nils-herrmann/clean_scirepeval huggingface dataset:
Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence

We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. The task is feasible only when some constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as "trajectory triangulation." We investigate the solutions for points moving along a straight-line and along conic-section trajectories, We show that if the point is moving along a straight line, then the parameters of the line (and, hence, the 3D position of the point at each time instant) can be uniquely recovered, and by linear methods, from at least five views. For the case of conic-shaped trajectory, we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type (like a circle in 3D Euclidean space for which seven views are sufficient). The paradigm of trajectory triangulation, in general, pushes the envelope of processing dynamic scenes forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point).
System obstacle detection displacement of a vehicle.

Un sistema de determinacion de estimacion de tiempo a contacto (12) para generar una estimacion sobre el tiempo a contacto de un vehiculo (10) que avanza a lo largo de una carretera (11) con un obstaculo (15) incluyendo: A. Un receptor de imagenes (13) configurado para recibir informacion de imagenes relativa a una serie de al menos dos imagenes cuando el vehiculo se mueve a lo largo de la carretera; y B. Un procesador (14); caracterizado porque el procesador esta configurado para determinar un factor de escala que define una relacion entre dimensiones del obstaculo en las imagenes y usa la relacion para generar una estimacion del tiempo a contacto del vehiculo con el obstaculo.
Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion

We describe a direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn and Weldon (1988) to three views. Adding the third view enables us to solve for motion and compute a dense depth map of the scene, directly from image spatio-temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow. We describe the advantages and limitations of this method which are then verified with experiments using real images.
On the Reprojection of 3D and 2D Scenes Without Explicit Model Selection

It is known that recovering projection matrices from planar configurations is ambiguous, thus, posing the problem of model selection -- is the scene planar (2D) or non-planar (3D)? For a 2D scene one would recover a homography matrix, whereas for a 3D scene one would recover the fundamental matrix or trifocal tensor. The task of model selection is especially problematic when the scene is neither 2D nor 3D -- for example a "thin" volume in space. 
 
In this paper we show that for certain tasks, such as reprojection, there is no need to select a model. The ambiguity that arises from a 2D scene is orthogonal to the reprojection process, thus if one desires to use multilinear matching constraints for transferring points along a sequence of views it is possible to do so under any situation of 2D, 3D or "thin" volumes.
Homography Tensors: On Algebraic Entities that Represent Three Views of Static or Moving Planar Points

We introduce a 3 × 3 × 3 tensor Hijk and its dual Hijk which represent the 2D projective mapping of points across three projections (views). The tensor Hijk is a generalization of the well known 2D collineation matrix (homography matrix) and it concatenates two homography matrices to represent the joint mapping across three views. The dual tensor Hijk concatenates two dual homography matrices (mappings of line space) and is responsible for representing the mapping associated with moving points along straight-line paths, i.e., Hijk can be recovered from line-of-sight measurements only.
3D Reconstruction from Tangent-of-Sight Measurements of a Moving Object Seen from a Moving Camera

Consider the situation of a monocular image sequence with known ego-motion observing a 3D point moving simultaneously but along a path of up to second order, i.e. it can trace a line in 3D or a conic shaped path. We wish to reconstruct the 3D path from the projection of the tangent to the path at each time instance. This problem is analogue to the "trajectory triangulation" of lines and conic sections recently introduced in , but instead of observing a point projection we observe a tangent projection and thus obtain a far simpler solution to the problem. 
 
We show that the 3D path can be solved in a natural manner, and linearly, using degenerate quadric envelopes - specifically the disk quadric. Our approach works seamlessly with both linear and second order paths, thus there is no need to know in advance the shape of the path as with the previous approaches for which lines and conics were treated as distinct. Our approach is linear in both straight line and conic paths, unlike the non-linear solution associated with point trajectory . 
 
