nils-herrmann/clean_scirepeval huggingface dataset:
Morphological filters-Part II: Their relations to median, order-statistic, and stack filters

This paper extends the theory of median, order-statistic (OS), and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions, dilations, openings, closings, and open-closings that commute with thresholding. The max-min representation of OS filters is introduced by showing that any median or other OS filter is equal to a maximum of erosions (moving local minima) and also to a minimum of dilations (moving local maxima). Thus, OS filters can be computed by a closed formula that involves a max-min on prespecified sets of numbers and no sorting. Stack filters are established as the class of filters that are composed exactly of a finite number of max-min operations. The kernels of median, OS, and stack filters are collections of input signals that uniquely represent these filters due to their translation-invariance. The max-min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal (with respect to a signal ordering) kernel elements, and also to a minimum of dilations by minimal kernel elements of dual filters. The representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum-of-products expressions of Boolean functions. It is also shown that median filtering (and its iterations) of any signal by convex 1-D windows is bounded below by openings and above by closings; a signal is a root (fixed point) of the median iff it is a root of both an opening and a closing; the open-closing and clos-opening yield median roots in one pass, suppress impulse noise similarly to the median, can discriminate between positive and negative noise impulses, and are computationally less complex than the median. Some similar results are obtained for 2-D median filtering.
Active Contours on Graphs: Multiscale Morphology and Graphcuts

In this paper we propose two novel methods for formulating and implementing the methodology of geodesic active contours on arbitrary graphs, as applied to multiscale morphology and segmentation. Firstly, we propose approximations to the calculation of the gradient and the divergence of vector functions defined on graphs and use these approximations to apply the technique of geodesic active contours for object detection on graphs. To this end, we extend existing work on graph morphology to multiscale dilation and erosion and implement them recursively usinglevel sets of functions defined on the graph. Second, we propose a graphcut based solution to the geodesic active contour problem on graphs. Appropriate weights are calculated for each edge for which the Riemannian length of a contour can be approximated by the weighted sum of intersections of the contour with the edges of the graph. Finding the minimum Riemannian length contour then becomes equivalent to solving a max flow problem for which efficient solutions have been proposed in the literature.
Differential morphology and image processing

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.
Image denoising in nonlinear scale-spaces: automatic scale selection via cross-validation

Multiscale, i.e. scale-space image analysis is a powerful framework for many image processing tasks. A fundamental issue with such scale-space techniques is the automatic selection of the most salient scale for a particular application. This paper considers optimal scale selection when nonlinear diffusion and morphological scale-spaces are utilized for image denoising. The problem is studied from a statistical model selection viewpoint and cross-validation techniques are utilized to address it in a principled way. The proposed novel algorithms do not require knowledge of the noise variance, have acceptable computational cost and are readily integrated with a wide class of scale-space inducing processes which require setting of a scale parameter. Our experiments show that this methodology leads to robust algorithms, which outperform existing scale-selection techniques for a wide range of noise types and noise levels.
Predicting audio-visual salient events based on visual, audio and text modalities for movie summarization

In this paper, we present a new and improved synergistic approach to the problem of audio-visual salient event detection and movie summarization based on visual, audio and text modalities. Spatio-temporal visual saliency is estimated through a perceptually inspired frontend based on 3D (space, time) Gabor filters and frame-wise features are extracted from the saliency volumes. For the auditory salient event detection we extract features based on Teager-Kaiser Energy Operator, while text analysis incorporates part-of-speech tagging and affective modeling of single words on the movie subtitles. For the evaluation of the proposed system, we employ an elementary and non-parametric classification technique like KNN. Detection results are reported on the MovSum database, using objective evaluations against ground-truth denoting the perceptually salient events, and human evaluations of the movie summaries. Our evaluation verifies the appropriateness of the proposed methods compared to our baseline system. Finally, our newly proposed summarization algorithm produces summaries that consist of salient and meaningful events, also improving the comprehension of the semantics.
Experimental validation of human pathological gait analysis for an assisted living intelligent robotic walker

