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Adaptive Periodic Noise Reduction in Digital Images Using Fuzzy Transform J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210122
Najmeh Alibabaie, AliMohammad LatifPeriodic noise degrades the image quality by overlaying similar patterns. This noise appears as peaks in the image spectrum. In this research, a method based on fuzzy transform has been developed to identify and reduce the peaks adaptively. We convert the periodic noise removal task as image compression and a smoothing problem. We first utilize the direct and inverse fuzzy transform of the spectrum

Levenberg–Marquardt Algorithm for AcoustoElectric Tomography based on the Complete Electrode Model J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210111
Changyou Li, Mirza Karamehmedović, Ekaterina Sherina, Kim KnudsenThe inverse problem in acoustoelectric tomography concerns the reconstruction of the electric conductivity in a body from knowledge of the power density function in the interior of the body. This interior power density results from currents prescribed at boundary electrodes, and it can be obtained through electrostatic boundary measurements together with auxiliary acoustic probing. Previous works

A Continuous Relaxation of the Constrained $$\ell _2\ell _0$$ ℓ 2  ℓ 0 Problem J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210109
Arne Henrik Bechensteen, Laure BlancFéraud, Gilles AubertWe focus on the minimization of the least square loss function under a ksparse constraint encoded by a \(\ell _0\) pseudonorm. This is a nonconvex, noncontinuous and NPhard problem. Recently, for the penalized form (sum of the least square loss function and a \(\ell _0\) penalty term), a relaxation has been introduced which has strong results in terms of minimizers. This relaxation is continuous

Point Cloud Registration Using Virtual Interest Points from Macaulay’s Resultant of Quadric Surfaces J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210107
Mirza Tahir Ahmed, Sheikh Ziauddin, Joshua A. Marshall, Michael GreenspanA novel formulation called Virtual Interest Point is presented and used to register point clouds. An implicit quadric surface representation is first used to model the point cloud segments. Macaulay’s resultant then provides the intersection of three such quadrics, which forms a virtual interest point (VIP). A unique feature descriptor for each VIP is computed, and correspondences in descriptor space

$$C^2$$ C 2 Rational Interpolation Splines with Region Control and Image Interpolation Application J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210106
Zhuo Liu, Shengjun Liu, Yuanpeng ZhuIn this work, we deal with the region control of \(C^2\) interpolation curves and surfaces using a class of rational interpolation splines in one and two dimensions. Simple sufficient datadependent constraints are derived on the local control parameters to generate \(C^2\) interpolation curves lying strictly between two given piecewise linear curves and \(C^2\) interpolation surfaces lying strictly

Predictive Online Optimisation with Applications to Optical Flow J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210104
Tuomo ValkonenOnline optimisation revolves around new data being introduced into a problem while it is still being solved; think of deep learning as more training samples become available. We adapt the idea to dynamic inverse problems such as video processing with optical flow. We introduce a corresponding predictive online primaldual proximal splitting method. The video frames now exactly correspond to the algorithm

Benefiting from Duplicates of Compressed Data: ShiftBased Holographic Compression of Images J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210104
Yehuda Dar, Alfred M. BrucksteinStorage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper, we show that a wiser method of duplication entails great potential benefits for data types tolerating approximate representations, like images and videos. We propose a method to produce a set of distinct compressed

Boundary Ghosts for Discrete Tomography J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210104
Matthew Ceko, Timothy Petersen, Imants Svalbe, Rob TijdemanDiscrete tomography reconstructs an image of an object on a grid from its discrete projections along relatively few directions. When the resulting system of linear equations is underdetermined, the reconstructed image is not unique. Ghosts are arrays of signed pixels that have zero sum projections along these directions; they define the image pixel locations that have nonunique solutions. In general

Gray Balance Adjusting in Electrophotography by Means of Discrete Geodesics of Gradation Surfaces J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210103
Dmitry A. Tarasov, Oleg B. MilderGray balance is one of the key issues of color balance and color appearance adjustment during printing. It takes into account the overlap of two or more colorants to achieve a visually neutral tone. It works in parallel with the adjustment of the main color channels. In electrophotography, the setting of color channels separately is usually carried out using tone reproduction curves. However, this

