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In the last several decades, application of affine transformation and optimization approaches have received enough attention in the domain of monomodal/multimodal image registration. A novel and robust image registration method is proposed which leverages teaching learning-based optimization (TLBO) to obtain the optimal value of rigid transformation parameters. Further, speeded up robust features (SURF) framework is employed to extract features along with Random sample consensus (RANSAC) algorithm. Afterwards, projective transformation is used to obtain more accurate registered image. To remove noise, gaussian filter is used during pre-processing and then normalization is carried out. TLBO is used to identify the optimal geometric transformation parameters by considering the mutual information (MI) as an objective function. This method detects keypoints (features) using SURF then K-nearest neighbour (KNN) is employed to match the detected features. Furthermore, RANSAC eliminates false matches. The registered image with optimal value of rigid transformation parameters is obtained and then enhanced by using SURF-RANSAC followed by projective transformation. Experiments are conducted on Whole Brain ATLAS and KAGGLE datasets. Robustness of proposed approach is verified by the improvement in evaluation metric, such as structure similarity index measure (SSIM) by 8%, MI by 12.71% on monomodal and root mean square error (RMSE) by 41.44% on multimodal images as compared to recent state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In the present communication studies have been carried out with special reference to infinitesimal projective and special projective transformations in a Finsler space and accordingly results have been derived in the form of theorems in a projective symmetric and non-symmetric Finsler space. [ABSTRACT FROM AUTHOR]

Aiming at the problem of tissue section images registration, a global non-rigid registration method based on local feature projective transformation was studied to obtain better matching effect. Firstly, the spatial domain enhancement and frequency domain enhancement were combined to preprocess the image, and the contour features around the tissue were highlighted by matching filtering. Secondly, the scale-invariant feature transform(SIFT) features of the processed image were extracted and preliminarily matched. According to the coordinates of the matched feature points, the projective transformation matrix parameters between the two images were calculated by random sample consensus(RANSAC) method, and the outliers were further removed. The matrix can be used for global registration. Thirdly, according to the feature points extracted by RANSAC method, the K-nearest neighbor method was used for image region divided, and projective registration matrix was solved for different local regions separately. Compared with the global registration matrix, the global non-rigid registration model of tissue section images was obtained. The experimental results show that for different tissue section images, the local projective transformation registration method can basically improve the registration accuracy, but for the image pairs with small local deformation, the improvement of the registration accuracy of the local projective registration is limited. [ABSTRACT FROM AUTHOR]

Line segment matching is important in applications that require recovering the 3D structure of objects (e.g., manmade objects in street-level scenarios). However, differentiating between true and false line matches is generally difficult without strong geometric constraints for line segments. Hence, additional constraints are forced to be used, sacrificing many true line matches. This study proposes a robust line segment matching method based on global projective transformation modeling. We develop a non-parametric motion regression formulation with a specially designed direct linear transformation-based cost function that reformulates the piecewise smoothly varying projective transformations as a global continuous model from highly noisy point matches. The resultant model can effectively approximate the real underlying image transformation and derive high-quality point matches. We apply the computed model and high-quality point matches to a point-correspondence-based line matching pipeline, which provides sufficient strict geometric constraints for first generating the pair-to-pair matches and then distilling the line-to-line matches. Extensive experiments conducted on two challenging line matching datasets show that the proposed method can obtain considerable correct line segment matches, outperforming the comparison methods in mean F-score by at least 15.5% on the benchmark dataset and 16.9% on the local dataset. Code is available at https://github.com/geovsion/SLEM. [ABSTRACT FROM AUTHOR]

In this article, we provide a simple geometric proof of the following fact: The existence of topologically transitive normalized maps induced by linear operators is possible only when the underlying space's real dimension is either 1 or 2 or infinity. A similar result holds for projective transformation as well. [ABSTRACT FROM AUTHOR]