A robust and effective gait analysis functionality is an essential characteristic for an assistance mobility robot dealing with elderly persons. The aforementioned functionality is crucial for dealing with mobility disabilities which are widespread in these parts of the population. In this work we present experimental validation of our in house developed system. We are using real data, collected from an ensemble of different elderly persons with a number of pathologies, and we present a validation study by using a GaitRite System. Our system, following the standard literature conventions, characterizes the human motion with a set of parameters which subsequently can be used to assess and distinguish between possible motion disabilities, using a laser range finder as its main sensor. The initial results, presented in this work, demonstrate the applicability of our framework in real test cases. Regarding such frameworks, a crucial technical question is the necessary complexity of the overall tracking system. To answer this question, we compare two approaches with different complexity levels. The first is a static rule based system acting on filtered laser data, while the second system utilizes a Hidden Markov Model for gait cycle estimation, and extraction of the gait parameters. The results demonstrate that the added complexity of the HMM system is necessary for improving the accuracy and efficacy of the system.
Texture Analysis and Segmentation Using Modulation Features, Generative Models, and Weighted Curve Evolution

In this work we approach the analysis and segmentation of natural textured images by combining ideas from image analysis and probabilistic modeling. We rely on AM-FM texture models and specifically on the Dominant Component Analysis (DCA) paradigm for feature extraction. This method provides a low-dimensional, dense and smooth descriptor, capturing essential aspects of texture, namely scale, orientation, and contrast. Our contributions are at three levels of the texture analysis and segmentation problems: First, at the feature extraction stage we propose a regularized demodulation algorithm that provides more robust texture features and explore the merits of modifying the channel selection criterion of DCA. Second, we propose a probabilistic interpretation of DCA and Gabor filtering in general, in terms of Local Generative Models. Extending this point of view to edge detection facilitates the estimation of posterior probabilities for the edge and texture classes. Third, we propose the weighted curve evolution scheme that enhances the Region Competition/ Geodesic Active Regions methods by allowing for the locally adaptive fusion of heterogeneous cues. Our segmentation results are evaluated on the Berkeley Segmentation Benchmark, and compare favorably to current state-of-the-art methods.
Advances in phonetics-based sub-unit modeling for transcription alignment and sign language recognition

We explore novel directions for incorporating phonetic transcriptions into sub-unit based statistical models for sign language recognition. First, we employ a new symbolic processing approach for converting sign language annotations, based on HamNoSys symbols, into structured sequences of labels according to the Posture-Detention-Transition-Steady Shift phonetic model. Next, we exploit these labels, and their correspondence with visual features to construct phonetics-based statistical sub-unit models. We also align these sequences, via the statistical sub-unit construction and decoding, to the visual data to extract time boundary information that they would lack otherwise. The resulting phonetic sub-units offer new perspectives for sign language analysis, phonetic modeling, and automatic recognition. We evaluate this approach via sign language recognition experiments on an extended Lemmas Corpus of Greek Sign Language, which results not only in improved performance compared to pure data-driven approaches, but also in meaningful phonetic sub-unit models that can be further exploited in interdisciplinary sign language analysis.
Tensor-based image diffusions derived from generalizations of the Total Variation and Beltrami Functionals

We introduce a novel functional for vector-valued images that generalizes several variational methods, such as the Total Variation and Beltrami Functionals. This functional is based on the structure tensor that describes the geometry of image structures within the neighborhood of each point. We first generalize the Beltrami functional based on the image patches and using embeddings in high dimensional spaces. Proceeding to the most general form of the proposed functional, we prove that its minimization leads to a nonlinear anisotropic diffusion that is regularized, in the sense that its diffusion tensor contains convolutions with a kernel. Using this result we propose two novel diffusion methods, the Generalized Beltrami Flow and the Tensor Total Variation. These methods combine the advantages of the variational approaches with those of the tensor-based diffusion approaches.
A PDE formulation for viscous morphological operators with extensions to intensity-adaptive operators

Viscous morphological operators have shown very good performance in regularizing various image analysis tasks such as detection of intensity-varying boundaries and segmentation. This paper presents a novel formulation of viscous morphological operators as solutions of nonlinear partial differential equations (PDEs) of the hyperbolic type with level-varying speed. Efficient numerical algorithms are also developed to solve these PDEs and generate the viscous operations. It also generalizes the viscous operators by studying the class of intensity level-varying operators, of which special cases are intensity adaptive connected operators such as volume openings and viscous reconstruction filters. We present both theoretical aspects and applications of the above ideas.
Synthesis and applications of lattice image operators based on fuzzy norms

