nils-herrmann/clean_scirepeval huggingface dataset:
Fast image and video denoising via nonlocal means of similar neighborhoods

In this letter, improvements to the nonlocal means image denoising method introduced by Buades et al. are presented. The original nonlocal means method replaces a noisy pixel by the weighted average of pixels with related surrounding neighborhoods. While producing state-of-the-art denoising results, this method is computationally impractical. In order to accelerate the algorithm, we introduce filters that eliminate unrelated neighborhoods from the weighted average. These filters are based on local average gray values and gradients, preclassifying neighborhoods and thereby reducing the original quadratic complexity to a linear one and reducing the influence of less-related areas in the denoising of a given pixel. We present the underlying framework and experimental results for gray level and color images as well as for video.
Shape preserving local histogram modification

A novel approach for shape preserving contrast enhancement is presented in this paper. Contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level-sets of the image. This basic property is violated by common local schemes, thereby introducing spurious objects and modifying the image information. The scheme is based on equalizing the histogram in all the connected components of the image, which are defined based both on the grey-values and spatial relations between pixels in the image, and following mathematical morphology, constitute the basic objects in the scene. We give examples for both grey-value and color images.
Histogram modification via partial differential equations

An algorithm for histogram modification via image evolution equations is presented. We show that the image histogram can be modified to achieve any given distribution as the steady state solution of this partial differential equation. We then prove that this equation corresponds to a gradient descent flow of a variational problem. That is, the proposed PDE is solving an energy minimization problem. This gives a new interpretation to histogram modification and contrast enhancement in general. This interpretation is completely formulated in the image domain, in contrast with classical techniques for histogram modification which are formulated in a probabilistic domain. From this, new algorithms for contrast enhancement, which include for example image modeling, can be derived. Based on the energy formulation and its corresponding PDE, we show that the proposed histogram modification algorithm can be combined with denoising schemes. This allows one to perform simultaneous contrast enhancement and denoising, avoiding common noise sharpening effects in classical algorithms. The approach is extended to focal contrast enhancement as well. Theoretical results regarding the existence of solutions to the proposed equations are presented.
Semiautomatic Segmentation of Brain Subcortical Structures From High-Field MRI

Volumetric segmentation of subcortical structures, such as the basal ganglia and thalamus, is necessary for noninvasive diagnosis and neurosurgery planning. This is a challenging problem due in part to limited boundary information between structures, similar intensity profiles across the different structures, and low contrast data. This paper presents a semiautomatic segmentation system exploiting the superior image quality of ultrahigh field (7 T) MRI. The proposed approach utilizes the complementary edge information in the multiple structural MRI modalities. It combines optimally selected two modalities from susceptibility-weighted, T2-weighted, and diffusion MRI, and introduces a tailored new edge indicator function. In addition to this, we employ prior shape and configuration knowledge of the subcortical structures in order to guide the evolution of geometric active surfaces. Neighboring structures are segmented iteratively, constraining oversegmentation at their borders with a nonoverlapping penalty. Several experiments with data acquired on a 7 T MRI scanner demonstrate the feasibility and power of the approach for the segmentation of basal ganglia components critical for neurosurgery applications such as deep brain stimulation surgery.
Vector median filters, morphology, and PDE's: theoretical connections

We formally connect between vector median filters, morphological operators, and geometric partial differential equations. Considering a lexicographic order, which permits us to define an order between vectors in IR/sup N/, we first show that the vector median filter of a vector valued image is equivalent to a collection of infimum-supremum morphological operations. We then proceed and study the asymptotic behavior of this filter. We also provide an interpretation of the infinitesimal iteration of this vectorial median filter in terms of systems of coupled geometric partial differential equations. The main component of the vector evolves according to curvature motion, while, intuitively, the others regularly deform their level sets toward those of this main component. These results extend to the vector case classical connections between scalar median filters, mathematical morphology, and mean curvature motion.
Learning to Sense Sparse Signals: Simultaneous Sensing Matrix and Sparsifying Dictionary Optimization

Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets.
Importance Sampling Spherical Harmonics to Improve Probabilistic Tractography

We consider the problem of improving the accuracy and reliability of probabilistic white matter tractography methods by improving the built-in sampling scheme, which randomly draws, from a diffusion model such as the orientation distribution function (ODF), a direction of propagation. Existing methods employing inverse transform sampling require an ad hoc thresholding step to prevent the less likely directions from being sampled. We herein propose to perform importance sampling of spherical harmonics, which redistributes an input point set on the sphere to match the ODF using hierarchical sample warping. This produces a point set that is more concentrated around the modes, allowing the subsequent inverse transform sampling to generate orientations that are in better accordance with the local fiber configuration. Integrated into a Kalman filter-based framework, our approach is evaluated through experiments on synthetic, phantom, and real datasets.
Color histogram equalization through mesh deformation