Effective progress monitoring is crucial for successful construction project delivery. Visual data, comprising images and videos of construction operations, has emerged as a valuable source for gaining comprehensive insights into project status. While various vision-based methods have been developed for automated progress monitoring at the element level (e.g., columns, beams, floors, walls), challenges persist in achieving accurate schedule activity-level (e.g., formwork, reinforcement, concrete placement) progress tracking. Existing methods often struggle to report progress status beyond binary form (built/not built). To address these limitations, this research proposes a novel framework for precisely measuring the percent completion of activities associated with under-construction building elements. The framework is implemented through an Activity-level progress monitoring system (ALPMS). ALPMS takes the input of construction site images and a four-dimensional building information model (BIM) and outputs the activity-wise completion percentage required for updating project schedules. It creates as-built point clouds from images, compares them with the as-planned BIM, generates orthographic views of under-construction elements through projective transformation or neural radiance fields (NeRF), applies deep learning-based semantic segmentation for progress reasoning, and estimates completion percentages. Finally, the activity-level rich semantic information is transferred to the as-built point cloud and BIM for three-dimensional visualization of the progress status. When the framework was applied to two building construction projects, on average, the ALPMS could report the activity-wise completion percentages with <6% mean absolute error. Future research shall focus on automating the mapping of project schedule activities and activity-level progress details for timely schedule updates and prediction of project completion dates. • Activity percent complete measurement framework for outdoor and indoor construction monitoring. • Percentage completion estimation of schedule activities through semantic segmentation of orthographic view images. • Methodology for orthographic view synthesis through projective transformation and neural radiance field (NeRF). • 3D progress visualization through semantic segmentation of the as-built point cloud and color-coded BIM. • Semantic image segmentation dataset for activity level progress monitoring. [ABSTRACT FROM AUTHOR]

A well-founded class of dependences, based on the theory of nonlinear electrical circuits, is proposed for the formal approximation of static characteristics for various electronic devices. The dependences are simple fractionally linear and fractionally quadratic expressions (a particular case of rational functions), convenient for engineering calculations. However, these expressions represent projective transformations in the sense of projective geometry. The projective transformations preserve an invariant in the form of a cross ratio (double proportion) of four samples of variable mode parameters (currents, resistances, voltage). The mutual reduction of measurement errors is an attractive practice property of the cross ratio. This leads to the direct formulas for recalculating the mode parameters that have group properties. An example of the approximation of the magnetization characteristic and relative magnetic permeability of the Nickel Steel Carpenter 49 is considered; invariants for the magnetic flux density and absolute permeability are established. The results are applicable in various fields of electronics and spintronics. [ABSTRACT FROM AUTHOR]

It is proven by elementary methods that in dimension 2, every locally injective continuous map, sending the curves of a Ck-spray to curves of another Ck-spray as oriented point sets, is a Ck-diffeomorphism. This extends the result [1] for dimension three and higher from 1965. [ABSTRACT FROM AUTHOR]

Mismatch removal is a key step in many computer vision problems that involve point matching. The existing methods for checking geometric consistency mainly focus on similarity or affine transformations. In this paper, we propose a novel mismatch removal method that can cope with the projective transformation between two corresponding point sets. Our approach is based on the augmented homogeneous coordinates matrix constructed from the coordinates of anchor matches, whose degeneracy can indicate the correctness of anchor matches. The set of anchor matches is initially all the matches and is iteratively updated by calculating the difference between the estimated matched points, which can be easily computed in a closed form, and the actually matched points and removing those with large differences. Experimental results on synthetic 2D point matching data sets and real image matching data sets verify that our method achieves the highest $F$ -score among all the methods under similarity, affine, and projective transformations with noises and outliers. Our method can also achieve faster speed than all other iterative methods. Those non-iterative methods with slight advantage in speed are not competitive in accuracy when compared with ours. We also show that the set of anchor matches is stable through the iteration and the computation time grows very slowly with respect to the number of matched points. When applied to mismatch removal in partial-duplicate image search, our method achieves the best retrieval precision, and its computing time is also highly competitive. [ABSTRACT FROM AUTHOR]