Effective TwoStage Image Segmentation: A New NonLipschitz Decomposition Approach with Convergent Algorithm J. Math. Imaging Vis. (IF 1.353) Pub Date : 20210101
Xueyan Guo, Yunhua Xue, Chunlin WuImage segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new twostage multiphase segmentation method trying to tackle this, where the key is to compute an inhomogeneityfree approximate image. For this, we propose to use a new nonLipschitz variational decomposition

On the Reconstruction of the Center of a Projection by Distances and Incidence Relations J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201218
András Pongrácz, Csaba VinczeUp to an orientationpreserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence

Efficient Position Estimation of 3D Fluorescent Spherical Beads in Confocal Microscopy via Poisson Denoising J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201119
Alessandro Benfenati, Francesco Bonacci, Tarik Bourouina, Hugues TalbotParticle estimation is a classical problem arising in many science fields, such as biophysics, fluid mechanics and biomedical imaging. Many interesting applications in these areas involve 3D imaging data: This work presents a technique to estimate the 3D coordinates of the center of spherical particles. This procedure has its core in the processing of the images of the scanned volume: It firstly applies

Rigidity Properties of the Blum Medial Axis J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201109
James DamonWe consider the Blum medial axis of a region in \(\mathbb R^n\) with piecewise smooth boundary and examine its “rigidity properties,”by which we mean properties preserved under diffeomorphisms of the regions preserving the medial axis. There are several possible versions of rigidity depending on what features of the Blum medial axis we wish to retain. We use a form of the cross ratio from projective

On ParticleSize Distribution of Convex Similar Bodies in $${\mathbb {R}}^3$$ R 3 J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201106
J. Kisel’ák, G. BaluchováWe have solved an old problem posed by Santaló of determining the size distribution of particles derived from the size distribution of their sections. We give an explicit form of particlesize distributions of convex similar bodies for random planes and random lines, which naturally generalize famous Wicksell’s corpuscle problem. The results are achieved by applying the method of model solutions for

Video Denoising by Combining Patch Search and CNNs J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201031
Axel Davy, Thibaud Ehret, JeanMichel Morel, Pablo Arias, Gabriele FaccioloNonlocal patchbased methods were until recently the state of the art for image denoising but are now outperformed by CNNs. In video denoising, however, they are still competitive with CNNs, as they can effectively exploit the video temporal redundancy, which is a key factor to attain high denoising performance. The problem is that CNN architectures are not compatible with the search for selfsimilarities

Ground Metric Learning on Graphs J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201030
Matthieu Heitz, Nicolas Bonneel, David Coeurjolly, Marco Cuturi, Gabriel PeyréOptimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for reallife applications strongly hinges on whether that ground metric parameter is suitably chosen. The challenge of selecting it adaptively and algorithmically from prior knowledge, the socalled ground metric learning (GML) problem, has therefore

BlockBased Refitting in $$\ell _{12}$$ ℓ 12 Sparse Regularization J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201017
CharlesAlban Deledalle, Nicolas Papadakis, Joseph Salmon, Samuel VaiterIn many linear regression problems, including illposed inverse problems in image restoration, the data exhibit some sparse structures that can be used to regularize the inversion. To this end, a classical path is to use \(\ell _{12}\) blockbased regularization. While efficient at retrieving the inherent sparsity patterns of the data—the support—the estimated solutions are known to suffer from a systematical

Image Reconstruction by Minimizing Curvatures on Image Surface J. Math. Imaging Vis. (IF 1.353) Pub Date : 20201015
Qiuxiang Zhong, Ke Yin, Yuping DuanThe curvature regularities are wellknown for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually nonconvex, nonsmooth, and highly nonlinear, the firstorder optimality condition of which are highorder partial differential equations. Thus, numerical computation is extremely

A bisector Line Field Approach to Interpolation of Orientation Fields J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200920
Nicolas Boizot, Ludovic SacchelliWe propose an approach to the problem of global reconstruction of an orientation field. The method is based on a geometric model called bisector line fields, which maps a pair of vector fields to an orientation field, effectively generalizing the notion of doubling phase vector fields. Endowed with a wellchosen energy minimization problem, we provide a polynomial interpolation of a target orientation

Temporal Huber Regularization for DCEMRI J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200918
Matti Hanhela, Mikko Kettunen, Olli Gröhn, Marko Vauhkonen, Ville KolehmainenDynamic contrastenhanced magnetic resonance imaging (DCEMRI) is used to study microvascular structure and tissue perfusion. In DCEMRI, a bolus of gadoliniumbased contrast agent is injected into the blood stream and spatiotemporal changes induced by the contrast agent flow are estimated from a time series of MRI data. Sufficient time resolution can often only be obtained by using an imaging protocol

Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200918
Bart M. N. Smets, Jim Portegies, Etienne StOnge, Remco DuitsTwo key ideas have greatly improved techniques for image enhancement and denoising: the lifting of image data to multiorientation distributions and the application of nonlinear PDEs such as total variation flow (TVF) and mean curvature flow (MCF). These two ideas were recently combined by Chambolle and Pock (for TVF) and Citti et al. (for MCF) for twodimensional images. In this work, we extend their

An ElasticaDriven Digital Curve Evolution Model for Image Segmentation J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200913
Daniel Antunes, JacquesOlivier Lachaud, Hugues TalbotGeometric priors have been shown to be useful in image segmentation to regularize the results. For example, the classical Mumford–Shah functional uses region perimeter as prior. This has inspired much research in the last few decades, with classical approaches like the Rudin–Osher–Fatemi and most graphcut formulations, which all use a weighted or binary perimeter prior. It has been observed that this

Equivalence between Digital WellComposedness and WellComposedness in the Sense of Alexandrov on n D Cubical Grids J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200907
Nicolas Boutry, Laurent Najman, Thierry GéraudAmong the different flavors of wellcomposednesses on cubical grids, two of them, called, respectively, digital wellcomposedness (DWCness) and wellcomposedness in the sense of Alexandrov (AWCness), are known to be equivalent in 2D and in 3D. The former means that a cubical set does not contain critical configurations, while the latter means that the boundary of a cubical set is made of a disjoint

Topological Properties of the First NonLocal Digitally WellComposed Interpolation on n D Cubical Grids J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200905
Nicolas Boutry, Laurent Najman, Thierry GéraudIn discrete topology, we like digitally wellcomposed (shortly DWC) interpolations because they remove pinches in cubical images. Usual wellcomposed interpolations are local and sometimes selfdual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in nD selfdual DWC interpolations to obtain a purely selfdual tree of shapes. However,

Nonblind and Blind Deconvolution Under Poisson Noise Using FractionalOrder Total Variation J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200825
Mujibur Rahman Chowdhury, Jing Qin, Yifei LouIn a wide range of applications such as astronomy, biology, and medical imaging, acquired data are usually corrupted by Poisson noise and blurring artifacts. Poisson noise often occurs when photon counting is involved in such imaging modalities as Xray, positron emission tomography, and fluorescence microscopy. Meanwhile, blurring is also inevitable due to the physical mechanism of an imaging system

An Additive Approximation to Multiplicative Noise J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200817
R. Nicholson, J. P. KaipioMultiplicative noise models are often used instead of additive noise models in cases in which the noise variance depends on the state. Furthermore, when Poisson distributions with relatively small counts are approximated with normal distributions, multiplicative noise approximations are straightforward to implement. There are a number of limitations in the existing approaches to deal with multiplicative

PDE Evolutions for MSmoothers in One, Two, and Three Dimensions J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200812
Martin Welk, Joachim WeickertLocal Msmoothers are interesting and important signal and image processing techniques with many connections to other methods. In our paper, we derive a family of partial differential equations (PDEs) that result in one, two, and three dimensions as limiting processes from Msmoothers which are based on local orderp means within a ball the radius of which tends to zero. The order p may take any nonzero

Learning Adaptive Regularization for Image Labeling Using Geometric Assignment J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200806
Ruben Hühnerbein, Fabrizio Savarino, Stefania Petra, Christoph SchnörrWe study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth. This is accomplished by a Riemannian gradient flow on the manifold of parameters that determines the regularization properties of the assignment flow. Using the symplectic partitioned Runge–Kutta method for numerical integration, it is shown that

Image Morphing in Deep Feature Spaces: Theory and Applications J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200719
Alexander Effland, Erich Kobler, Thomas Pock, Marko Rajković, Martin RumpfThis paper combines image metamorphosis with deep features. To this end, images are considered as maps into a highdimensional feature space and a structuresensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller and Younes (Int J Comput Vis 41(1):61–84, 2001) and Trouvé and Younes (Found Comput Math 5(2):173–198, 2005). For this model, a variational

