nils-herrmann/clean_scirepeval huggingface dataset:
Three-View Multibody Structure from Motion

We propose a geometric approach to 3D motion segmentation from point correspondences in three perspective views. We demonstrate that after applying a polynomial embedding to the point correspondences, they become related by the so-called multibody trilinear constraint and its associated multibody trifocal tensor, which are natural generalizations of the trilinear constraint and the trifocal tensor to multiple motions. We derive a rank constraint on the embedded correspondences from which one can estimate the number of independent motions, as well as linearly solve for the multibody trifocal tensor. We then show how to compute the epipolar lines associated with each image point from the common root of a set of univariate polynomials and the epipoles by solving a pair of plane clustering problems using Generalized Principal Component Analysis (GPCA). The individual trifocal tensors are then obtained from the second-order derivatives of the multibody trilinear constraint. Given epipolar lines and epipoles or trifocal tensors, one can immediately obtain an initial clustering of the correspondences. We use this clustering to initialize an iterative algorithm that alternates between the computation of the trifocal tensors and the segmentation of the correspondences. We test our algorithm on various synthetic and real scenes and compare it with other algebraic and iterative algorithms.
L1 rotation averaging using the Weiszfeld algorithm

We consider the problem of rotation averaging under the L1 norm. This problem is related to the classic Fermat-Weber problem for finding the geometric median of a set of points in IRn. We apply the classical Weiszfeld algorithm to this problem, adapting it iteratively in tangent spaces of SO(3) to obtain a provably convergent algorithm for finding the L1 mean. This results in an extremely simple and rapid averaging algorithm, without the need for line search. The choice of L1 mean (also called geometric median) is motivated by its greater robustness compared with rotation averaging under the L2 norm (the usual averaging process). We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global L1 optimum) and multiple rotation averaging (for which no such proof exists). The algorithm is demonstrated to give markedly improved results, compared with L2 averaging. We achieve a median rotation error of 0.82 degrees on the 595 images of the Notre Dame image set.
Identifying Anatomical Shape Difference by Regularized Discriminative Direction

Identifying the shape difference between two groups of anatomical objects is important for medical image analysis and computer-aided diagnosis. A method called ldquodiscriminative directionrdquo in the literature has been proposed to solve this problem. In that method, the shape difference between groups is identified by deforming a shape along the discriminative direction. This paper conducts a thorough study about inferring this discriminative direction in an efficient and accurate way. First, finding the discriminative direction is reformulated as a preimage problem in kernel-based learning. This provides a complementary but conceptually simpler solution than the previous method. More importantly, we find that a shape deforming along the original discriminative direction cannot faithfully maintain its anatomical correctness. This unnecessarily introduces spurious shape differences and leads to inaccurate analysis. To overcome this problem, this paper further proposes a regularized discriminative direction by requiring a shape to conform to its underlying distribution when it deforms. Two different approaches are developed to impose the regularization, one from the perspective of probability distributions and the other from a geometric point of view, and their relationship is discussed. After verifying their superior performance through controlled experiments, we apply the proposed methods to detecting and localizing the hippocampal shape difference between sexes. We get results consistent with other independent research, providing a more compact representation of the shape difference compared with the established discriminative direction method.
Motion estimation for multi-camera systems using global optimization

We present a motion estimation algorithm for multi-camera systems consisting of more than one calibrated camera securely attached on a moving object. So, they move all together, but do not require to have overlapping views across the cameras. The geometrically optimal solution of the motion for the multi-camera systems under Linfin norm is provided in this paper using a global optimization technique which has been introduced recently in the computer vision research field. Taking advantage of an optimal estimate of the essential matrix through searching rotation space, we provide the optimal solution for translation by using linear programming and branch & bound algorithm. Synthetic and real data experiments are conducted, and they show more robust and improved performance than the previous methods.
Global Optimization through Searching Rotation Space and Optimal Estimation of the Essential Matrix

This paper extends the set of problems for which a global solution can be found using modern optimization methods. In particular, the method is applied to estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose under a geometric cost function, in this case, the L-infinity cost function. Convex optimization techniques has been shown to provide optimal solutions to many of the common problems in structure from motion. However, they do not apply to problems involving rotations. In this paper, we introduce a search method that allows such problems to be solved optimally. Apart from the essential matrix, the algorithm is applied to the camera pose problem, providing an optimal algorithm.
L/sub /spl infin// minimization in geometric reconstruction problems

