nils-herrmann/clean_scirepeval huggingface dataset:
Sparse Spectral-based Feature Selection with Side Information

We address the problem of selecting a subset of the most relevant features from a set of sample data in cases where there are multiple (equally reasonable) solutions. In particular, this topic includes the suppression of one of the solutions given “side” data, i.e., when one is given information about undesired aspects of the data. Such situations often arise when there are several, even conflicting, dimensions to the data. For example, documents can be clustered based on topic, authorship or writing style; images of human faces can be clustered based on illumination conditions, facial expressions or by person identity; gene expressions levels can be clustered by pathologies or by correlations that also exist in other conditions, and so forth. We address this problem by extending the recently introduced algorithm for feature selection . The algorithm uses spectral properties of the affinity (or Laplacian) matrix of the input data sample to guide the search for a relevant subset of features (coordinates). The most relevant subset of coordinates is the one that induces the most coherent collection of clusters in the subspace defined by the selected coordinates. In this work we address the problem which arises when different coordinate selections induce equally good clusters in their respective subspaces. We derive a principled manner to represent unwanted cluster arrangements, such as “side” data in various forms, as part of the optimization functional for feature selection and also derive a topographical structure of all selected feature subsets.
Vision-based ACC with a single camera: bounds on range and range rate accuracy

This paper describes a vision-based adaptive cruise control (ACC) system which uses a single camera as input. In particular, we discuss how to compute the range and range-rate from a single camera and discuss how the imaging geometry affects the range and range rate accuracy. We determine the bound on the accuracy given a particular configuration. These bounds in turn determine what steps must be made to achieve good performance. The system has been implemented on a test vehicle and driven on various highways over thousands of miles.
Revisiting Single-View Shape Tensors: Theory and Applications

Given the projection of a sufficient number of points it is possible to algebraically eliminate the camera parameters and obtain view invariant functions of image coordinates and space coordinates. These single view invariants have been introduced in the past, however, they are not as well understood as their dual multi-view tensors. In this paper we revisit the dual tensors (bilinear, trilinear and quadlinear), both the general and the reference-plane reduced version, and describe the complete set of synthetic constraints, properties of the tensor slices, reprojection equations, non-linear constraints and reconstruction formulas. We then apply some of the new results, such as the dual reprojection equations, for multi-view point tracking under occlusions.
Manifold pursuit: a new approach to appearance based recognition

Manifold pursuit extends principal component analysis to be invariant to a desired group of image-plane transformations of an ensemble of un-aligned images. We derive a simple technique for projecting a misaligned target image onto the linear subspace defined by the superpositions of a collection of model images. We show that it is possible to generate a fixed projection matrix which would separate the projected image into the aligned projected target and a residual image which accounts for the mis-alignment. An iterative procedure is then introduced for eliminating the residual image and leaving the correct aligned projected target image. Taken together, we demonstrate a simple and effective technique for obtaining invariance to image-plane transformations within a linear dimensionality reduction approach.
Ranking with Large Margin Principle: Two Approaches

We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to v-SVM when the number of classes k - 2. Both approaches are optimal in size of 2l where l is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.
On Representation Theory in Computer Vision Problems

We introduce the following general question: Let V be a complex n-dimensional space and for m k consider the GL V -module V n m k V m defined by V n m k f v vm V m dimSpanfv vmg k g We would like to determine dimV n m k for any choice of n m k. This question appears in various disguises in computer vision problems where the constraints of a multi-linear problem occupy a lowdimensional subspace. We discuss two such problems: analysis of constraints in single view indexing functions (the 8-point shape tensor), and the analysis of the constraints in dynamic P n P alignments, i.e., where the point sets are allowed to move within a k-dimensional subspace while the n-dimensional space is being multiply projected (multiple views) onto copies of the m-dimensional space. We then derive the solution to the general problem using tools from representation theory.
Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces

Principal Component Analysis (PCA)is one of the most popular techniques for dimensionality reduction of multivariate data points with application areas covering many branches of science. However, conventional PCA handles the multivariate data in a discrete manner only, i.e., the covariance matrix represents only sample data points rather than higher-order data representations.In this paper we extend conventional PCA by proposing techniques for constructing the covariance matrix of uniformly sampled continuous regions in parameter space. These regions include polytops defined by convex combinations of sample data, and polyhedral regions defined by intersection of half spaces. The applications of these ideas in practice are simple and shown to be very effective in providing much superior generalization properties than conventional PCA for appearance-based recognition applications.
Taxonomy of Large Margin Principle Algorithms for Ordinal Regression Problems

