Multiple images of a scene are related through 2D#3D view transformations and linear and non-linear camera transformations. In the traditional techniques to compute these transformations, especially the ones relying on direct intensity gradients, one image and its coordinate system have been assumed to be ideal and distortion free. In this paper, we present an algorithm for true multiimage alignment that does not rely on the measurements of a reference image being distortion free. The algorithm is developed to speci#cally align and mosaic images using parametric transformations in the presence of lens distortion. When lens distortion is present none of the images can be assumed to be ideal. In our formulation, all the images are modeled as intensity measurements represented in their respective coordinate systems, each of which is related to an ideal coordinate system through an interior camera transformation and an exterior view transformation. The goal of the accompanying algorithm is...

A bugbear of uncalibrated stereo reconstruction is that cameras which deviate from the pinhole model have to be pre-calibrated in order to correct for nonlinear lens distortion. If they are not, and point correspondence is attempted using the uncorrected images, the matching constraints provided by the fundamental matrix must be set so loose that point matching is significantly hampered. This paper shows how linear estimation of the fundamental matrix from two-view point correspondences may be augmented to include one term of radial lens distortion. This is achieved by (1) changing from the standard radiallens model to another which (as we show) has equivalent power, but which takes a simpler form in homogeneous coordinates, and (2) expressing fundamental matrix estimation as a Quadratic Eigenvalue Problem (QEP), for which efficient algorithms are well known. I derive the new estimator, and compare its performance against bundle-adjusted calibration-grid data. The new estimator is fast enough to be included in a RANSAC-based matching loop, and we show cases of matching being rendered possible by its use. I show how the same lens can be calibrated in a natural scene where the lack of straight lines precludes most previous techniques. The modification when the multi-view relation is a planar homography or trifocal tensor is described. 1.

This tutorial reviews image alignment and image stitching algorithms. Image alignment algorithms can discover the correspondence relationships among images with varying degrees of overlap. They are ideally suited for applications such as video stabilization, summarization, and the creation of panoramic mosaics. Image stitching algorithms take the alignment estimates produced by such registration algorithms and blend the images in a seamless manner, taking care to deal with potential problems such as blurring or ghosting caused by parallax and scene movement as well as varying image exposures. This tutorial reviews the basic motion models underlying alignment and stitching algorithms, describes effective direct (pixel-based) and feature-based alignment algorithms, and describes blending algorithms used to produce seamless mosaics. It ends with a discussion of open research problems in the area. 1

The thesis investigates the problem of how information contained in multiple, overlapping images of the same scene may be combined to produce images of superior quality. This area, generically titled frame fusion, offers the possibility of reducing noise, extending the field of view, removal of moving objects, removing blur, increasing spatial resolution and improving dynamic range. As such, this research has many applications in fields as diverse as forensic image restoration, computer generated special effects, video image compression, and digital video editing. An essential enabling step prior to performing frame fusion is image registration, by which an accurate estimate of the point-to-point mapping between views is computed. A robust and efficient algorithm is described to automatically register multiple images using only information contained within the images themselves. The accuracy of this method, and the statistical assumptions upon which it relies, are investigated empirically. Two forms of frame-fusion are investigated. The first is image mosaicing, which is the alignment of multiple images into a single composition representing part of a 3D scene.

We describe a new method for motion estimation and 3D reconstruction from stereo image sequences obtained by a stereo rig moving through a rigid world. Weshowthatgiven two stereo pairs, one can compute the motion of the stereo rig directly from the image derivatives (spatial and temporal). Correspondences are not required. One can then use the images from both pairs combined, to compute a dense depth map.

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We describe a new direct method for estimating structure and motion from image intensities of multiple views. We extend the direct methods of [9] 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 spatiotemporal 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. 1. Introduction We present a new method for computing ego-motion and dense structure from three views. This method can be viewed as an extension of the 'direct methods' of Horn & Weldon [9] from two views (one motion) to three views (two motions). These methods are dubbed 'direct methods' because they do not require prior computation of optical flow. Within a coarse-to-fine implementation our method can handle displacements averaging up to 50 pixels for 640\Theta 480 resolut...

A framework for analyzing distortions in non-single viewpoint imaging systems is presented. Such systems possess loci of viewpoints called caustics. In general, perspective (or undistorted) views cannot be computed from images acquired with such systems without knowing scene structure. Views computed without scene structure will exhibit distortions which we call caustic distortions. We first introduce a taxonomy of distortions based on the geometry of imaging systems. Then, we derive a metric to quantify caustic distortions. We present an algorithm to compute minimally distorted views using simple priors on scene structure. These priors are defined as parameterized primitives such as spheres, planes and cylinders with simple uncertainty models for the parameters. To

With the advent of laboratories containing dozens of cameras, and the possibility of laboratories containing hundreds of cameras, the question of how to calibrate all the cameras has become pressing. While it is certainly possible to calibrate these networks in a labor intensive manner, a simple, stable, and accurate calibration method is still needed. This paper presents such a method, based on textures printable on a laser printer and mounted on a board. We will show what the problems with the current methods are, and show how these problems can be overcome with a novel use of a trilinear constraint related to the vanishing point constraint, which we call the primsatic line constraint. High accuracy with little user effort is achieved with this method.

Epipolar geometry and relative camera pose computation are examples of tasks which can be formulated as minimal problems and solved from a minimal number of image points. Finding the solution leads to solving systems of algebraic equations. Often, these systems are not trivial and therefore special algorithms have to be designed to achieve numerical robustness and computational efficiency. In this paper we provide a solution to the problem of estimating radial distortion and epipolar geometry from eight correspondences in two images. Unlike previous algorithms, which were able to solve the problem from nine correspondences only, we enforce the determinant of the fundamental matrix be zero. This leads to a system of eight quadratic and one cubic equation in nine variables. We simplify the system by eliminating six of these variables. Then, we solve the system by finding eigenvectors of an action matrix of a suitably chosen polynomial. We show how to construct the action matrix without computing complete Gröbner basis, which provides an efficient and robust solver. The quality of the solver is demonstrated on synthetic and real data. 1.