The dynamics of a projective transformation on a real projective space are studied in this paper. The two main aspects of these transforma-tions that are studied here are the topological entropy and the zeta function. Topological entropy is an inherent property of a dynami-cal system whereas the zeta function is a useful tool for the study of periodic points. We find the zeta function for a general projective transformation but entropy only for certain transformations on the real projective line. [ABSTRACT FROM AUTHOR]

This article is born as a game in which art, geometry, physics and mathematics are related to reveal a space that remained trapped in the form of a reflection in one of the best-known works of the fascinating Dutch artist M. C. Escher, entitled: Hand with reflecting sphere. This work is a self-portrait in which the artist reproduces his own hand holding a specular globe in which he himself is reflected sitting in his Rome studio. Thanks to the meticulousness and perfection with which the artist executed his works, it has been possible to restore this space from his reflection, using software designed specifically for the occasion that transforms the reflection into a spherical panorama of the scene, in which we can feel immersed together with the disappeared artist, thanks to the novel techniques and visors of virtual reality. [ABSTRACT FROM AUTHOR]

This article presents the results of research on determining inland vessel position using a single stationary, non-metric camera, which was positioned on the Długi Bridge in Szczecin. Studies included a comparison of graphical methods (i.e. geometric transformation and the bunch of rays method) and analytical methods (i.e. 2D to 2D transformation and 3D to 2D transformation). The research material was a collection of video images of an inland vessel navigating the West Odra River between the Długi and Kolejowy bridges in Szczecin. The results of the research were compared to reference points determined using tachymetric surveys and material acquired by an Unmanned Aerial Vehicle (UAV) and the onboard GNSS satellite receiver with Real Time Kinematic (RTK) correction. [ABSTRACT FROM AUTHOR]

In this article we provide a classification of the projective transformations in P S L ( n + 1 , C ) considered as automorphisms of the complex projective space P C n . Our classification is an interplay between algebra and dynamics. Just as in the case of isometries of C A T ( 0 ) -spaces, this is given by means of three types of transformations, namely: elliptic, parabolic and loxodromic. We describe the dynamics in each case, more precisely we determine the corresponding Kulkarni's limit set, the equicontinuity region, minimal sets, the discontinuity region and maximal regions where the corresponding cyclic group acts properly discontinuously. We also provide, in each case, some equivalent ways to classify the projective transformations. [ABSTRACT FROM AUTHOR]

Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] "Consider in space RP2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space RP2 such that h(Pi) = Qi for i = 1, 2, 3, 4." (Existence Statement 52 and Existence Statement 53) [3]. Or, using notations of Richter [11] "Let [a], [b], [c], [d] in RP2 be four points of which no three are collinear and let [a'],[b'],[c'],[d'] in RP2 be another four points of which no three are collinear, then there exists a 3 × 3 matrix M such that [Ma] = [a'], [Mb] = [b'], [Mc] = [c'], and [Md] = [d']" Makarios has formalized the same results in Isabelle/Isar (the collineations form a group, lemma statement52-existence and lemma statement 53-existence) and published it in Archive of Formal Proofs1 [10], [9]. [ABSTRACT FROM AUTHOR]

The paper deals with a generalization of the notions of geodesic and magnetic curve, namely (F, H)-geodesic, on a manifold endowed with a linear connection and two (1, 1)-tensor fields F and H. [ABSTRACT FROM AUTHOR]

The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17]. Then we show that the projective space induced (in the sense defined in [9]) by ℝ3 is a projective plane (in the sense defined in [10]). Finally, in the real projective plane, we define the homography induced by a 3-by-3 invertible matrix and we show that the images of 3 collinear points are themselves collinear. [ABSTRACT FROM AUTHOR]