We provide experiments that show that our method behaves extremely well on a wide variety of scenarios, including those with multiple moving objects along lines and conic shaped paths.
A robust method for computing vehicle ego-motion

We describe a robust method for computing the ego-motion of the vehicle relative to the road using input from a single camera mounted next to the rear view mirror. Since feature points are unreliable in cluttered scenes we use direct methods where image values in the two images are combined in a global probability function. Combined with the use of probability distribution matrices, this enables the formulation of a robust method that can ignore large number of outliers as one would encounter in real traffic situations. The method has been tested in real world environments and has been shown to be robust to glare, rain and moving objects in the scene.
Trajectory triangulation of lines: reconstruction of a 3D point moving along a line from a monocular image sequence

We consider the problem of reconstructing the location of a moving 3D point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. Since the point is moving while the camera is moving, then even if the camera motion is known, it is impossible to reconstruct the 3D location of the point under general circumstances. However we show that if the point is moving along a straight line, then the parameters of the line (and hence the 3D position of the point at each time instance) can be uniquely recovered, and by linear methods, from at least 5 views. Consequently, we propose a new approach for dealing with dynamic scenes (rich with moving objects) in which once the camera motion is recovered, the 3D trajectory (straight line) of the moving target can be recovered-even when the moving target consists of a single point.
Trajectory triangulation over conic section

We consider the problem of reconstructing the 3D coordinates of a moving point seen from a monocular moving camera, i.e., to reconstruct moving objects from line-of-sight measurements only. The task is feasible only when same constraints are placed on the shape of the trajectory of the moving point. We coin the family of such tasks as "trajectory triangulation". In this paper we focus on trajectories whose shape is a conic-section and show that generally 9 views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is a known type (like a circle in 3D Euclidean space for which 7 views are sufficient). Experiments demonstrate that our solutions are practical. The paradigm of Trajectory Triangulation in general pushes the envelope of processing dynamic scenes forward. Thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects (where an object could be a single point).
On Degeneracy of Linear Reconstruction From Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) when the scene is a linear line complex [LLC] (a set of lines in space intersecting at a common line). The LLC situation is only linearly degenerate, and one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.
The quotient image: Class based recognition and synthesis under varying illumination conditions

The paper addresses the problem of "class-based" recognition and image-synthesis with varying illumination. The class-based synthesis and recognition tasks are defined as follows: given a single input image of an object, and a sample of images with varying illumination conditions of other objects of the same general class, capture the equivalence relationship (by generation of new images or by invariants) among all images of the object corresponding to new illumination conditions. The key result in our approach is based on a definition of an illumination invariant signature image, we call the "quotient" image, which enables an analytic generation of the image space with varying illumination from a single input image and a very small sample of other objects of the class-in our experiments as few as two objects. In many cases the recognition results outperform by far conventional methods and the image-synthesis is of remarkable quality considering the size of the database of example images and the mild pre-process required for making the algorithm work.
On the Equivalence between the Support Vector Machine for Classiication and Sparsiied Fisher's Linear Discriminant

We show that the orientation and location of the separating hyperplane for 2-class supervised pattern classi cation obtained by the Support Vector Machine (SVM) proposed by Vapnik and his colleagues, is equivalent to the solution obtained by Fisher's Linear Discriminant on the set of Support Vectors. In other words, SVM can be seen as a way to \sparsify" Fisher's Linear Discriminant in order to obtain the most generalizing classi cation from the training set.
Q-warping: direct computation of quadratic reference surfaces

We consider the problem of wrapping around an object, of which two views are available, a reference surface and recovering the resulting parametric flow using direct computations (via spatio-temporal derivatives). The well known examples are affine flow models and B-parameter flow models - both describing a flow field of a planar reference surface. We extend those classic flow models to deal with a quadric reference surface and work out the explicit parametric form of the flow field. As a result we derive a simple warping algorithm that maps between two views and leaves a residual flow proportional to the 30 deviation of the surface from a virtual quadric surface. The applications include image morphing, model building, image stabilization, and disparate view correspondence.
Novel View Synthesis by Cascading Trilinear Tensors

Presents a new method for synthesizing novel views of a 3D scene from two or three reference images in full correspondence. The core of this work is the use and manipulation of an algebraic entity, termed the "trilinear tensor", that links point correspondences across three images. For a given virtual camera position and orientation, a new trilinear tensor can be computed based on the original tensor of the reference images. The desired view can then be created using this new trilinear tensor and point correspondences across two of the reference images.
Direct estimation of motion and extended scene structure from a moving stereo rig