We use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that can be expressed as nonlinear convolutions that are suprema or infima of fuzzy intersection or union norms. Our emphasis (different from previous works) is the construction of pairs of fuzzy dilation and erosion operators that form lattice adjunctions. This guarantees that their composition will be a valid algebraic opening or closing. The power, but also the difficulty, in applying these fuzzy operators to image analysis is the large variety of fuzzy norms and the absence of systematic ways in selecting them. Towards this goal, we have performed extensive experiments in applying these fuzzy operators to various nonlinear filtering and image analysis tasks, attempting first to understand the effect that the type of fuzzy norm and the shape/size of the structuring function has on the resulting new image operators. Further, we have developed some new fuzzy edge gradients and optimized their usage for edge detection on test problems via a parametric fuzzy norm.
Evolution equations for continuous-scale morphological filtering

Multiscale signal analysis has emerged as a useful framework for many computer vision and signal processing tasks. Morphological filters can be used to develop nonlinear multiscale operations that have certain advantages over linear multiscale approaches in that they preserve important signal features such as edges. The authors discuss several nonlinear partial differential equations that model the scale evolution associated with continuous-space multiscale morphological erosions, dilations, openings, and closings. These equations relate the rate of change of the multiscale signal ensemble as scale increases to a nonlinear operator acting on the space of signals. The nonlinear operator is characterized by the shape and dimensionality of the structuring element used by the morphological operators, generally taking the form of a nonlinear function of certain partial differential operators.
FMRI-based perceptual validation of a computational model for visual and auditory saliency in videos

In this study, we make use of brain activation data to investigate the perceptual plausibility of a visual and an auditory model for visual and auditory saliency in video processing. These models have already been successfully employed in a number of applications. In addition, we experiment with parameters, modifications and suitable fusion schemes. As part of this work, fMRI data from complex video stimuli were collected, on which we base our analysis and results. The core part of the analysis involves the use of well-established methods for the manipulation of fMRI data and the examination of variability across brain responses of different individuals. Our results indicate a success in confirming the value of these saliency models in terms of perceptual plausibility.
Morphological skeleton representation and coding of binary images

This paper presents the results of a study on the use of morphological set operations to represent and encode a discrete binary image by parts of its skeleton, a thinned version of the image containing complete information about its shape and size. Using morphological erosions and openings, a finite image can be uniquely decomposed into a finite number of skeleton subsets and then the image can be exactly reconstructed by dilating the skeleton subsets. The morphological skeleton is shown to unify many previous approaches to skeletonization, and some of its theoretical properties are investigated. Fast algorithms that reduce the original quadratic complexity to linear are developed for skeleton decomposition and reconstruction. Partial reconstructions of the image are quantified through the omission of subsets of skeleton points. The concepts of a globally and locally minimal skeleton are introduced and fast algorithms are developed for obtaining minimal skeletons. For images containing blobs and large areas, the skeleton subsets are much thinner than the original image. Therefore, encoding of the skeleton information results in lower information rates than optimum block-Huffman or optimum runlength-Huffman coding of the original image. The highest level of image compression was obtained by using Elias coding of the skeleton.
Two-dimensional linear prediction and its application to adaptive predictive coding of images

This paper summarizes a study on two-dimensional linear prediction of images and its application to adaptive predictive coding of monochrome images. The study was focused on three major areas: two-dimensional linear prediction of images and its performance, implementation of an adaptive predictor and adaptive quantizer for use in image coding, and linear prediction and adaptive predictive coding of density (logarithm of intensity) images. Among the issues investigated are: autoregressive modeling of 2-D image sequences, estimation of the nonzero average bias of the image samples, stability of the inverse prediction error filter, and estimation of the parameters of a 2-D separable linear predictor. The implementation of the adaptive predictor is based on the results of linear predictive analysis. The adaptive quantization of the prediction error signal is done by using a flexible three-level quantizer for code words of fixed or variable length. The above ideas are further applied to density images for exploiting the multiplicative structure of images. The results of this research indicate that by using adaptive prediction and quantization, intensity and density coded images of high quality can be obtained at information rates as low as 0.7 bits/pixel.
Image decomposition into structure and texture subcomponents with multifrequency modulation constraints