We investigate the use of the L/sub /spl infin// cost function in geometric vision problems. This cost function measures the maximum of a set of model-fitting errors, rather than the sum-of-squares, or L/sub 2/ cost function that is commonly used (in least-squares fitting). We investigate its use in two problems; multiview triangulation and motion recovery from omnidirectional cameras, though the results may also apply to other related problems. It is shown that for these problems the L/sub /spl infin// cost function is significantly simpler than the L/sub 2/ cost. In particular L/sub /spl infin// minimization involves finding the minimum of a cost function with a single local (and hence global) minimum on a convex parameter domain. The problem may be recast as a constrained minimization problem and solved using commonly available software. The optimal solution was reliably achieved on problems of small dimension.
Keynote lecture 2: “Riemannian manifolds, kernels and learning”

I will talk about recent results from a number of people in my group on Riemannian manifolds in computer vision. In many Vision problems Riemannian manifolds come up as a natural model. Data related to a problem can be naturally represented as a point on a Riemannian manifold. This talk will give an intuitive introduction to Riemannian manifolds, and show how they can be applied in many situations. Manifolds of interest include the manifold of Positive Definite matrices and the Grassman Manifolds, which have a role in object recognition and classification, and the Kendall shape manifold, which represents the shape of 2D objects. Of particular interest is the question of when one can define positive-definite kernels on Riemannian manifolds. This would allow the application of kernel techniques of SVMs, Kernel FDA, dictionary learning etc directly on the manifold.
A framework for generating realistic synthetic sequences of total internal reflection fluorescence microscopy images

Since generation of reliable ground truth annotation of fluorescence microscopy sequences is usually a laborious and expensive task, many proposed detection and tracking methods have been evaluated using synthetic data with known ground truth. However, differences between real and synthetic images may lead to inaccurate judgment about the performance of an algorithm. In this paper, we present a framework for generating realistic synthetic sequences of total internal reflection fluorescence microscope (TIRFM) through simulation of the image formation process and accurate measurement and dynamic models. The sequences generated using this framework appropriately reflect the complexities existing in real TIRFM sequences.
Projective reconstruction from line correspondences

The paper gives a practical rapid algorithm for doing projective reconstruction of a scene consisting of a set of lines seen in three or more images with uncalibrated cameras. The algorithm is evaluated on real and ideal data to determine its performance in the presence of varying degrees of noise. By carefully consideration of sources of error, it is possible to get accurate reconstruction with realistic levels of noise. The algorithm can be applied to images from different cameras or the same camera. For images with the same camera with unknown calibration, it is possible to do a complete Euclidean reconstruction of the image. This extends to the case of uncalibrated cameras previous results on scene reconstruction from lines,.<<ETX>>
Verifying global minima for L2 minimization problems

We consider the least-squares (L2) triangulation problem and structure-and-motion with known rotatation, or known plane. Although optimal algorithms have been given for these algorithms under an L-infinity cost function, finding optimal least-squares (L2) solutions to these problems is difficult, since the cost functions are not convex, and in the worst case can have multiple minima. Iterative methods can usually be used to find a good solution, but this may be a local minimum. This paper provides a method for verifying whether a local-minimum solution is globally optimal, by providing a simple and rapid test involving the Hessian of the cost function. In tests of a data set involving 277,000 independent triangulation problems, it is shown that the test verifies the global optimality of an iterative solution in over 99.9% of the cases.
A silicon compiler for digital signal processing: Methodology, implementation, and applications

This paper describes a fully integrated silicon compilation tool geared towards digital signal processing applications. The silicon compiler presented here uses a bit-serial architecture with a 1.25- µm CMOS cell library. It accepts as its input a high-level description language tailored for digital signal processing algorithms. The language supports the basic signal processing constructs such as multiplication, addition, subtraction, sample delays, logical operators, relational operators, as well as a conditional assignment. The compiler is equipped with behavioral, logic, and fault simulators, and performs placement and routing. The paper also details the use of the silicon compiler for the implementation of classical DSP algorithms: digital filters, FFT, programmable filters, as well as other more specialized applications such as adaptive algorithms and waveform synthesis. Moreover, some techniques are presented to implement more complex mathematical functions commonly used in DSP. The results of chip designs using the compiler and its impact on future designs are highlighted.
Multi-Target Tracking With Time-Varying Clutter Rate and Detection Profile: Application to Time-Lapse Cell Microscopy Sequences