Geometric Interpretation of the Multisolution Phenomenon in the P3P Problem J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200717
Bo Wang, Hao Hu, Caixia ZhangIt is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its three control points and the position of the optical center. Since in any real applications, the knowledge on the exact number of possible solutions is a prerequisite for selecting the right one among all the possible solutions, and the study on the phenomenon of multiple

Towards PDEBased Video Compression with Optimal Masks Prolongated by Optic Flow J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200713
Michael Breuß, Laurent Hoeltgen, Georg RadowLossy image compression methods based on partial differential equations have received much attention in recent years. They may yield highquality results but rely on the computationally expensive task of finding an optimal selection of data. For the possible extension to video compression, this data selection is a crucial issue. In this context, one could either analyse the video sequence as a whole

Testing that a Local Optimum of the Likelihood is Globally Optimum Using Reparameterized Embeddings J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200714
Joel W. LeBlanc; Brian J. Thelen; Alfred O. HeroMany mathematical imaging problems are posed as nonconvex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formulated in terms of maximizing the likelihood function under a statistical model for

Power Spectral Clustering J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200711
Aditya Challa, Sravan Danda, B. S. Daya Sagar, Laurent NajmanSpectral clustering is one of the most important image processing tools, especially for image segmentation. This specializes at taking local information such as edge weights and globalizing them. Due to its unsupervised nature, it is widely applicable. However, traditional spectral clustering is \({\mathcal {O}}(n^{3/2})\). This poses a challenge, especially given the recent trend of large datasets

Variational Models for Color Image Correction Inspired by Visual Perception and Neuroscience J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200710
Thomas Batard, Johannes Hertrich, Gabriele SteidlReproducing the perception of a realworld scene on a display device is a very challenging task which requires the understanding of the camera processing pipeline, the display process, and the way the human visual system processes the light it captures. Mathematical models based on psychophysical and physiological laws on color vision, named Retinex, provide efficient tools to handle degradations produced

Stable Backward Diffusion Models that Minimise Convex Energies J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200707
Leif Bergerhoff; Marcelo Cárdenas; Joachim Weickert; Martin WelkThe inverse problem of backward diffusion is known to be illposed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a backward diffusion model which implements a smart stabilisation approach that can be used in combination with an easytohandle numerical scheme. So far, existing stabilisation

Computed Tomography Reconstruction with Uncertain View Angles by Iteratively Updated Model Discrepancy J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200704
Nicolai André Brogaard Riis, Yiqiu Dong, Per Christian HansenWe propose a new model and a corresponding iterative algorithm for Computed Tomography (CT) when the view angles are uncertain. The uncertainty is described by an additive model discrepancy term which is included in the data fidelity term of a total variation regularized variational model. We approximate the model discrepancy with a Gaussian distribution. Our iterative algorithm alternates between

A Stochastic Multilayer Algorithm for Semidiscrete Optimal Transport with Applications to Texture Synthesis and Style Transfer J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200701
Arthur Leclaire, Julien RabinThis paper investigates a new stochastic algorithm to approximate semidiscrete optimal transport for largescale problem, i.e., in high dimension and for a large number of points. The proposed technique relies on a hierarchical decomposition of the target discrete distribution and the transport map itself. A stochastic optimization algorithm is derived to estimate the parameters of the corresponding

A Nonlocal LaplacianBased Model for Bituminous Surfacing Crack Recovery and its MPI Implementation J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200627
Noémie Debroux; Carole Le Guyader; Luminita A. VeseThis paper is devoted to the challenging problem of fine structure detection with applications to bituminous surfacing crack recovery. Drogoul (SIAM J Imag Sci 7(4):2700–2731, 2014) shows that such structures can be suitably modeled by a sequence of smooth functions whose Hessian matrices blow up in the perpendicular direction to the crack, while their gradient is null. This observation serves as the

Stochastic Distance Transform: Theory, Algorithms and Applications J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200619
Johan Öfverstedt; Joakim Lindblad; Nataša SladojeDistance transforms (DTs) are standard tools in image analysis, with applications in image registration and segmentation. The DT is based on extremal (minimal) distance values and is therefore highly sensitive to noise. We present a stochastic distance transform (SDT) based on discrete random sets, in which a model of elementwise probability is utilized and the SDT is computed as the first moment