We prove rigidity facts for groups acting on pseudo-Riemannian manifolds by preserving unparameterized geodesics. [ABSTRACT FROM AUTHOR]

Methods of close-range photogrammetry, which can be efficiently used to supplement the conventional measurements of displacements during the investigation of the mechanical capacity of structural elements, are presented. In the first part of the paper, an overview of photogrammetric procedures employing automatic measurements that enable the acquisition of measuring data in real time is given. The focus is placed on the single-image photogrammetric methods that use successive images taken with a camera for deformation measurements in the object plane. A description of the photogrammetric workflow follows, which assures precise measurements of deformations, as well as a demonstration of the proposed procedure by means of the cyclic test of the reinforced concrete wall, which was loaded with the prescribed cycles of the horizontal displacements and a constant axial force. The results of the measurements are the displacement field of the measuring points and the deformations, which are calculated on the basis of the single-image photogrammetric method applying projective transformation. We have demonstrated that the pattern of calculated deformations fits very well with the damage observed in the wall. [ABSTRACT FROM AUTHOR]

We consider transformations preserving asymptotic directions of surfaces in Minkowski 3-space and show that a transformation preserves the asymptotic directions of a surface if only if it is the projective one. Therefore, we obtain a characterization of the projective transformation. [ABSTRACT FROM AUTHOR]

Highlights: [•] Automatic error reduction without pre-processing and user interference. [•] Required information is automatically extracted from correspondences. [•] Rearrange the image for minimum vertical disparities and uniform view intervals. [•] Modify color distributions using relative luminance and chrominance properties. [•] Provide more comfortable multi-view images to viewers. [ABSTRACT FROM AUTHOR]

Abstract: An optimization method for registration and mosaicking of remote sensing images has been proposed. More than four pairs of control points extracted by scale invariant feature transform (SIFT) detector have been used to obtain the projective transformation relation between the reference image and text image. A method based on gradient information of the region has been proposed to assign the weighted value to the feature points. The weighted value reflects the importance of the area, which can change the result of optimization. The combination method of seam cutting and feathering technique is used to stitch two overlapped images. Our experiment shows that the alignment error of interest area is smaller than that of normal area. If the weighted parameter is given proper value, the alignment error of interest area can reduced to less than one pixel. [Copyright &y& Elsevier]

Highlights: [•] New non-linear least squares circle fitting algorithm with analytic estimators. [•] Novel use of the polarity transformation for circle fitting. [•] The algorithm is at the accuracy level of other well-known algebraic methods. [•] We develop a geometrical link between the orthogonal and the algebraic fittings. [ABSTRACT FROM AUTHOR]

In the structured light three-dimensional measurement system, calibration is the key to the measurement accuracy; however, conventional calibration methods for the projector are either too complex or inaccurate. Therefore, we propose a simple and accurate method to calibrate the projector. In this method, the calibration points in the camera image plane can be mapped to the projector according the homography of the planar projection. In addition, an error surface compensation method is developed to minimize mapping errors caused by lens distortion of the camera and projector. As a result, the projector can be calibrated with the same method as the camera. Experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in Okamoto et al. (1991). By introducing a dual conformal curvature quantity, we clarify the conditions for the covariance minimization of sequential estimators. These conditions are further elaborated for the multidimensional curved exponential family. The theoretical results are then numerically examined by using typical statistical models, von Mises-Fisher, and hyperboloid models. [ABSTRACT FROM AUTHOR]

