16 research outputs found

    A New Affine Invariant Image Transform Based on Ridgelets

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    Quadtree Structured Approximation Algorithms

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    The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Many sparse promoting transforms exist, including wavelets, the so called ‘lets’ family of transforms and more recent non-local learned transforms. The first part of this thesis reviews sparse approximation theory, particularly in relation to 2-D piecewise polynomial signals. We also show the connection between this theory and current state of the art algorithms that cover the following image restoration and enhancement applications: denoising, deconvolution, interpolation and multi-view super resolution. In [63], Shukla et al. proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewise polynomial images. In the second part of this thesis we adapt this model to image restoration by changing the rate-distortion penalty to a description-length penalty. Moreover, one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree. We address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations. Novel algorithms are developed to tackle the four problems previously mentioned. Simulation results indicate that we beat state of the art results when the original signal is in the model (e.g. depth images) and are competitive for natural images when the degradation is high.Open Acces

    Quadrature Radon Transform for Smoother Tomographic Reconstruction

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    Tomographic reconstruction using Radon projections taken at an angle introduce a redundancy of four. Hence the projection in one quadrant are used for tomographic reconstruction to reduce computational overheads. In this paper, we present that the though the projections at an angle do not introduce any redundancy, the achieved tomographic reconstruction is very poor. A qudrature Radon transform is further introduced as a combination of Radon transforms at projection angles. The individual back projections are computed in two parts separately; 1) considering them real and imaginary parts of a complex number 2) considering average of the individual back projections. It is observed that the quadrature Radon transform yields better results numerically and/or visually compared to conventional Radon transform. Keywords: Single quadrant Radon transform, quadrature Radon transform, Magnitude of complex projection, average, reconstruction

    Directional edge and texture representations for image processing

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    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

    A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

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    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

    Pattern detection and recognition using over-complete and sparse representations

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    Recent research in harmonic analysis and mammalian vision systems has revealed that over-complete and sparse representations play an important role in visual information processing. The research on applying such representations to pattern recognition and detection problems has become an interesting field of study. The main contribution of this thesis is to propose two feature extraction strategies - the global strategy and the local strategy - to make use of these representations. In the global strategy, over-complete and sparse transformations are applied to the input pattern as a whole and features are extracted in the transformed domain. This strategy has been applied to the problems of rotation invariant texture classification and script identification, using the Ridgelet transform. Experimental results have shown that better performance has been achieved when compared with Gabor multi-channel filtering method and Wavelet based methods. The local strategy is divided into two stages. The first one is to analyze the local over-complete and sparse structure, where the input 2-D patterns are divided into patches and the local over-complete and sparse structure is learned from these patches using sparse approximation techniques. The second stage concerns the application of the local over-complete and sparse structure. For an object detection problem, we propose a sparsity testing technique, where a local over-complete and sparse structure is built to give sparse representations to the text patterns and non-sparse representations to other patterns. Object detection is achieved by identifying patterns that can be sparsely represented by the learned. structure. This technique has been applied. to detect texts in scene images with a recall rate of 75.23% (about 6% improvement compared with other works) and a precision rate of 67.64% (about 12% improvement). For applications like character or shape recognition, the learned over-complete and sparse structure is combined. with a Convolutional Neural Network (CNN). A second text detection method is proposed based on such a combination to further improve (about 11% higher compared with our first method based on sparsity testing) the accuracy of text detection in scene images. Finally, this method has been applied to handwritten Farsi numeral recognition, which has obtained a 99.22% recognition rate on the CENPARMI Database and a 99.5% recognition rate on the HODA Database. Meanwhile, a SVM with gradient features achieves recognition rates of 98.98% and 99.22% on these databases respectivel

    New method to find corner and tangent vertices in sketches using parametric cubic curves approximation