Two Polynomial Time Graph Labeling Algorithms Optimizing MaxNormBased Objective Functions J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200616
Filip Malmberg; Krzysztof Chris CiesielskiMany problems in applied computer science can be expressed in a graph setting and solved by finding an appropriate vertex labeling of the associated graph. It is also common to identify the term “appropriate labeling” with a labeling that optimizes some applicationmotivated objective function. The goal of this work is to present two algorithms that, for the objective functions in a general format

CorticalInspired Wilson–CowanType Equations for OrientationDependent Contrast Perception Modelling J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200611
Marcelo Bertalmío, Luca Calatroni, Valentina Franceschi, Benedetta Franceschiello, Dario PrandiWe consider the evolution model proposed in Bertalmío (Front Comput Neurosci 8:71, 2014), Bertalmío et al. (IEEE Trans Image Process 16(4):1058–1072, 2007) to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson–Cowan equations (Wilson and Cowan in BioPhys J 12(1):1–24, 1972), mainly in terms

An Optimized Framework for PlaneProbing Algorithms J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200609
JacquesOlivier Lachaud; Jocelyn Meyron; Tristan RoussillonA planeprobing algorithm computes the normal vector of a digital plane from a starting point and a predicate “Is a point \({x}\) in the digital plane?”. This predicate is used to probe the digital plane as locally as possible and decide on the fly the next points to consider. However, several existing planeprobing algorithms return the correct normal vector only for some specific starting points

Hexagonality as a New ShapeBased Descriptor of Object J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200608
Vladimir Ilić; Nebojša M. RalevićIn this paper, we define a new shapebased measure which evaluates how much a given shape is hexagonal. Such an introduced measure ranges through the interval (0, 1] and reaches the maximal possible value 1 if and only if the shape considered is a hexagon. The new measure is also invariant with respect to rotation, translation and scaling transformations. A number of experiments, performed on both

On the Generalized Essential Matrix Correction: An Efficient Solution to the Problem and Its Applications J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200606
Pedro Miraldo; João R. CardosoThis paper addresses the problem of finding the closest generalized essential matrix from a given \(6\times 6\) matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large number of constraints, and any optimization method to solve it would

Background Subtraction using Adaptive Singular Value Decomposition J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200605
Günther Reitberger; Tomas SauerAn important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors spanning a subspace of the image space, thus providing a way to determine the amount of new information contained in an incoming frame. We update the singular vectors spanning

A Measure of Q convexity for Shape Analysis J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200602
Péter Balázs; Sara BrunettiIn this paper, we study three basic novel measures of convexity for shape analysis. The convexity considered here is the socalled Qconvexity, that is, convexity by quadrants. The measures are based on the geometrical properties of Qconvex shapes and have the following features: (1) their values range from 0 to 1; (2) their values equal 1 if and only if the binary image is Qconvex; and (3) they

Filtration Simplification for Persistent Homology via Edge Contraction J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200519
Tamal K. Dey; Ryan SlechtaPersistent homology is a popular data analysis technique that is used to capture the changing homology of an indexed sequence of simplicial complexes. These changes are summarized in persistence diagrams. A natural problem is to contract edges in complexes in the initial sequence to obtain a sequence of simplified complexes while controlling the perturbation between the original and simplified persistence

Shape Analysis of Surfaces Using General Elastic Metrics J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200514
Zhe Su; Martin Bauer; Stephen C. Preston; Hamid Laga; Eric KlassenIn this article, we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vectorvalued oneforms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant under rigid motions and reparametrizations; hence, it induces a metric on the “shape

Efficiently Testing Digital Convexity and Recognizing Digital Convex Polygons J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200511
Loïc Crombez; Guilherme D. da Fonseca; Yan GerardA set \(S \subset \mathbb {Z}^2\) of integer points is digital convex if \({{\,\mathrm{conv}\,}}(S) \cap \mathbb {Z}^2 = S\), where \({{\,\mathrm{conv}\,}}(S)\) denotes the convex hull of S. In this paper, we consider the following two problems. The first one is to test whether a given set S of n lattice points is digital convex. If the answer to the first problem is positive, then the second problem

Efficient Relative Pose Estimation for Cameras and Generalized Cameras in Case of Known Relative Rotation Angle J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200502
Evgeniy Martyushev; Bo LiWe propose two minimal solvers to the problem of relative pose estimation for a camera with known relative rotation angle. In practice, such angle can be derived from the readings of a 3D gyroscope. Different from other relative pose formulations fusing a camera and a gyroscope, the use of relative rotation angle does not require extrinsic calibration between the two sensors. The first proposed solver