In this paper, the 1-D mapping is studied for estimating a general projective transformation between images. First, a ray model of image patches is proposed to convert a complex projective deformation of a patch in the Cartesian space into two simple rigid shifts of radial lines in the log-polar/inverse-polar space. To capture these shifts via direct search, two types of radial image line matching, viz. 1-D log-polar mapping and 1-D inverse-polar mapping, are formally defined. Also, the unique features of these shifts are analyzed. Then, a novel two-step mathematical framework is devised for transformation estimation. In the first step, the 1-D log-polar mapping is applied to estimating four affine parameters via two alternative methods for simulated/real images. In the second step, the 1-D inverse-polar mapping is applied to estimating two projective parameters. By a direct search combined with the two-step line matching, two translational parameters are also determined. Finally, the performance of the framework is evaluated first in estimating a variety of projective transformations by comparing the estimates with their ground truths and between the two proposed methods, and second in registering a wide range of challenging image pairs by comparing with a state-of-the-art feature-based method. [ABSTRACT FROM PUBLISHER]

Abstract: Functions of moments of 2D images that are invariant under some changes are important in image analysis and pattern recognition. One of the most basic changes to a 2D image is geometric change. Two images of the same plane taken from different viewpoints are related by a projective transformation. Unfortunately, it is well known that geometric moment invariants for projective transformations do not exist in general. Yet if we generalize the standard definition of the geometric moments and utilize some additional information from the images, certain type of projective invariants of 2D images can be derived. This paper first defines co-moment as a moment-like function of image that contains two reference points. Then a set of functions of co-moments that is invariant under general projective transformations is derived. The invariants are simple and in explicit form. Experimental results validated the mathematical derivations. [Copyright &y& Elsevier]

In this paper, we define a new projective invariant and call it W̃-curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃-curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. [ABSTRACT FROM AUTHOR]

We show that for any finite set F of nonidentity elements in PSLn() for n ≥ 3, consisting of hyperbolic, finite order, or unipotent elements, there exists an element g of infinite order in PSLn() such that for any h ∈ F, the subgroup 〈 g, h 〉 generated by g and h is canonically isomorphic to the free product 〈 g 〉 * 〈 h 〉. We also show that the set of such elements in PSLn() is Zariski dense in PSLn(). [ABSTRACT FROM AUTHOR]

We consider the six-dimensional pseudo-Riemannian space V 6(gij) with the signature [++−−−−], which admits projective motions, i.e., continuous transformation groups preserving geodesics. We find necessary and sufficient conditions for the six-dimensional rigid h-spaces to have constant curvature. [ABSTRACT FROM AUTHOR]

The author describes how Bion took Freud's conception of dreams as a form of thought and used it as the basis of his theory of transformations. Bion developed an expanded theory of 'dream thought', understood as a process of selection and transformation of sensory and emotional experiences. In this theory, the work of analysis is in turn conceived as a process not only of deciphering symbols, of revealing already existing unconscious meanings, but also of symbol production- of a process for generating thoughts and conferring meaning on experiences that have never been conscious and never been repressed because they have never been 'thought'. Analysis, in its specific operational sense, becomes a system of transformation whereby unconscious somatopsychic processes acquire the conditions for representability and become capable of translation into thoughts, words and interpretations. The rules of transformation applied by the patient in his representations and those applied by the analyst in his interpretations have the same importance for the analytic process as those described by Freud for the process of dreaming. The author discusses the broad categories of transformation adduced by Bion (rigid motion, projective, and in hallucinosis) and introduces some further distinctions within them. [ABSTRACT FROM AUTHOR]

The popularity of the iris biometric has grown considerably over the past two to three years. Most research has been focused on the development of new iris processing and recognition algorithms for frontal view iris images. However, a few challenging directions in iris research have been identified, including processing of a nonideal iris and iris at a distance. In this paper, we describe two nonideal iris recognition systems and analyze their performance. The word "nonideal" is used in the sense of compensating for off-angle occluded iris images. The system is designed to process nonideal iris images in two steps: 1) compensation for off-angle gaze direction and 2) processing and encoding of the rotated iris image. Two approaches are presented to account for angular variations in the iris images. In the first approach, we use Daugman's integrodifferential operator as an objective function to estimate the gaze direction. After the angle is estimated, the off-angle iris image undergoes geometric transformations involving the estimated angle and is further processed as if it were a frontal view image. The encoding technique developed for a frontal image is based on the application of the global independent component analysis. The second approach uses an angular deformation calibration model. The angular deformations are modeled, and calibration parameters are calculated. The proposed method consists of a closed-form solution, followed by an iterative optimization procedure. The images are projected on the plane closest to the base calibrated plane. Biorthogonal wavelets are used for encoding to perform iris recognition. We use a special dataset of the off-angle iris images to quantify the performance of the designed systems. A series of receiver operating characteristics demonstrate various effects on the performance of the nonideal-iris-based recognition system. [ABSTRACT FROM AUTHOR]