Texture information in images is coupled with geometric macrostructures and piecewise-smooth intensity variations. Decomposing an image f into a geometric structure component u and a texture component v is an inverse estimation problem, essential for understanding and analyzing images depending on their content. In this paper, we present a novel combined approach for simultaneous texture from structure separation and multiband texture modeling. First, we formulate a new, variational decomposition scheme, involving an explicit texture reconstruction constraint (prior) formed by the responses of selected frequency-tuned linear filters. This forms a dasiau + Kvpsila image model of K + 1 components. Subsequent texture modeling is applied to the estimated v component and its consistency is compared to using the complete, initial image f. The decomposition step, functioning as an advanced texture-front end, improves clustering and classification performance, for various multiband features. The proposed method can be generalized to other texture models or applications.
Differential morphology: multiscale image dynamics, max-min difference equations, and slope transforms

We develop 2D max-min difference equations that model the space dynamics of 2D morphological systems and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in a way conceptually analogous to the application of Fourier transforms to linear systems. Further, we discuss some nonlinear partial differential equations (PDEs) that model the evolution of multiscale morphological filters of the max-min type. These PDEs are related to the eikonal equation. Solutions of the eikonal PDE are proposed based on 2D min difference equations that can compute distance transforms. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via max-min equations as a unified area in nonlinear image processing which we call differential morphology. Its potential applications include distance-path finding, segmentation, gridless halftoning, and shape from shading.<<ETX>>
Morphological/rank neural networks and their adaptive optimal design for image processing

We formulate a general class of neural network based filters, where each node is a morphological/rank operation. This type of system is computationally efficient since no multiplications are necessary. The introduction of such networks is partially motivated from observations that internal structures of a neuron can generate logic operations. An efficient adaptive optimal design procedure is proposed for these networks, based on the back-propagation algorithm. The procedure is optimal under the LMS criterion. Finally, experimental results are illustrated in problems of noise cancellation, encouraging the use of such class of systems and its training algorithm as important tools for nonlinear signal and image processing.
Overview of adaptive morphology: Trends and perspectives

In this paper we briefly overview emerging trends in ‘Adaptive Morphology’, i.e. work related to the theory and/or applications of image analysis filters, systems, or algorithms based on mathematical morphology, that are adaptive w.r.t. to space or intensity or use any other adaptive scheme. We present a new classification of work in this area structured along several major theoretical perspectives. We then sample specific approaches that develop spatially-variant structuring elements or intensity level-adaptive operators, modeled and implemented either via conventional nonlinear digital filtering or via geometric PDEs. Finally, we discuss some applications.
Slope transforms: theory and application to nonlinear signal processing

Fourier transforms are among the most useful linear signal transformations for quantifying the frequency content of signals and for analyzing their processing by linear time-invariant systems. Some nonlinear signal transforms are developed that can provide information about the slope content of signals and are useful analytic tools for large classes of nonlinear systems. Many of their theoretical properties are examined, showing a striking conceptual resemblance to Fourier transforms and their application to linear systems. These novel transforms, called slope transforms, are originally derived from the eigenvalues of morphological dilation and erosion systems, where the corresponding eigenfunctions are lines /spl alpha/t+b parameterized by their slope /spl alpha/. They obey a nonlinear superposition principle of the supremum- or infimum-of-sums type. Applied to the impulse response of dilation or erosion systems, the slope transforms provide a slope response function for these systems, which allows their analysis and design in a transform domain, the slope domain. Applied to arbitrary signals, the slope transforms provide information about upper or lower tangents to the signal's graph at varying slopes. The upper or lower envelopes of the signal can be obtained from the inverse transforms. Overall, the slope transforms provide a new transform domain for signals and morphological systems where time lines become slope impulses, time cones become slope bandpass filters, and time dilation/erosion transform into addition of slope transforms. Their application to the design of slope-selective filters is also presented.