nils-herrmann/clean_scirepeval huggingface dataset:
Scale Space Analysis and Active Contours for Omnidirectional Images

A new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras, namely catadioptric cameras, is slowly emerging. These omnidirectional images will most probably deeply impact computer vision in the forthcoming years, provided that the necessary algorithmic background stands strong. In this paper, we propose a general framework that helps define various computer vision primitives. We show that geometry, which plays a central role in the formation of omnidirectional images, must be carefully taken into account while performing such simple tasks as smoothing or edge detection. Partial differential equations (PDEs) offer a very versatile tool that is well suited to cope with geometrical constraints. We derive new energy functionals and PDEs for segmenting images obtained from catadioptric cameras and show that they can be implemented robustly using classical finite difference schemes. Various experimental results illustrate the potential of these new methods on both synthetic and natural images.
Adaptive Regularization With the Structure Tensor

Natural images exhibit geometric structures that are informative of the properties of the underlying scene. Modern image processing algorithms respect such characteristics by employing regularizers that capture the statistics of natural images. For instance, total variation (TV) respects the highly kurtotic distribution of the pointwise gradient by allowing for large magnitude outlayers. However, the gradient magnitude alone does not capture the directionality and scale of local structures in natural images. The structure tensor provides a more meaningful description of gradient information as it describes both the size and orientation of the image gradients in a neighborhood of each point. Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor. Our method alternates two minimization steps: 1) robust estimation of the structure tensor as a semidefinite program and 2) reconstruction of the image with an adaptive regularizer defined from this tensor. This two-step procedure allows us to extend anisotropic diffusion into the convex setting and develop robust, efficient, and easy-to-code algorithms for image denoising, deblurring, and compressed sensing. Our method extends naturally to nonlocal regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV and diffusion operators. Our experiments show a consistent accuracy improvement over classic regularization.
Geodesic Active Fields—A Geometric Framework for Image Registration

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.
Song recommendation with non-negative matrix factorization and graph total variation

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.
Image Segmentation Model using Active Contour and Image Decomposition

This paper proposes an image segmentation model based on the active contour model, the Mumford-Shah functional and the image decomposition process. Generally speaking, the active contour model detects boundaries in images from sharp intensities variations and the Mumford-Shah model finds smooth regions from homogeneous intensities. Our model merges these two complementary approaches while considering the Four Color Theorem to globally partition any given image. We also consider the textural part lying in natural images by separating it from the geometric part, which contains the meaningful objects, to help the segmentation process. Our segmentation model is experimented with a 1-D signal and 2-D images.
Harmonic active contours for multichannel image segmentation

We propose a segmentation method based on the geometric representation of images as surfaces embedded in a higher dimensional space, handling naturally multichannel images. The segmentation is based on an active contour embedded in the image manifold, along with a set of image features. Hence, both data-fidelity and regularity terms of the active contour are jointly optimized minimizing a single Polaykov energy representing the hyper-surface of this manifold. Compared to previous methods, our approach is purely geometrical and does not require additional weighting of the energy functional to drive the segmentation to the image contours. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, validating the proposed technique for scale-space methods, volumetric data or catadioptric images. We present here the segmentation technique called Harmonic Active Contours, give an implementation for multichannel images including gradient and region-based segmentation criteria and apply it to color images.
Functional correspondence by matrix completion

In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold geometric structure and inducing functional localization with the L1 norm. We discuss efficient numerical procedures for the solution of our problem. Our method compares favorably to the accuracy of state-of-the-art correspondence algorithms on non-rigid shape matching benchmarks, and is especially advantageous in settings when only scarce data is available.
Enhanced Compressed Sensing Recovery With Level Set Normals

We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal vectors of the image level curves, and 2) reconstruction of an image fitting the normal vectors, the compressed sensing measurements, and the sparsity constraint. The proposed technique can naturally extend to nonlocal operators and graphs to exploit the repetitive nature of textured images to recover fine detail structures. In both cases, the problem is reduced to a series of convex minimization problems that can be efficiently solved with a combination of variable splitting and augmented Lagrangian methods, leading to fast and easy-to-code algorithms. Extended experiments show a clear improvement over related state-of-the-art algorithms in the quality of the reconstructed images and the robustness of the proposed method to noise, different kind of images, and reduced measurements.
Nonlocal Mumford-Shah Regularizers for Color Image Restoration