Abstract: Suppose that the sphere has initially a homogeneous distribution of mass and let be the Lie group of orientation preserving projective diffeomorphisms of . A projective motion of the sphere, that is, a smooth curve in , is called force free if it is a critical point of the kinetic energy functional. We find explicit examples of force free projective motions of and, more generally, examples of subgroups of such that a force free motion initially tangent to remains in for all time (in contrast with the previously studied case for conformal motions, this property does not hold for ). The main tool is a Riemannian metric on , which turns out to be not complete (in particular not invariant, as happens with non-rigid motions), given by the kinetic energy. [Copyright &y& Elsevier]

Abstract: We discuss the infinitesimal affine transformations of the Berwald connection of a spray, and the relation between the projective transformations of a spray and the affine transformations of its Berwald–Thomas–Whitehead connection. [Copyright &y& Elsevier]

Challenging object detection and segmentation tasks can be facilitated by the availability of a reference object. However, accounting for possible transformations between the different object views, as part of the segmentation process, remains difficult. Recent statistical methods address this problem by using comprehensive training data. Other techniques can only accommodate similarity transformations. We suggest a novel variational approach to prior-based segmentation, using a single reference object, that accounts for planar projective transformation. Generalizing the Chan-Vese level set framework, we introduce a novel shape-similarity measure and embed the projective homography between the prior shape and the image to segment within a region-based segmentation functional. The proposed algorithm detects the object of interest, extracts its boundaries, and concurrently carries out the registration to the prior shape. We demonstrate prior-based segmentation on a variety of images and verify the accuracy of the recovered transformation parameters. [ABSTRACT FROM AUTHOR]

Abstract: Superimposition is an efficient method for evaluation of coincidence between a skull and a photo portrait. The principle of superimposition method lies in the projection of the skull into the face image. During the projection of an object with a perspective camera, the mapping of a three-dimensional object into a two-dimensional image takes place. The acquired images of the same object are more or less distorted due to various photographic conditions, due to extrinsic and intrinsic parameters of the camera. The distortions have important influence onto reliability of human identification by the superimposition method. Mathematically we can describe most of the distortions. On the basis of the description the divergences could be simulated and in some cases eliminated by geometric transformation of the compared images. We are presenting a mathematical model of the standard projective camera and the mathematical description of distortions which are important for the superimposition process. The results show the distortions and the elimination of the distortions by means of the projection model. [Copyright &y& Elsevier]

Abstract: We investigate the evolution of active contours in terms of progressive modification of an initial contour following the chosen Lie group of object-to-image transformations. Because of non-fronto-parallel viewing of an object or due to relative motion between the camera and the object, the resultant image may undergo affine or projective object-to-image transformations. In a recent paper we have shown that in the case of object tracking, frame-to-frame deformations of an initial curve obtained through Euler–Lagrange descent equations of a curve functional can be used to enact a desired Lie group of plane transformations [A.-R. Mansouri, D.P. Mukherjee, S.T. Acton, Constraining active contour evolution via Lie groups of transformation, IEEE Trans. Image Process. 13 (2004) 853–863]. In this work, we propose an energy functional that encodes the Lie group transformation parameters, which in turn guide shape distortion due to oblique viewing. Additional constraints, such as transformation smoothness, are imposed on the active contour by modifying the energy functional. The functional is minimized using numerical schemes similar to the conjugate gradient technique, and the convergence properties are discussed. The success of the technique for affine and projective scenes is demonstrated with both synthetic and real image examples and compared with the related approaches. [Copyright &y& Elsevier]