In this paper we propose an extension of grayscale histogram equalization for color images. For aesthetic reasons, previously proposed color histogram equalization techniques do not generate uniform color histograms. Our method will always generate an almost uniform color histogram thus making an optimal use of the color space. This is particularly interesting for pseudo-color scientific visualization. The method is based on deforming a mesh in color space to fit the existing histogram and then map it to a uniform histogram. It is a natural extension of grayscale histogram equalization and it can be applied to spatial and color space of any dimension.
Task-Driven Adaptive Statistical Compressive Sensing of Gaussian Mixture Models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity.
Compressive Sensing by Learning a Gaussian Mixture Model From Measurements

Compressive sensing of signals drawn from a Gaussian mixture model (GMM) admits closed-form minimum mean squared error reconstruction from incomplete linear measurements. An accurate GMM signal model is usually not available a priori, because it is difficult to obtain training signals that match the statistics of the signals being sensed. We propose to solve that problem by learning the signal model in situ, based directly on the compressive measurements of the signals, without resorting to other signals to train a model. A key feature of our method is that the signals being sensed are treated as random variables and are integrated out in the likelihood. We derive a maximum marginal likelihood estimator (MMLE) that maximizes the likelihood of the GMM of the underlying signals given only their linear compressive measurements. We extend the MMLE to a GMM with dominantly low-rank covariance matrices, to gain computational speedup. We report extensive experimental results on image inpainting, compressive sensing of high-speed video, and compressive hyperspectral imaging (the latter two based on real compressive cameras). The results demonstrate that the proposed methods outperform state-of-the-art methods by significant margins.
Affine invariant medial axis and skew symmetry

Affine invariant medial axes and symmetry sets of planar shapes are introduced and studied in this paper. Two different approaches are presented. The first one is based on affine invariant distances, and defines the symmetry set, a set containing the medial axis; as the closure of the locus of points on (at least) two affine normals an affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) three-point contact with two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set (medial axis) are equivalent, this is not the case for the affine group. We then show how to use the symmetry set to detect affine skew symmetry, proving that the contact based symmetry set is a straight line if and only if the given shape is the affine transformation of a symmetric object.
Texture Synthesis for 3D Shape Representation

Considerable evidence suggests that a viewer's perception of the 3D shape of a polygonally-defined object can be significantly affected (either masked or enhanced) by the presence of a surface texture pattern. However, investigations into the specific mechanisms of texture's effect on shape perception are still ongoing and the question of how to design and apply a texture pattern to a surface in order to best facilitate shape perception remains open. Recently, we have suggested that, for anisotropic texture patterns, the accuracy of shape judgments may be significantly affected by the orientation of the surface texture pattern anisotropy with respect to the principal directions of curvature over the surface. However, it has been difficult, until this time, to conduct controlled studies specifically investigating the effect of texture orientation on shape perception because there has been no simple and reliable method for texturing an arbitrary doubly curved surface with a specified input pattern such that the dominant orientation of the pattern everywhere follows a predefined directional vector field over the surface, while seams and projective distortion of the pattern are avoided. In this paper, we present a straightforward and highly efficient method for achieving such a texture and describe how it can potentially be used to enhance shape representation. Specifically, we describe a novel, efficient, automatic algorithm for seamlessly synthesizing, from a sample 2D pattern, a high resolution fitted surface texture in which the dominant orientation of the pattern locally follows a specified vector field over the surface at a per-pixel level and in which seams, projective distortion, and repetition artifacts in the texture pattern are nearly completely avoided. We demonstrate the robustness of our method with a variety of texture swatches applied to standard graphics data sets and we explain how our method can be used to facilitate research in the perception of shape from texture.
Fast L1 smoothing splines with an application to Kinect depth data

Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a (sometimes weighted) L2 norm while the latter ensures smoothness. In this work we propose to replace the L2 norm in the fitting term with an L1 norm, leading to automatic robustness to outliers. To solve the resulting minimization problem we propose an extremely simple and efficient numerical scheme based on split-Bregman iteration and a DCT-based filter. The algorithm is applied to the problem of smoothing and impainting range data, where high-quality results are obtained in short processing times.
On the level lines and geometry of vector-valued images

In this letter, we extend the concept of level lines of scalar images to vector-valued data. Consistent with the scalar case, we define the level-lines of vector-valued images as the integral curves of the directions of minimal vectorial change. This direction, and the magnitude of the change, are computed using classical Riemannian geometry. As an example of the use of this new concept, we show how to visualize the basic geometry of vector-valued images with a scalar image.
Color image enhancement via chromaticity diffusion