We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.
Fast texture segmentation model based on the shape operator and active contour

We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape operator borrowed from differential geometry. Then, we use the popular Kullback-Leibler distance to define an active contour model which distinguishes the background and textural objects of interest represented by the probability density functions of our new texture descriptor. We prove the existence of a solution to the proposed segmentation model. Finally, a fast and easy to implement texture segmentation algorithm is introduced to extract meaningful objects. We present promising synthetic and real-world results and compare our algorithm to other state-of-the-art techniques.
Source localization on graphs via ℓ1 recovery and spectral graph theory

We cast the problem of source localization on graphs as the simultaneous problem of sparse recovery and diffusion kernel learning. An ℓ1 regularization term enforces the sparsity constraint while we recover the sources of diffusion from a single snapshot of the diffusion process. The diffusion kernel is estimated by assuming the process to be as generic as the standard heat diffusion. We show with synthetic data that we can concomitantly learn the diffusion kernel and the sources, given an estimated initialization. We validate our model with cholera mortality and atmospheric tracer diffusion data, showing also that the accuracy of the solution depends on the construction of the graph from the data points.
Active Contours Based on Chambolle's Mean Curvature Motion

This paper proposes an algorithm to solve most of existing active contour problems based on the approach of mean curvature motion proposed by Chambolle (2004) and the image denoising model of Rudin, Osher and Fatemi (ROF) (1992). More precisely, the motion of active contours is discretized by the ROF model applied to the signed distance of the evolving contour. The advantage of this new discretization scheme is to use a time step much larger than in standard explicit schemes, which means that less iterations are needed to converge to the steady state solution. We present results on 2-D natural images.
Enhanced lasso recovery on graph

This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on graphs. More precisely, we present a non-convex, non-smooth algorithm that outperforms the standard convex Lasso technique. We carry out numerical experiments on three benchmark graph datasets.
Representing Diffusion MRI in 5-D Simplifies Regularization and Segmentation of White Matter Tracts

We present a new five-dimensional (5-D) space representation of diffusion magnetic resonance imaging (dMRI) of high angular resolution. This 5-D space is basically a non-Euclidean space of position and orientation in which crossing fiber tracts can be clearly disentangled, that cannot be separated in three-dimensional position space. This new representation provides many possibilities for processing and analysis since classical methods for scalar images can be extended to higher dimensions even if the spaces are not Euclidean. In this paper, we show examples of how regularization and segmentation of dMRI is simplified with this new representation. The regularization is used with the purpose of denoising and but also to facilitate the segmentation task by using several scales, each scale representing a different level of resolution. We implement in five dimensions the Chan-Vese method combined with active contours without edges for the segmentation and the total variation functional for the regularization. The purpose of this paper is to explore the possibility of segmenting white matter structures directly as entirely separated bundles in this 5-D space. We will present results from a synthetic model and results on real data of a human brain acquired with diffusion spectrum magnetic resonance imaging (MRI), one of the dMRI of high angular resolution available. These results will lead us to the conclusion that this new high-dimensional representation indeed simplifies the problem of segmentation and regularization.
Region level segmentation based on a derivative approach for video tracking process

In this paper a new video tracking process is proposed. Our approach uses two description levels for the segmentation mechanism. The first one, the pixel level, performs the extraction of every point in movement, forming, as result, connected regions. For this stage, a new adaptive reference image (ARI) algorithm is described, based on a derivative approach. This choice presents a robust method facing changes in illumination. The second level, the region level, is driven by the contents of a model set. This high level object description, defined by geometric attributes and a motion model lets us associate the ARI process with the handle objects. This stage sets this up as a Bayesian model formulation. The identification and updating process is done by a modified expectation-maximization (EM) algorithm. This step establishes the relationship between regions (the ARI process output) and the object models (OM). For each correspondence, the EM procedure is started, updating every attribute of the object description. This framework defines a complete unsupervised tracking procedure, robust regarding occlusions, over- or sub-segmentations and background brightness variations. Several real traffic examples are included at the end of the paper.
Classification of hyperspectral data with ensemble of subspace ICA and edge-preserving filtering