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    Some recent approaches have been presented as simple and highly accurate corner finders in the sketches including curves, which is useful to support natural human-computer interaction, but these in most cases do not consider tangent vertices (smooth points between two geometric entities, present in engineering models), what implies an important drawback in the field of design. In this article we present a robust approach based on the approximation to parametric cubic curves of the stroke for further radius function calculation in order to detect corner and tangent vertices. We have called our approach Tangent and Corner Vertices Detection (TCVD), and it works in the following way. First, corner vertices are obtained as minimum radius peaks in the discrete radius function, where radius is obtained from differences. Second, approximated piecewise parametric curves on the stroke are obtained and the analytic radius function is calculated. Then, curves are obtained from stretches of the stroke that have a small radius. Finally, the tangent vertices are found between straight lines and curves or between curves, where no corner vertices are previously located. The radius function to obtain curves is calculated from approximated piecewise curves, which is much more noise free than discrete radius calculation. Several tests have been carried out to compare our approach to that of the current best benchmarked, and the obtained results show that our approach achieves a significant accuracy even better finding corner vertices, and moreover, tangent vertices are detected with an Accuracy near to 92% and a False Positive Rate near to 2%.Spanish Ministry of Science and Education and the FEDER Funds, through CUESKETCH (Ref. DPI2007-66755-C02-01) and HYMAS projects (Ref. DPI2010-19457) partially supported this work.Albert Gil, FE.; García Fernández-Pacheco, D.; Aleixos Borrás, MN. (2013). New method to find corner and tangent vertices in sketches using parametric cubic curves approximation. Pattern Recognition. 46(5):1433-1448. https://doi.org/10.1016/j.patcog.2012.11.006S1433144846

    Multiresolution image models and estimation techniques

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    The SURE-LET approach to image denoising

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    Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by photosensors, one usually distinguish between two main regimes: in the first scenario, the measured intensities are sufficiently high and the noise is assumed to be signal-independent. In the second scenario, only few photons are detected, which leads to a strong signal-dependent degradation. When the noise is considered as signal-independent, it is often modeled as an additive independent (typically Gaussian) random variable, whereas, otherwise, the measurements are commonly assumed to follow independent Poisson laws, whose underlying intensities are the unknown noise-free measures. We first consider the reduction of additive white Gaussian noise (AWGN). Contrary to most existing denoising algorithms, our approach does not require an explicit prior statistical modeling of the unknown data. Our driving principle is the minimization of a purely data-adaptive unbiased estimate of the mean-squared error (MSE) between the processed and the noise-free data. In the AWGN case, such a MSE estimate was first proposed by Stein, and is known as "Stein's unbiased risk estimate" (SURE). We further develop the original SURE theory and propose a general methodology for fast and efficient multidimensional image denoising, which we call the SURE-LET approach. While SURE allows the quantitative monitoring of the denoising quality, the flexibility and the low computational complexity of our approach are ensured by a linear parameterization of the denoising process, expressed as a linear expansion of thresholds (LET).We propose several pointwise, multivariate, and multichannel thresholding functions applied to arbitrary (in particular, redundant) linear transformations of the input data, with a special focus on multiscale signal representations. We then transpose the SURE-LET approach to the estimation of Poisson intensities degraded by AWGN. The signal-dependent specificity of the Poisson statistics leads to the derivation of a new unbiased MSE estimate that we call "Poisson's unbiased risk estimate" (PURE) and requires more adaptive transform-domain thresholding rules. In a general PURE-LET framework, we first devise a fast interscale thresholding method restricted to the use of the (unnormalized) Haar wavelet transform. We then lift this restriction and show how the PURE-LET strategy can be used to design and optimize a wide class of nonlinear processing applied in an arbitrary (in particular, redundant) transform domain. We finally apply some of the proposed denoising algorithms to real multidimensional fluorescence microscopy images. Such in vivo imaging modality often operates under low-illumination conditions and short exposure time; consequently, the random fluctuations of the measured fluorophore radiations are well described by a Poisson process degraded (or not) by AWGN. We validate experimentally this statistical measurement model, and we assess the performance of the PURE-LET algorithms in comparison with some state-of-the-art denoising methods. Our solution turns out to be very competitive both qualitatively and computationally, allowing for a fast and efficient denoising of the huge volumes of data that are nowadays routinely produced in biomedical imaging
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