A novel approach for color image denoising is proposed in this paper. The algorithm is based on separating the color data into chromaticity and brightness, and then processing each one of these components with partial differential equations or diffusion flows. In the proposed algorithm, each color pixel is considered as an n-dimensional vector. The vectors' direction, a unit vector, gives the chromaticity, while the magnitude represents the pixel brightness. The chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals. This theory deals with the regularization of vectorial data, while satisfying the intrinsic unit norm constraint of directional data such as chromaticity. Both isotropic and anisotropic diffusion flows are presented for this n-dimensional chromaticity diffusion flow. The brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement. We present the underlying theory, a number of examples, and briefly compare with the current literature.
Morse description and geometric encoding of DEM data

Two complementary geometric structures for the topographic representation of an image are developed in this work. The first one computes a description of the Morse structure of the image, while the second one computes a simplified version of its drainage structure. The topographic significance of the Morse and drainage structures of digital elevation maps (DEM) suggests that they can been used as the basis of an efficient encoding scheme. We combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for DEM. This algorithm permits to obtain compression results while controlling the maximum error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEM.
Low-Cost Compressive Sensing for Color Video and Depth

A simple and inexpensive (low-power and low-bandwidth) modification is made to a conventional off-the-shelf color video camera, from which we recover multiple color frames for each of the original measured frames, and each of the recovered frames can be focused at a different depth. The recovery of multiple frames for each measured frame is made possible via high-speed coding, manifested via translation of a single coded aperture, the inexpensive translation is constituted by mounting the binary code on a piezoelectric device. To simultaneously recover depth information, a liquid lens is modulated at high speed, via a variable voltage. Consequently, during the aforementioned coding process, the liquid lens allows the camera to sweep the focus through multiple depths. In addition to designing and implementing the camera, fast recovery is achieved by an anytime algorithm exploiting the group-sparsity of wavelet/DCT coefficients.
Visualization of high dynamic range images

A novel paradigm for information visualization in high dynamic range images is presented in this paper. These images, real or synthetic, have luminance with typical ranges many orders of magnitude higher than that of standard output/viewing devices, thereby requiring some processing for their visualization. In contrast with existent approaches, which compute a single image with reduced range, close in a given sense to the original data, we propose to look for a representative set of images. The goal is then to produce a minimal set of images capturing the information all over the high dynamic range data, while at the same time preserving a natural appearance for each one of the images in the set. A specific algorithm that achieves this goal is presented and tested on natural and synthetic data.
Morse description and geometric encoding of digital elevation maps

Two complementary geometric structures for the topographic representation of an image are developed in this work. The first one computes a description of the Morse-topological structure of the image, while the second one computes a simplified version of its drainage structure. The topographic significance of the Morse and drainage structures of digital elevation maps (DEMs) suggests that they can been used as the basis of an efficient encoding scheme. As an application, we combine this geometric representation with an interpolation algorithm and lossless data compression schemes to develop a compression scheme for DEMs. This algorithm achieves high compression while controlling the maximum error in the decoded elevation map, a property that is necessary for the majority of applications dealing with DEMs. We present the underlying theory and compression results for standard DEM data.
Semi-supervised multi-domain regression with distinct training sets

We address the problems of multi-domain and single-domain regression based on distinct labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as ones of Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of audio-visual word recognition and provide comparisons to several recently proposed multi-modal learning algorithms.
Sparse coding and dictionary learning based on the MDL principle

The power of sparse signal coding with learned overcomplete dictionaries has been demonstrated in a variety of applications and fields, from signal processing to statistical inference and machine learning. However, the statistical properties of these models, such as underfitting or overfitting given sets of data, are still not well characterized in the literature. This work aims at filling this gap by means of the Minimum Description Length (MDL) principle - a well established information-theoretic approach to statistical inference. The resulting framework derives a family of efficient sparse coding and modeling (dictionary learning) algorithms, which by virtue of the MDL principle, are completely parameter free. Furthermore, such framework allows to incorporate additional prior information in the model, such as Markovian dependencies, in a natural way. We demonstrate the performance of the proposed framework with results for image denoising and classification tasks.
Collaborative hierarchical sparse modeling

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an ℓ1-regularized linear regression problem, usually called Lasso. In this work we first combine the sparsity-inducing property of the Lasso model, at the individual feature level, with the block-sparsity property of the group Lasso model, where sparse groups of features are jointly encoded, obtaining a sparsity pattern hierarchically structured. This results in the hierarchical Lasso, which shows important practical modeling advantages. We then extend this approach to the collaborative case, where a set of simultaneously coded signals share the same sparsity pattern at the higher (group) level but not necessarily at the lower one. Signals then share the same active groups, or classes, but not necessarily the same active set. This is very well suited for applications such as source separation. An efficient optimization procedure, which guarantees convergence to the global optimum, is developed for these new models. The underlying presentation of the new framework and optimization approach is complemented with experimental examples and preliminary theoretical results.