Conventional feature extraction methods cannot fully exploit both the spectral and spatial information of hyperspectral imagery. In this paper, we propose an ensemble method of subspace independent component analysis (ICA) and edge-preserving filtering (EPF) for the classification of hyper-spectral data to achieve this task. First, several subsets are randomly selected from the original feature space. Second, ICA is used to extract spectral independent components followed by a recent and effective EPF method, rolling guidance filter (RGF), to produce spatial features. The spatial features are treated as the input of a random forest (RF) classifier. Finally, the classification results from each subset are integrated together to produce the final map. Experimental results on real hyperspectral data demonstrate the effectiveness of the proposed method. A sensitivity analysis of this new classifier is also performed.
2-D Wavelet Packet Spectrum for Texture Analysis

This brief derives a 2-D spectrum estimator from some recent results on the statistical properties of wavelet packet coefficients of random processes. It provides an analysis of the bias of this estimator with respect to the wavelet order. This brief also discusses the performance of this wavelet-based estimator, in comparison with the conventional 2-D Fourier-based spectrum estimator on texture analysis and content-based image retrieval. It highlights the effectiveness of the wavelet-based spectrum estimation.
Target radial velocity estimation robust against additive disturbances for ISAR application

In radar processing, inverse synthetic aperture radar (ISAR) takes advantage of the target rotational motion to provide a 2-D image of the target. The “quality” of this image must be sufficient to be used for target recognition. However, among the main problems to be addressed, the translation motion which is another component of the target motion must be foremost compensated. If this is not the case, a blurred image is obtained. In this paper, we propose a new approach for translation-motion compensation based on the target radial velocity estimation. This method consists in characterizing the radar echoes by several features (mean and wavelet coefficients for instance) and in storing them in sequences which represent the parameter evolution over time. Spectrum analysis methods are then used to get Doppler frequency estimates. To make the estimation robust against additive noise and sea clutter, several estimates are combined to deduce the target radial velocity estimation. Tests on experimental data confirm the validity of the approach.
Recursive Texture Orientation Estimation Based on Space Transformation and Hypersurface Reconstruction

The most common scheme for estimating the orientation field of space-varying directional textures is based on a local nonlinear spatial averaging of the gradient field. This leads to locally biased orientations, especially in regions of nonlinearly distributed convergence, asymmetrically distributed curvature, or geometry superposition. In this paper, we propose an orientation estimation framework that is invariant toward the local geometry. Instead of applying the spatial averaging in the initial space, it is performed in a flattened space which is obtained from a parametric space transformation model deduced from the reconstruction of local hypersurfaces. The flattening can either be applied to the initial gradient field or to the intensity image, on which the flattened gradient field is computed. The process is iterated in order to define more accurate space transformations leading to refined orientation estimation. The computational efficiency is improved without noticeable loss of orientation accuracy by a patch-based approach. Experiments, both on synthetic as well as real-life fingerprint and fibrous material images, exhibit enhanced performance in comparison with conventional methods such as the structure tensor method.
A geometric learning approach on the space of complex covariance matrices

Many signal and image processing applications, including SAR polarimetry and texture analysis, require the classification of complex covariance matrices. The present paper introduces a geometric learning approach on the space of complex covariance matrices based on a new distribution called Riemannian Gaussian distribution. The proposed distribution has two parameters, the centre of mass Ȳ and the dispersion parameter σ. After having derived its maximum likelihood estimator and its extension to mixture models, we propose an application to texture recognition on the VisTex database.
ECG Beat Detection Using a Geometrical Matching Approach

In the framework of the electrocardiography (ECG) signals, this paper describes an original approach to identify heartbeat morphologies and to detect R-wave events. The proposed approach is based on a "geometrical matching" rule evaluated using a decision function in a local moving-window procedure. The decision function is a normalized measurement of a similarity criterion comparing the windowed input signal with the reference beat-pattern into a nonlinear-curve space. A polynomial expansion model describes the reference pattern. For the curve space, an algebraic-fitting distance is built according to the canonical equation of the unit circle. The geometrical matching approach operates in two stages, i.e., training and detection ones. In the first stage, a learning-method based on genetic algorithms allows us estimating the decision function from training beat-pattern. In the second stage, a level-detection algorithm evaluates the decision function to establish the threshold of similarity between the reference pattern and the input signal. Finally, the findings for the MIT-BIH Arrhythmia Database present about 98% of sensitivity and 99% of positive predictivity for the R-waves detection, using low-order polynomial models