We discuss the problem of ranking instances where an instance is associated with an integer from 1 to k. In other words, the specialization of the general multi-class learning problem when there exists an ordering among the instances — a problem known as “ordinal regression” or “ranking learning”. This problem arises in various settings both in visual recognition and other information retrieval tasks. In the context of applying a large margin principle to this learning problem, we introduce two main approaches for implementing the large margin optimization criteria for k margins. The first is the “fixed margin” policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k different margins where the sum of margins is maximized, thus effectively having the solution biased towards the pairs of neighboring classes which are the farthest apart from each other. This approach is shown to reduce to SVM when the number of classes k . Both approaches are optimal in size (of the dual functional) of l where l is the total number of training examples. Experiments performed on visual classification and “collaborative filtering” show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification.
On Projection Matrices Pk-> P2k=3, ..., 6, and their Applications in Computer Vision

Projection matrices from projective spaces P 3 to P 2 have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings P k → P 2 , k = 3, 4, 5, 6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.
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 trifocal 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 across a sequence, and multi-view image based rendering.
Time-varying shape tensors for scenes with multiply moving points

We derive single view indexing functions for dynamic scenes - where dynamic is defined as a scene consisting of multiply moving points each moving independently with constant velocity. The indexing functions we derive are view independent and form a generalization of the "shape tensors" associated with rigid scenes by introducing a time-varying parameter We derive those indexing functions under full 3D projective, 3D affine, and various reduced configurations. The indexing functions were implemented and tested for matching against objects for which their non-rigid motion is an intrinsic part of their character - human gait recognition and hand gesture identification are the two chosen application examples.
The Quotient Image: Class-Based Re-Rendering and Recognition with Varying Illuminations

The paper addresses the problem of "class-based" image-based recognition and rendering with varying illumination. The rendering problem is 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, re-render the input image to simulate new illumination conditions. The class-based recognition problem is similarly defined: Given a single image of an object in a database of images of other objects, some of them multiply sampled under varying illumination, identify (match) any novel image of that object under varying illumination with the single image of that object in the database. We focus on Lambertian surface classes and, in particular, the class of human faces. The key result in our approach is based on a definition of an illumination invariant signature image which enables an analytic generation of the image space with varying illumination. We show that a small database of objects-in our experiments as few as two objects-is sufficient for generating the image space with varying illumination of any new object of the class from a single input image of that object. In many cases, the recognition results outperform by far conventional methods and the re-rendering is of remarkable quality considering the size of the database of example images and the mild preprocess required for making the algorithm work.
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 eight-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 3D deviation of the surface from a virtual quadric surface. The applications include image morphing, model building, image stabilization, and disparate view correspondence.
Affine 3-D reconstruction from two projective images of independently translating planes

Consider two views of a multi-body scene consisting of k planar bodies moving in pure translation one relative to the other. We show that the fundamental matrices, one per body, live in a 3-dimensional subspace, which when represented as a step-3 extensor is the common transversal on the collection of extensors defined by the homograph matrices H/sub 1/,...,H/sub k/ of the moving planes. We show that as much as five bodies are necessary for recovering the common transversal from the homograph matrices, from which we show how to recover the fundamental matrices and the affine calibration between the two cameras.
Multi-frame infinitesimal motion model for the reconstruction of (dynamic) scenes with multiple linearly moving objects

We introduce new small-motion multi-frame equations applicable to the reconstruction of dynamic scenes in which points are allowed to move along straight-line paths with constant velocity. The motion equations apply to both static and dynamic points, thus prior segmentation is not necessary. We present a reconstruction algorithm of camera motion, scene structure, and point trajectories embedded into a multi-frame factorization principle which requires the minimum of 11 images and 7 points (out of which at feast 3 are dynamic).
Linear image coding for regression and classification using the tensor-rank principle

Given a collection of images (matrices) representing a "class" of objects we present a method for extracting the commonalities of the image space directly from the matrix representations (rather than from the vectorized representation which one would normally do in a PCA approach, for example). The general idea is to consider the collection of matrices as a tensor and to look for an approximation of its tensor-rank. The tensor-rank approximation is designed such that the SVD decomposition emerges in the special case where all the input matrices are the repeatition of a single matrix. We evaluate the coding technique both in terms of regression, i.e., the efficiency of the technique for functional approximation, and classification. We find that for regression the tensor-rank coding, as a dimensionality reduction technique, significantly outperforms other techniques like PCA. As for classification, the tensor-rank coding is at is best when the number of training examples is very small.
On Projection Matrices

Projection matrices from projective spaces P to P have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings P ! P, k = 4; 5; 6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices and methods for extracting the (nonrigid) structure and motion for each application.
Two-body segmentation from two perspective views

We consider a scene containing two independently and generally moving objects, viewed by two general perspective views. Using matching points arising from both objects simultaneously we derive a geometrical constraint, applicable to points from both objects, we call the segmentation matrix. We then use this constraint in order to recover the fundamental matrices associated with, each object, or simply to segment the scene into the two objects. Moreover, when the two bodies move in pure translation relative to each other we can both segment the scene and recover the affine calibration (homography at infinity) of the camera geometry. Unlike algorithms suggested in the past we need only two images, we work with general projective cameras (rather than affine or orthographic) and with general body motion, and no prior information beyond point matches is required.
Omni-rig: linear self-recalibration of a rig with varying internal and external parameters

