nils-herrmann/clean_scirepeval huggingface dataset:
Image-based View Synthesis

We present a new method for rendering novel images of exible 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 signi cantly 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 su cient in practice to synthesize a signi cant 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.  This report describes research done within the Arti cial Intelligence Laboratory and the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology. This research is sponsored by grants from ONR under contracts N00014-96-1-0342 and N00014-93-1-0385; by a grant from ONR/ARPA under contract N00014-92-J-1879 by the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program) and by grants ACTS AC 074 and VANGUARDUS-IS94-00120.
Model-based brightness constraints: on direct estimation of structure and motion

We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of B.K.P. Horn and E.J. 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 complete optical flow. We describe the advantages and limitations of this method which are then verified with experiments using real images.
Trilinear Tensor: The Fundamental Construct of Multiple-view Geometry and Its Applications

The topic of representation, recovery and manipulation of three-dimensional (3D) scenes from two-dimensional (2D) images thereof, provides a fertile ground for both intellectual theoretically inclined questions related to the algebra and geometry of the problem and to practical applications such as Visual Recognition, Animation and View Synthesis, recovery of scene structure and camera ego-motion, object detection and tracking, multi-sensor alignment, etc.
Tensorial Transfer: Representation of N > 3 Views of 3D scenes

The recently discovered \trilinear tensor" has been shown to play a similar role to the \funda-mental" matrix, but with three views instead of two views, in representing the relative motion parameters of an observer moving in the 3D projective world. The issue of a general representation for any number of views remains an open problem. The main result presented here is the closed-form concatenation of any number of views. The concatenation operation shows that N tensors are suucient for representing a set of N +2 views, i.e., the tensor of any triplet of views from the set can be generated in closed-form from an arbitrary collection of N tensors over this set. These concatenation operators may be useful in the context of image synthesis , image mosaicing and video compression.
Duality of Multi-Point and Multi-Frame Geometry: Fundamental Shape Matrices and Tensors

We provide a complete analysis of the geometry of N points in 1 image, employing a formalism in which multi-frame and multi-point geometries appear in symmetry: points and projections are interchangeable. We derive bilinear equations for 6 points, trilinear equations for 7 points, and quadrilinear equations for 8 points. The new equations are used to design new algorithms for the reconstruction of projective shape from many frames. Shape is represented by shape descriptors, which are sufficient for object recognition, and for the simulation of new images of the object. We further propose a linear shape reconstruction scheme which uses all the available data — all points and all frames — simultaneously. Unlike previous approaches, the equations developed here lead to direct and linear computation of shape, without going through the cameras' geometry.
Relative Affine Structure: Canonical Model for 3D From 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work-including Euclidean, projective and affine-in a natural and simple way, and introduces new, extremely simple algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.
Robust recovery of camera rotation from three frames

Computing camera rotation from image sequences can be used for image stabilization, and when the camera rotation is known the computation of translation and scene structure are much simplified as well. A robust approach for recovering camera rotation is presented, which does not assume any specific scene structure (e.g. no planar surface is required), and which avoids prior computation of the epipole. Given two images taken from two different viewing positions, the rotation matrix between the images can be computed from any three homography matrices. The homographies are computed using the trilinear tensor which describes the relations between the projections of a 3D point into three images. The entire computation is linear for small angles, and is therefore fast and stable. Iterating the linear computation can then be used to recover larger rotations as well.
Degenerate n Point Configura-tions of Three Views: Do Critical Surfaces Exist

When the geometry of 3D space is reconstructed from a pair of views, using the \Fundamental matrix" as the object of analysis, then it is known (as early as the 1940s) that there exists a \critical surface" for which the solution of 3-space is ambiguous. We show that when 3-space is reconstructed from a triplet of views, using the \Trilinear Tensor" as the object of analysis, there are no critical surfaces. In addition to theoretical interest of solving an open problem, this result has profound practical signiicance. The numerical instability associated with Structure from Motion is largely attributed to the existence of \critical volumes" that arise from the existence of critical surfaces coupled with errors in the image measurements. The lack of critical surfaces in the context of three views (provided that the trilinear tensor is used) suggests that better stability in the presence of errors can be gained.
Direct methods for estimation of structure and motion from three views