Quantitative analysis of the dynamics of tiny cellular and sub-cellular structures, known as particles, in time-lapse cell microscopy sequences requires the development of a reliable multi-target tracking method capable of tracking numerous similar targets in the presence of high levels of noise, high target density, complex motion patterns and intricate interactions. In this paper, we propose a framework for tracking these structures based on the random finite set Bayesian filtering framework. We focus on challenging biological applications where image characteristics such as noise and background intensity change during the acquisition process. Under these conditions, detection methods usually fail to detect all particles and are often followed by missed detections and many spurious measurements with unknown and time-varying rates. To deal with this, we propose a bootstrap filter composed of an estimator and a tracker. The estimator adaptively estimates the required meta parameters for the tracker such as clutter rate and the detection probability of the targets, while the tracker estimates the state of the targets. Our results show that the proposed approach can outperform state-of-the-art particle trackers on both synthetic and real data in this regime.
An L∞ approach to structure and motion problems in ID-vision

The structure and motion problem of multiple one- dimensional projections of a two-dimensional environment is studied. One-dimensional cameras have proven useful in several different applications, most prominently for autonomous guided vehicles, but also in ordinary vision for analysing planar motion and the projection of lines. Previous results on one-dimensional vision are limited to classifying and solving minimal cases, bundle adjustment for finding local minima to the structure and motion problem and linear algorithms based on algebraic cost functions. In this paper, we present a method for finding the global minimum to the structure and motion problem using the max norm of reprojection errors. We show how the optimal solution can be computed efficiently using simple linear programming techniques. The algorithms have been tested on a variety of different scenarios, both real and synthetic, with good performance. In addition, we show how to solve the multiview triangulation problem, the camera pose problem and how to dualize the algorithm in the Carlsson duality sense, all within the same framework.
Handling Significant Scale Difference for Object Retrieval in a Supermarket

We propose an object retrieval application which can retrieve user specified objects from a big supermarket. Significant and unpredictable scale difference between the query and the database image is the major obstacle encountered. The widely used local invariant features show their deficiency in such an occasion. To improve the situation, we first design a new weighting scheme which can assess the repeatability of local features against scale variance. Also, another method which deals with scale difference through retrieving a query under multiple scales is also developed. Our methods have been tested on a real image database collected from a local supermarket and outperform the existing local invariant feature based image retrieval approaches. A new spatial check method is also briefly discussed.
Linear pushbroom cameras

Modeling and analyzing pushbroom sensors commonly used in satellite imagery is difficult and computationally intensive due to the motion of an orbiting satellite with respect to the rotating Earth, and the nonlinearity of the mathematical model involving orbital dynamics. In this paper, a simplified model of a pushbroom sensor (the linear pushbroom model) is introduced. It has the advantage of computational simplicity while at the same time giving very accurate results compared with the full orbiting pushbroom model. Besides remote sensing, the linear pushbroom model is also useful in many other imaging applications. Simple noniterative methods are given for solving the major standard photogrammetric problems for the linear pushbroom model: computation of the model parameters from ground-control points; determination of relative model parameters from image correspondences between two images; and scene reconstruction given image correspondences and ground-control points. The linear pushbroom model leads to theoretical insights that are approximately valid for the full model as well. The epipolar geometry of linear pushbroom cameras is investigated and shown to be totally different from that of a perspective camera. Nevertheless, a matrix analogous to the fundamental matrix of perspective cameras is shown to exist for linear pushbroom sensors. From this it is shown that a scene is determined up to an affine transformation from two views with linear pushbroom cameras.
A rapid-prototyping environment for digital-signal processors

A description is given of the Diodes system, a complete rapid prototyping, debugging, and test environment including both hardware and software, for the design of digital-signal-processing chips. The test circuitry in Diodes differs from that in many systems, including those based on boundary scan, by offering full-speed circuit testing and the observation of internal nodes during real time. Diodes also achieves nearly 100% fault coverage because chips are composed of numerous chunks, each of which is tested exhaustively. The discussion covers the high-density interconnection technology and the concepts on which Diodes is based, two types of chips that have been designed, fabricated, and tested for Diodes: module assembly and fabrication; synthesis software; on-chip testing; Diodes test circuitry; test modes; and hardware and software debugging. Diodes is compared with other testing approaches and other rapid prototyping systems.<<ETX>>
Plane-based projective reconstruction

A linear method for computing a projective reconstruction from a large number of images is presented and then evaluated. The method uses planar homographies between views to linearize the resecting of the cameras. Constraints based on the fundamental matrix, trifocus tensor or quadrifocal tensor are used to derive relationship between the position vectors of all the cameras at once. The resulting set of equations are solved using a SVD. The algorithm is computationally efficient as it is linear in the number of matched points used. A key feature of the algorithm is that all of the images are processed simultaneously, as in the Sturm-Triggs factorization method, but it differs in not requiring that all points be visible in all views. An additional advantage is that it works with any mixture of line and point correspondence through the constraints these impose on the multilinear tensors. Experiments on both synthetic and real data confirm the method's utility.
Camera calibration for 2.5-D X-ray metrology

