2. Distortion-control capability, which is a very desirable feature in medical 2. Distortion-control capability, which is a very desirable feature in medical
image compression applications, is superior to the rate-parameterized methods
in achieving a user specified quality requirement.
The result is a three-dimensional image compression method, which has outstanding
compression performance, measured objectively, for volumetric microscopic images.
The distortion-constraint feature, by which users can expect to achieve a target image
quality rather than the compressed file size, offers more flexible control of the
reconstructed image quality than its rate-constraint counterparts in medical image
applications. Additionally, it effectively reduces the artifacts presented in other
approaches at low bit rates and also attenuates noise in the pre-compressed images.
Furthermore, its advantages in progressive transmission and fast decoding make it
suitable for bandwidth limited tele-communications and web-based image browsing
applications
Directional edge and texture representations for image processing
An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations
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