We investigate the relationship between the kinematics (infinitesimal motion model) of a calibrated Stereo Rig and point and line image feature measurements seen at two time instances of the rig's motion (four images in all). In particular we are interested in the byproduct of this analysis providing a direct connection between the spatio-temporal derivatives of the images at two time instances and kinematics of the 3D motion of the Rig. We establish a fundamental result showing that 3 quadruples of point-line-line-line matches (i.e., point in the reference image and lines coincident with the corresponding points in the remaining three images) are sufficient for a unique linear solution for the kinematics of the rig. In other words, the projected instantaneous motion of "one and a half" 3D lines is sufficient for recovering the kinematics of the moving rig. In particular, spatio-temporal derivatives across 3 points are sufficient for a direct estimation of the rig's motion. Consequently, we describe a new direct estimation method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. Correspondences (optic flow) are not required as spatio-temporal derivative are used instead. One can then use the images from both pairs combined, to compute a dense depth map. Finally, since the basic equations are linear, we combine the contribution coming from all pixels in the image using a Least Squares approach.
Tensor Embedding of the Fundamental Matrix

We revisit the bilinear matching constraint between two perspective views of a 3D scene. Our objective is to represent the constraint in the same manner and form as the trilinear constraint among three views. The motivation is to establish a common terminology that bridges between the fundamental matrix F (associated with the bilinear constraint) and the trifocal tensor Τijk (associated with the trilinearities). By achieving this goal we can unify both the properties and the techniques introduced in the past for working with multiple views for geometric applications. 
 
Doing that we introduce a 3 × 3 × 3 tensor Fijk, we call the bifocal tensor, that represents the bilinear constraint. The bifocal and trifocal tensors share the same form and share the same contraction properties. By close inspection of the contractions of the bifocal tensor into matrices we show that one can represent the family of rank-2 homography matrices by [δ]×F where ffi is a free vector. We then discuss four applications of the new representation: (i) Quasi-metric viewing of projective data, (ii) triangulation, (iii) view synthesis, and (iv) recovery of camera ego-motion from a stream of views.
Threading Fundamental Matrices

We present a new function that operates on Fundamental matrices across a sequence of views. The operation, we call “threading”, connects two consecutive Fundamental matrices using the Trilinear tensor as the connecting thread. The threading operation guarantees that consecutive camera matrices are consistent with a unique 3D model, without ever recovering a 3D model. Applications include recovery of camera ego-motion from a sequence of views, image stabilization (plane stabilization) across a sequence, and multi-view image-based rendering.
Non-Rigid Parallax for 3D Linear Motion

We consider the problem of reconstructing the location of a moving 3D point seen from a monocular moving camera. Since the point is movingwhile the camera is moving, then even if the camera motion is known, it is impossible to reconstruct the 3D location of the point under general circumstances. However, we show that if the point is moving along a straight line, then the parameters of the line (and hence the 3D position of the point at each time instance) can be uniquely recovered, and by linear methods, from at least 5 views. Consequently, we propose a new approach for dealing with dynamic scenes (rich with moving objects) in which once the camera motion is recovered, the 3D trajectory (straight line) of the moving target can be recovered | even when the moving target consists of a single point.
g Sensors: What Can be Done With a Non- gid Vision Platform?

We describe the principles of building a moving vision platform (a Rig) that once calibrated can thereon selfadjust to changes in its internal configuration and maintain an Euclidean representation of the 30 world using only projective measurements. Formally, we address the question of how to obtain an invariant 30 projective representation from a dynamic collection of cameras. such as visual recognition by alignment, image transfer in Photogrammetry and image-based rendering in Computer Graphics in which a projective representation is sufficient (for example, [ 17, 2, 121). However, in mensuration, navigation and robot guidance tasks an Euclidean representation is necessary - and to that end a growing body of literature is dedicated to the problem of obtaining an Euclidean representation [7,4, 11, 22, 11. We divide the various approaches into the following classes: We show that the maximal generality is reached when the rig consists of 5 cameras whose center of projection remain $xed relative to each other during the motion. In other words, the non-rigid component motion may consist of change of internal parameters and relative camera orientations. The configuration reduces to 3 views when the Rig is built using a single physical camera with half-mirrors (beam-splitters) for creating 3 distinct views. We also briefly discuss 2-view configurations using hawmirrors and the principle behind adapting the conjguration to allow for zoom lenses in the system. The new research paradigm on non-rigid rigs (we term “Omni-Rig ’7 is applicable to the design of hion-based
On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) when the scene is a Linear Line Complex (set of lines in space intersecting at a common line). The LLC situation is only linearly degenerate, and one can obtain a unique solution when the admissibility constraints of the tensor are accounted for.
Omni-Rig sensors: what can be done with a non-rigid vision platform?