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. We term this calibration paradigm "Omni-Rig". We assume that after calibration the cameras may change critical elements of their configuration, including internal parameters and centers of projection. Theoretically we show that knowing only the rotations between a set of cameras is sufficient for Euclidean calibration even with varying internal parameters and unknown translations. No other information of the world is required.
Multiple view geometry of non-planar algebraic curves

We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the derivation of the extended Kruppa's equations which are responsible for describing the epipolar constraint of two projections of a general (non-planar) algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus. We then establish new results on the reconstruction of general algebraic curves from multiple views. We address three different representations of curves: (i) the regular point representation for which we show that the reconstruction from two views of a curve of degree d admits two solutions, one of degree d and the other of degree d(d-1), (ii) the dual space representation (tangents) for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus, and (iii) a new representation (to computer vision) based on the set of lines meeting the curve which does not require any curve fitting in image space, for which we also derive lower bounds for the number of views necessary for reconstruction as a function of the curve degree alone.
On projection matrices P/sup k//spl rarr/P/sup 2/, k=3,...,6, and their applications in computer vision

Projection matrices from projective spaces P/sup 3/ to P/sup 2/ have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings P/sup k//spl rarr/P/sup 2/, k=4,5,6 for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices and methods for extracting the (non-rigid) structure and motion for each application.
Omni-Rig: Linear Self-Recalibration of a Rig with Varying Internal and External Parameters

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. We term this calibration paradigm “OmniRig”. We assume that after calibration the cameras may change critical elements of their configuration, including internal parameters and centers of projection. Theoretically we show that knowing only the rotations between a set of cameras is sufficient for Euclidean calibration even with varying internal parameters and unknown translations. No other information of the world is required.
Join tensors: On 3D-to-3D alignment of dynamic sets

Introduces a family of 4/spl times/4/spl times/4 tensors, referred to as "join tensors" or Jtensors for short, which perform "3D to 3D" alignment between coordinate systems of sets of dynamic 3D points. 3D configurations of points are obtained by a 3D measuring device (such as a structured light or laser range sensor, or a stereo rig) at times t/sub 1/, t/sub 2/, t/sub 3/ from different viewing positions in addition to the motion of the sensor the points are also allowed to move in space; each point can move along an arbitrary straight-line path-we refer to this situation as "dynamic". The problem is to recover the motion of the sensor given the 3D correspondences of the points over time. We introduce Jtensors to capture the problem described above. Three observations P, P', P'' of a point measured at three time instants contribute a linear measurement to the Jtensor, regardless of whether the point has moved in space or has remained stationary while the sensor has changed position.
On the synthesis of dynamic scenes from reference views

We consider a scene, containing many objects moving with constant velocity along straight line paths, seen from three reference viewpoints at three different times. The scene may even consist only of moving objects with no static features. We wish to create a new image sequence showing the scene from arbitrary viewing position and arbitrary time. We make use of a newly discovered tool, the "dual Htensor" that connects together three views of a coplanar configuration of (unlabeled) static and moving points. The newly synthesized images use constant velocity in the world to achieve realistic and physically correct images.
On the Structure and Properties of the Quadrifocal Tensor

The quadrifocal tensor which connects image measurements along 4 views is not yet well understood as its counterparts the fundamental matrix and the trifocal tensor. This paper establishes the structure of the tensor as an "epipole-homography" pairing Qijkl = v′j Hikl - v″k Hijl + v‴l Hijk where v′, v″, v‴ are the epipoles in views 2,3,4, H is the "homography tensor" the 3-view analogue of the homography matrix, and the indices i, j, k, l are attached to views 1,2,3,4 respectively -- i.e., Hikl is the homography tensor of views 1,3,4. 
 
In the course of deriving the structure Qijkl we show that Linear Line Complex (LLC) mappings are the basic building block in the process.We also introduce a complete break-down of the tensor slices: 3×3×3 slices are homography tensors, and 3×3 slices are LLC mappings. Furthermore, we present a closed-form formula of the quadrifocal tensor described by the trifocal tensor and fundamental matrix, and also show how to recover projection matrices from the quadrifocal tensor. We also describe the form of the 51 non-linear constraints a quadrifocal tensor must adhere to.
On Calibration and Reconstruction from Planar Curves

We describe in this paper closed-form solutions to the following problems in multi-view geometry of n'th order curves: (i) recovery of the fundamental matrix from 4 or more conic matches in two views, (ii) recovery of the homography matrix from a single n'th order (n ≥ 3) matching curve and, in turn, recovery of the fundamental matrix from two matching n'th order planar curves, and (iii) 3D reconstruction of a planar algebraic curve from two views. 
 
Although some of these problems, notably (i) and (iii), were introduced in the past [15,3], our derivations are analytic with resulting closed form solutions. We have also conducted synthetic experiments on (i) and real image experiments on (ii) and (iii) with subpixel performance levels, thus demonstrating the practical use of our results.