We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of Horn- and-Weldon 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 through simulation and experiments with real images.
The Rank 4 Constraint in Multiple (>=3) View Geometry

It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients . Further investigations have shown the existence of quadlinear forms across four views with the negative result that further views would not add any new constraints [3, 12, 5]. We show in this paper first general results on any number of views. Rather than seeking new constraints (which we know now is not possible) we seek connections across trilinear tensors of triplets of views. Two main results are shown: (i) trilinear tensors across m>3 views are embedded in a low dimensional linear subspace, (ii) given two views, all the induced homography matrices are embedded in a four-dimensional linear subspace. The two results, separately and combined, offer new possibilities of handling the consistency across multiple views in a linear manner (via factorization), some of which are further detailed in this paper.
Algebraic Functions For Recognition

In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment-yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks.
Shape tensors for efficient and learnable indexing

Multi-point geometry: The geometry of 1 point in N images under perspective projection has been thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point in 2, 3 and 4 frames respectively. The dual problem-the geometry of N points in 1 image-has been studied mostly in the context of object recognition, often assuming weak perspective or affine projection. We provide here a complete description of this problem. We employ a formalism in which multiframe and multi-point geometries appear in symmetry. Points and projections are interchangeable. We then derive bilinear equations for 6 points (dual to 3-frame geometry), trilinear equations for 7 points (dual to 3-frame geometry), and quadrilinear equations for 8 points (dual to the epipolar geometry). We show that the quadrilinear equations are dependent on the the bilinear and trilinear equations, and we show that adding more points will not generate any new equation. The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a database.
Trilinearity of three perspective views and its associated tensor

It has been established that certain trilinear forms of three perspective views give rise to a tensor of 27 intrinsic coefficients. We show in this paper that a permutation of the the trilinear coefficients produces three homography matrices (projective transformations of planes) of three distinct intrinsic planes, respectively. This, in turn, yields the result that 3D invariants are recovered directly-simply by appropriate arrangement of the tensor's coefficients. On a secondary level, we show new relations between fundamental matrix, epipoles, Euclidean structure and the trilinear tensor. On the practical side, the new results extend the existing envelope of methods of 3D recovery from 2D views-for example, new linear methods that cut through the epipolar geometry, and new methods for computing epipolar geometry using redundancy available across many views.<<ETX>>
Shape Tensors for Eecient and Learnable Indexing

Multi-point geometry: The geometry of 1 point in N images under perspective projection has been thoroughly investigated, identifying bilinear, trilinear, and quadrilinear relations between the projections of 1 point in 2, 3 and 4 frames respectively. The dual problem-the geometry of N points in 1 image-has been studied mostly in the context of object recognition , often assuming weak perspective or aane projection. We provide here a complete description of this problem. We employ a formalism in which multi-frame and multi-point geometries appear in symmetry: points and projections are interchangeable. We then derive bilinear equations for 6 points (dual to 4-frame geometry), trilinear equations for 7 points (dual to 3-frame geometry), and quadrilinear equations for 8 points (dual to the epipolar geometry). We show that the quadrilinear equations are dependent on the the bi-linear and trilinear equations, and we show that adding more points will not generate any new equation. Applications to reconstruction and recognition: The new equations are used to design new algorithms for the reconstruction of shape from many frames, and for learning invariant relations for indexing into a database. We describe algorithms which require matching 6 (or more) corresponding points from at least 4 images, 7 (or more) points from at least 3 images, or 8 (or more) points from at least 2 images. Unlike previous approaches, the equations developed here lead to direct and linear solutions without going through the cameras' geometry. Our nal linear shape computation uses all the available data { all points and all frames simultaneously: it uses a factorization of the matrix of invariant relations into 2 components of rank 4, a shape matrix and a coordinate-system matrix .
Fundamental Tensor: On the Geometry of Three Perspective Views