This paper presents a new methodology for camera calibration of stereo X-ray projections. The image acquisition systems typically used in nondestructive evaluation result in views that are orthographic along one image axis and perspective along the other. A camera model for this sensing geometry, called the linear pushbroom model, is described. Four methods of calibration, which make different assumptions about what is known about the camera parameters, are presented and compared.
Motion from 3D line correspondences: linear and nonlinear solutions

We address the problem of aligning two reconstructions of lines and cameras in projective, affine, metric or Euclidean space. We propose several 3D (three-dimensional) and image-related linear algorithms. The result can be used to initialize the nonlinear minimization of several proposed error functions, as well as the maximum likelihood estimator that we derive. We evaluate and compare our algorithms to existing ones using simulated and real data.
Convex Optimization for Deformable Surface 3-D Tracking

3-D shape recovery of non-rigid surfaces from 3-D to 2-D correspondences is an under-constrained problem that requires prior knowledge of the possible deformations. State-of-the-art solutions involve enforcing smoothness constraints that limit their applicability and prevent the recovery of sharply folding and creasing surfaces. Here, we propose a method that does not require such smoothness constraints. Instead, we represent surfaces as triangulated meshes and, assuming the pose in the first frame to be known, disallow large changes of edge orientation between consecutive frames, which is a generally applicable constraint when tracking surfaces in a 25 frames- per-second video sequence. We will show that tracking under these constraints can be formulated as a Second Order Cone Programming feasibility problem. This yields a convex optimization problem with stable solutions for a wide range of surfaces with very different physical properties.
Memory Efficient Max Flow for Multi-label Submodular MRFs

Multi-label submodular Markov Random Fields (MRFs) have been shown to be solvable using max-flow based on an encoding of the labels proposed by Ishikawa, in which each variable Xi is represented by l nodes (where l is the number of labels) arranged in a column. However, this method in general requires 2 l2 edges for each pair of neighbouring variables. This makes it inapplicable to realistic problems with many variables and labels, due to excessive memory requirement. In this paper, we introduce a variant of the max-flow algorithm that requires much less storage. Consequently, our algorithm makes it possible to optimally solve multi-label submodular problems involving large numbers of variables and labels on a standard computer.
An Efficient Hidden Variable Approach to Minimal-Case Camera Motion Estimation

In this paper, we present an efficient new approach for solving two-view minimal-case problems in camera motion estimation, most notably the so-called five-point relative orientation problem and the six-point focal-length problem. Our approach is based on the hidden variable technique used in solving multivariate polynomial systems. The resulting algorithm is conceptually simple, which involves a relaxation which replaces monomials in all but one of the variables to reduce the problem to the solution of sets of linear equations, as well as solving a polynomial eigenvalue problem (polyeig). To efficiently find the polynomial eigenvalues, we make novel use of several numeric techniques, which include quotient-free Gaussian elimination, Levinson-Durbin iteration, and also a dedicated root-polishing procedure. We have tested the approach on different minimal cases and extensions, with satisfactory results obtained. Both the executables and source codes of the proposed algorithms are made freely downloadable.
Computing matched-epipolar projections

A new method is given for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of matched epipolar projections. These are projections in which the epipolar lines run parallel with the x-axis and disparities between the images are in the x-direction only. The method is based on an examination of the essential matrix of Longuet-Higgins (1981), which describes the epipolar geometry of the image pair. The approach taken is consistent with that advocated by O. Faugeras (1992) of avoiding camera calibration. A matrix called the epipolar transformation matrix is defined. It is used to determine a pair of 2-D projective transforms to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2-D projective transformation, which allows very fast resampling, as well as subsequent simplification in identifying matched points and in scene reconstruction.<<ETX>>
Use of digit-serial computation to create fault-tolerant designs

It is shown how digit-serial computation may be used to provide a degree of fault-tolerance in linear computations in cases where parallelism cannot be used, because of excessive cost. By splitting a parallel input stream into several bit-serial streams and using one extra stream for error checking, it is possible to detect intermittent and permanent faults in the circuit. The proposed method is useful for digital implementation of filters and other linear circuits in cases where throughput requirements preclude the use of parallelism. By using this method, it is possible to achieve fault-detection with a modest increase in hardware.<<ETX>>