Abstract: The research of Mario Pieri (1860–1913) can be classified into three main areas: metric differential and algebraic geometry and vector analysis; foundations of geometry and arithmetic; logic and the philosophy of science. In writing this article, I intend to reveal some important aspects of his contributions to the foundations of projective geometry, notably those that emanated from his intensive study of the works of Georg Karl Christian von Staudt (1798–1867). Pieri was the first geometer to successfully establish projective geometry as an independent subject (rigorous mathematical theory), freed from all ties to Euclidean geometry. The path to this achievement began with Staudt, and involved the reformulation of the classical ideas of cross ratio and projectivity in terms of harmonic sets, as well as a critical analysis of the proof of a fundamental theorem that connects these ideas. Included is a brief overview of Pieri''s life and work. [Copyright &y& Elsevier]

This paper presents a Hopfield neural network model for matching features invariant to projective transformations. The projective invariance has been embedded into the compatibility constraint for the first time, such that the problem of finding point correspondences can be formulated by minimizing the predefined energy function through a Hopfield network. The neighborhood information of the data can help to reduce the fifth-order constraint to a second-order one, such as points along the silhouettes, or convex hull of a discrete set of points. The proposed method has been tested with a series of real images and performs well. [Copyright &y& Elsevier]

An exact solution is constructed, which describes a gas glow in a strip between a rectilinear source and sink. With time, the strip turns and expands. In the case of consistent boundary conditions, the flow in the strip is continuous. If the consistency constraints are violated, a shock wave is formed inside the strip. [ABSTRACT FROM AUTHOR]

We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence. [ABSTRACT FROM AUTHOR]

Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the aim of our work is to find and to discuss suitable assessments of smoothness of polyhedral surfaces that only take the geometry of the polyhedral surface itself into account. Motivated by analogies to classical differential geometry, we propose a theory of smoothness of polyhedral surfaces including suitable notions of normal vectors, tangent planes, asymptotic directions, and parabolic curves that are invariant under projective transformations. It is remarkable that seemingly mild conditions significantly limit the shapes of faces of a smooth polyhedral surface. Besides being of theoretical interest, we believe that smoothness of polyhedral surfaces is of interest in the architectural context, where vertices and edges of polyhedral surfaces are highly visible. [ABSTRACT FROM AUTHOR]

This paper is devoted to the investigation of selected situations when computing projective (and other) equivalences of algebraic varieties can be efficiently solved via finding projective equivalences of finite sets of points on the projective line. In particular, we design a method that finds for two algebraic varieties X , Y from special classes an associated set of automorphisms of the projective line (the so called good candidate set) consisting of suitable candidates for the subsequent construction of possible mappings X → Y. The functionality of the designed approach is presented for computing projective equivalences of rational curves, determining projective equivalences of rational ruled surfaces, detecting affine transformations between planar algebraic curves, and computing similarities between two implicitly given algebraic surfaces. When possible, symmetries of given shapes are also discussed as special cases. [ABSTRACT FROM AUTHOR]

The ray projection and its application to recovering a projective geometric transformation and an affine lighting change between two objects are mathematically studied. A novel technique, viz., variable contour, is proposed for accurately evaluating the ray projection. Moreover, a novel flexible framework of the ray projection is devised for the joint recovery of the eight parameters for the projective transformation and the two parameters for the lighting change. Finally, the framework is experimentally evaluated by recovering a variety of geometric and photometric transformations between real images of indoor and outdoor scenes. Its robustness to image blur and occlusion is demonstrated. Its versatility is illustrated through matching different objects in different classes. [ABSTRACT FROM AUTHOR]