Reconstruction of 3D space from 2D images is generally a \2-view" problem. That is, the algebra and geometry of the problem is all contained in measurements across two views, the rest (i.e., when more than two views are available) is statistics. This paper embarks on the investigation of the algebra and geometry of three views. Based on the recent result 18] showing the existence of certain trilinear functions of three views with a corresponding tensor of 27 intrinsic coeecients, we derive a set of relations between the tensor and geometric invariants of the 3D world, intrinsic structures of two views (fundamental matrix and epipoles), and show the existence of new intrinsic structures (beside the tensor itself) associated with three views. On the practical side, the tensor ooers a host of new algorithms for recovering 3D information from 2D views. These methods cut through the epipolar geometry (i.e., three views are used simultaneously, rather than in pairs, reconstruction proceeds independently of epipolar geometry), make room for statistics (additional views can be incorporated to obtain further redundant equations, just like in traditional 2-view-based schemes), and generally exploit the information available from measurements across views in a more eecient manner than any technique based on 2-view geometry.
The study of 3D-from-2D using elimination

The paper unifies most of the current literature on 3D geometric invariants from point correspondences across multiple 2D views by using the tool of elimination from algebraic geometry. The technique allows one to predict results by counting parameters and reduces many complicated results obtained in the past (reconstructuon from two and three views, epipolar geometry from seven points, trilinearity of three views, the use of a priori 3D information such as bilateral symmetry, shading and color constancy, and more) into a few lines of reasoning each. The tool of Grobner base computation is used in the elimination process. In the process we obtain several results on N view geometry, and obtain a general result on invariant functions of 4 views and its corresponding quadlinear tensor: 4 views admit minimal sets of 16 invariant functions (of quadlinear forms) with 81 distinct coefficients that can be solved linearly from 6 corresponding points across 4 views. This result has non trivial implications to the understanding of N view geometry. We show a new result on single view invariants based on 6 points and show that certain relationships are impossible. One of the appealing features of the elimination approach is that it is simple to apply and does not require any understanding of the underlying 3D from 2D geometry and algebra.<<ETX>>
'IFilinearity 01 'lhree Yerspect ive

It has been established that certain trilinear froms of three perspective views give rise to a tensor of 27 intrinsic coefficients [ll]. We show in this paper that a permutation of the the trilinear coefficients produces three homograph y matrices (projective t ransfonn at ions of planes) of three distinct intrinsic planes, respectively. This, in turn, yields the result that 30 invariants are recovered directly - simply by appropriate arrangement of the tensor’s coefficients. On a secondary level, we show new relations between fundamental matrix, epipoles, Euclidean structure and the trilinear tensor. On the practical side, the new results extend the existing envelope of methods of 30 recovery from 20 views -for example, new linear methods that cut through the epipolar geometry, and new methods for computing epipolar geometry using redundancy available across many views.
Multiple-View Geometry and Photometry

The issue of how to represent and manipulate the information arising from a multitude of perspective pictures of a 3D scene is a recent and growing topic of interest. In this paper we present a summary account of up-to-date research, my own and with colleagues, on this topic, including: the trilinear constraints and associated tensor; the properties of the trilinear tensor and their relevance to camera geometry and invariance; rank deficiencies and N >4 multiple-view geometry; and the photometric duality in the form of the “Tensor Brightness Constraint”.
Fast protein classification with multiple networks

Support vector machines (SVMs) have been successfully used to classify proteins into functional categories. Recently, to integrate multiple data sources, a semidefinite programming (SDP) based SVM method was introduced. In SDP/SVM, multiple kernel matrices corresponding to each of data sources are combined with weights obtained by solving an SDP. However, when trying to apply SDP/SVM to large problems, the computational cost can become prohibitive, since both converting the data to a kernel matrix for the SVM and solving the SDP are time and memory demanding. Another application-specific drawback arises when some of the data sources are protein networks. A common method of converting the network to a kernel matrix is the diffusion kernel method, which has time complexity of O(n(3)), and produces a dense matrix of size n x n.