We describe the principles of building a moving vision platform (a Rig) that once calibrated can thereon self-adjust to changes in its internal configuration and maintain an Euclidean representation of the 3D world using only projective measurements. Formally, we address the question of how to obtain an invariant 3D projective representation from a dynamic collection of cameras. We show that the maximal generality is reached when the rig consists of 5 cameras whose center of projection remain fixed relative to each other during the motion. In other words, the non-rigid component motion may consist of change of internal parameters and relative camera orientations. The configuration reduces to 3 views when the Rig is built using a single physical camera with half-mirrors (beam-splitters) for creating 3 distinct views. We also briefly discuss 2-view configurations using half-mirrors and the principle behind adapting the configuration to allow for zoom lenses in the system. The new research paradigm on non-rigid rigs (we term "Omni-Rig") is applicable to the design of Vision-based sensors that after calibration can move in space while changing critical elements of their configuration-such as changing focus on the fly, zoom, relative camera orientation and inclination of focal plane to object's surface orientation-without the need for recalibration, i.e., using only projective calculations throughout its motion.
Ambiguity in reconstruction from images of six points

Let S be a set of six points in space, let /spl psi/ be any hyperboloid of one sheet containing S, and let I be a sequence of images of S taken by an uncalibrated camera moving over /spl psi/. Then reconstruction from I is subject to a three way ambiguity which is unbroken as long as the optical centre of the camera remains on /spl psi/. Let p be an image of S taken from a point on /spl psi/. The images 'near' p define a tangent space which splits into a direct sum W/sub p//spl oplus/N/sub p//spl oplus/F/sub p/, where W/sub p/ corresponds to images near p for which the ambiguity is maintained, N/sub p/ corresponds to images for which the ambiguity is broken and F/sub p/ corresponds to images which are physically impossible.
Novel view synthesis in tensor space

We present a new method for synthesizing novel views of a 3D scene from few model images in full correspondence. The core of this work is the derivation of a tensorial operator that describes the transformation from a given tensor of three views to a novel tensor of a new configuration of three views. By repeated application of the operator on a seed tensor with a sequence of desired virtual camera positions we obtain a chain of warping functions (tensors) from the set of model images to create the desired virtual views.
Unifying two-view and three-view geometry

The core of multiple-view geometry is governed by the fundamental matrix and the trilinear tensor. In this paper we unify both representations by rst deriving the fundamental matrix as a rank-2 trivalent tensor, and secondly by deriving a uniied set of operators that are transparent to the number of views. As a result, we show that the basic building block of the geometry of multiple views is a trivalent tensor that specializes to the fundamental matrix in the case of two views, and is the trilinear tensor (rank-4 triva-lent tensor) in case of three views. The properties of the tensor (geometric interpretation, contraction properties , etc.) are independent of the number of views (two or three). As a byproduct, every two-view algorithm can be considered as a degenerate three-view algorithm and three-view algorithms can work with either two or three images, all using one standard set of tensor operations. To highlight the usefulness of this paradigm we provide two practical applications. First we present a novel view synthesis algorithm that starts with the rank-2 tensor and seamlessly move to the general rank-4 trilinear tensor, all using one set of tensor operations. The second application is a camera stabilization algorithm, originally introduced for three views, now working with two views without any modi-cation.
Image-based view synthesis by combining trilinear tensors and learning techniques

We present a new method for rendering novel images of flexible 3D objects from a small number of example images in correspondence. The strength of the method is the ability to synthesize images whose viewing position is significantly far away from the viewing cone of the example images (“view extrapolation”), yet without ever modeling the 3D structure of the scene. The method relies on synthesizing a chain of “trilinear tensors” that governs the warping function from the example images to the novel image, together with a multi-dimensional interpolation function that synthesizes the non-rigid motions of the viewed object from the virtual camera position. We show that two closely spaced example images alone are sufficient in practice to synthesize a significant viewing cone, thus demonstrating the ability of representing an object by a relatively small number of model images — for the purpose of cheap and fast viewers that can run on standard hardware.