Local TurnBoundedness: A Curvature Control for Continuous Curves with Application to Digitization J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200407
Étienne Le Quentrec; Loïc Mazo; Étienne Baudrier; Mohamed TajineThis article focuses on the classical problem of the control of information loss during the digitization step. The properties proposed in the literature rely on smoothness hypotheses that are not satisfied by the curves including angular points. The notion of turn introduced by Milnor in the article On the Total Curvature of Knots generalizes the notion of integral curvature to continuous curves. Thanks

A Characterization of Proximity Operators J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200328
Rémi Gribonval; Mila NikolovaWe characterize proximity operators, that is to say functions that map a vector to a solution of a penalized leastsquares optimization problem. Proximity operators of convex penalties have been widely studied and fully characterized by Moreau. They are also widely used in practice with nonconvex penalties such as the \(\ell ^0\) pseudonorm, yet the extension of Moreau’s characterization to this setting

Optimum Cuts in Graphs by General Fuzzy Connectedness with Local Band Constraints J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200327
Caio de Moraes Braz; Paulo A. V. Miranda; Krzysztof Chris Ciesielski; Fábio A. M. CappabiancoThe goal of this work is to describe an efficient algorithm for finding a binary segmentation of an image such that the indicated object satisfies a novel highlevel prior, called local band, LB, constraint; the returned segmentation is optimal, with respect to an appropriate graphcut measure, among all segmentations satisfying the given LB constraint. The new algorithm has two stages: expanding the

2D Geometric Moment Invariants from the Point of View of the Classical Invariant Theory J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200319
Leonid BedratyukThe aim of this paper is to clear up the question of the connection between the geometric moment invariants and the invariant theory, considering a problem of describing the 2D geometric moment invariants as a problem of the classical invariant theory. We give a precise statement of the problem of computation of the 2D geometric invariant moments, introducing the notions of the algebras of simultaneous

Variational Networks: An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration. J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200311
Alexander Effland,Erich Kobler,Karl Kunisch,Thomas PockWe investigate a wellknown phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox originates from a tradeoff between optimization and modeling errors of the underlying variational model and holds true even if deep learning methods are used to learn highly

Characterization of GraphBased Hierarchical Watersheds: Theory and Algorithms J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200309
Deise Santana Maia; Jean Cousty; Laurent Najman; Benjamin PerretWatershed is a wellestablished clustering and segmentation method. In this article, we aim to achieve a better theoretical understanding of the hierarchical version of the watershed operator. More precisely, we propose a characterization of hierarchical watersheds in the framework of edgeweighted graphs. The proposed characterization leads to an efficient algorithm to recognize hierarchical watersheds

A twostage method for spectral–spatial classification of hyperspectral images J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200303
Raymond H. Chan; Kelvin K. Kan; Mila Nikolova; Robert J. PlemmonsWe propose a novel twostage method for the classification of hyperspectral images. Pixelwise classifiers, such as the classical support vector machine (SVM), consider spectral information only. As spatial information is not utilized, the classification results are not optimal and the classified image may appear noisy. Many existing methods, such as morphological profiles, superpixel segmentation

Single Image Blind Deblurring Based on Salient EdgeStructures and ElasticNet Regularization J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200219
XiaoYuan Yu; Wei XieIn single image blind deblurring, the blur kernel and latent image are estimated from a single observed blurry image. The associated mathematical problem is illposed, and an acceptable solution is difficult to obtain without additional priors or heuristics. Inspired by the nonlocal selfsimilarity in image denoising problem, we introduce elasticnet regularization as a rank prior to improve the estimation

Geodesic Analysis in Kendall’s Shape Space with Epidemiological Applications J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200217
Esfandiar NavaYazdani; HansChristian Hege; T. J. Sullivan; Christoph von TycowiczWe analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common, nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical

New Set of Nonseparable Orthogonal Invariant Moments for Image Recognition J. Math. Imaging Vis. (IF 1.353) Pub Date : 20200217
Amal Hjouji; Jaouad ELMekkaoui; Mostafa Jourhmane; Belaid BouikhaleneIt is known that the rotation, scaling and translation invariant property of image moments has a high significance in image recognition. For this reason, the seven invariant moments presented by Hu are widely used in the field of image analysis. These moments are of finite order; therefore, they do not comprise a complete set of image descriptors. For this reason, we introduce in this paper another