We propose an efficient method of protein classification using multiple protein networks. Available protein networks, such as a physical interaction network or a metabolic network, can be directly incorporated. Vectorial data can also be incorporated after conversion into a network by means of neighbor point connection. Similar to the SDP/SVM method, the combination weights are obtained by convex optimization. Due to the sparsity of network edges, the computation time is nearly linear in the number of edges of the combined network. Additionally, the combination weights provide information useful for discarding noisy or irrelevant networks. Experiments on function prediction of 3588 yeast proteins show promising results: the computation time is enormously reduced, while the accuracy is still comparable to the SDP/SVM method.


AVAILABILITY
Software and data will be available on request.
An Alignment Algorithm by Matching Fixed-Length Stem Fragments for Comparing RNA Sequences

The functions of non-coding RNAs are strongly related to their secondary structures, but it is known that a secondary structure prediction of a single sequences is not reliable. Therefore, we have to collect similar RNA sequences with a common secondary structure for the analyses of a new non-coding RNA without knowing the exact secondary structure itself. Therefore, the sequence comparison in searching similar RNAs should consider not only their sequence similarities but their potential secondary structures. The Sankoff’s algorithm predicts the common secondary structures of the sequences, but it is computationally too expensive to apply to largescale analyses. Because we often want to compare a large number of cDNA sequences or to search similar RNAs in the whole genome sequences, much faster algorithms are required. We propose a new method of comparing RNA sequences based on the structural alignments of the fixed-length fragments of the stem candidates. The implemented software, SCARNA (Stem Candidate Aligner for RNAs), is fast enough to apply to the long sequences in the large-scale analyses. The accuracy of the alignments is better or comparable to the much slower existing algorithms. The web server of SCARNA with graphical structural alignment viewer is available at http://www.scarna.org/ (It currently works only on Internet Explorer).
Image reconstruction by linear programming

One way of image denoising is to project a noisy image to the subspace of admissible images derived, for instance, by PCA. However, a major drawback of this method is that all pixels are updated by the projection, even when only a few pixels are corrupted by noise or occlusion. We propose a new method to identify the noisy pixels by /spl lscr//sub 1/-norm penalization and to update the identified pixels only. The identification and updating of noisy pixels are formulated as one linear program which can be efficiently solved. In particular, one can apply the /spl nu/ trick to directly specify the fraction of pixels to be reconstructed. Moreover, we extend the linear program to be able to exploit prior knowledge that occlusions often appear in contiguous blocks (e.g., sunglasses on faces). The basic idea is to penalize boundary points and interior points of the occluded area differently. We are also able to show the /spl nu/ property for this extended LP leading to a method which is easy to use. Experimental results demonstrate the power of our approach.
Selective integration of multiple biological data for supervised network inference

Inferring networks of proteins from biological data is a central issue of computational biology. Most network inference methods, including Bayesian networks, take unsupervised approaches in which the network is totally unknown in the beginning, and all the edges have to be predicted. A more realistic supervised framework, proposed recently, assumes that a substantial part of the network is known. We propose a new kernel-based method for supervised graph inference based on multiple types of biological datasets such as gene expression, phylogenetic profiles and amino acid sequences. Notably, our method assigns a weight to each type of dataset and thereby selects informative ones. Data selection is useful for reducing data collection costs. For example, when a similar network inference problem must be solved for other organisms, the dataset excluded by our algorithm need not be collected.



First, we formulate supervised network inference as a kernel matrix completion problem, where the inference of edges boils down to estimation of missing entries of a kernel matrix. Then, an expectation-maximization algorithm is proposed to simultaneously infer the missing entries of the kernel matrix and the weights of multiple datasets. By introducing the weights, we can integrate multiple datasets selectively and thereby exclude irrelevant and noisy datasets. Our approach is favorably tested in two biological networks: a metabolic network and a protein interaction network.


AVAILABILITY
Software is available on request.