David Liebowitz

Bio: David Liebowitz is an academic researcher from University of Oxford. The author has contributed to research in topics: Computer science & Camera resectioning. The author has an hindex of 4, co-authored 5 publications receiving 942 citations.

Metric rectification for perspective images of planes

Abstract: We describe the geometry constraints and algorithmic implementation for metric rectification of planes. The rectification allows metric properties, such as angles and length ratios, to be measured on the world plane from a perspective image. The novel contributions are: first, that in a stratified context the various forms of providing metric information, which include a known angle, two equal though unknown angles, and a known length ratio; can all be represented as circular constraints on the parameters of an affine transformation of the plane-this provides a simple and uniform framework for integrating constraints; second, direct rectification from right angles in the plane; third, it is shown that metric rectification enables calibration of the internal camera parameters; fourth, vanishing points are estimated using a Maximum Likelihood estimator; fifth, an algorithm for automatic rectification. Examples are given for a number of images, and applications demonstrated for texture map acquisition and metric measurements.

Creating Architectural Models from Images

Abstract: We present methods for creating 3D graphical models of scenes from a limited numbers of images, i.e. one or two, in situations where no scene co-ordinate measurements are available. The methods employ constraints available from geometric relationships that are common in architectural scenes - such as parallelism and orthogonality - together with constraints available from the camera. In particular, by using the circular points of a plane simple, linear algorithms are given for computing plane rectification, plane orientation and camera calibration from a single image. Examples of image based 3D modelling are given for both single images and image pairs.

Combining scene and auto-calibration constraints

Abstract: We present a simple approach to combining scene and auto-calibration constraints for the calibration of cameras from single views and stereo pairs. Calibration constraints are provided by imaged scene structure, such as vanishing points of orthogonal directions, or rectified planes. In addition, constraints are available from the nature of the cameras and the motion between views. We formulate these constraints in terms of the geometry of the imaged absolute conic and its relationship to pole-polar pairs and the imaged circular points of planes. Three significant advantages result: first, constraints from scene features, camera characteristics and auto-calibration constraints provide linear equations in the elements of the image of the absolute conic. This means that constraints may easily be combined, and their solution is straightforward. Second, the degeneracies that occur when constraints are not independent may be easily identified. Lastly, the constraints from scene planes and image planes may be treated uniformly. Examples of various cases of constraint combination and degeneracy as well as computational techniques are presented.

Resolving ambiguities in auto–calibration

Abstract: Three dimensional projective structure, that is structure modulo, a projectivity of 3D space, can be recovered from its projection in multiple perspective images. The images might be acquired, for example, by a moving monocular camera or a stereo rig. This projective structure can be upgraded to Euclidean structure by identifying two entities, the plane at infinity and the absolute conic. Autocalibration methods use constraints induced by the rigid motion of the camera to determine the Euclidean structure (or, equivalently, the camera calibration). Often these motion constraints are supplemented by known values of the camera's internal parameters or scene constraints in order to resolve ambiguities or stabilize the algorithms. It is shown in this paper that in certain common situations this supplementary information may not resolve the ambiguity. This is illustrated for the particular ambiguity arising for motions with a single direction of the rotation axis. Four types of constraint are analyzed, and the...

Simulated fluid flow in feature enhancement

Abstract: This paper describes a technique for enhancing certain features in grayscale images. Of particular interest are the class of objects that are reasonably large in extent, but are only faintly darker or lighter than the background. An example of such objects is the mandibular canal which appears in panoramic dental X-ray images. Identification of this canal is required in some dental and orthodontal investigations. Traditional image segmentation techniques often fail to detect the full extent of the canal due to the large amount of structural noise in the image. We propose a new method for the enhancement of this class of objects and the subsequent segmentation task. The flow of a fluid is simulated over the image topology, allowing fluid to settle in local minima and, by application of a difference image, enhancing the visibility of features that are characterized by a significant spatially-distributed local minimum. The procedure is similar to the watershed algorithm in concept, visualizing the movement of fluid over the image surface to draw conclusions about significant local minima. Our approach is different however since it is not aimed at segmenting the image, but enhancing distributed local minima. We consider the flow of fluid from high lying to lower lying areas under gravity. This is analogous to the rain fall method of filling the catchment basins in watershed segmentation. Various models of flow, based on co- operative networks are presented and discussed. Post processing is applied to reduce the amount of false outputs. We demonstrate that our proposed method is more suitable than simple edge detection or the watershed algorithms for the enhancement and segmentation of the mandibular canal.

Multiple View Geometry in Computer Vision.

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A flexible new technique for camera calibration

Abstract: We propose a flexible technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one more step from laboratory environments to real world use.

Computer Vision: Algorithms and Applications

Abstract: Humans perceive the three-dimensional structure of the world with apparent ease. However, despite all of the recent advances in computer vision research, the dream of having a computer interpret an image at the same level as a two-year old remains elusive. Why is computer vision such a challenging problem and what is the current state of the art? Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of recipes, this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Flexible camera calibration by viewing a plane from unknown orientations

Abstract: Proposes a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closed-form solution followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment, such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real-world use. The corresponding software is available from the author's Web page ( ).

Image-based 3d modelling: a review

Abstract: In this paper the main problems and the available solutions are addressed for the generation of 3D models from terrestrial images. Close range photogrammetry has dealt for many years with manual or automatic image measurements for precise 3D modelling. Nowadays 3D scanners are also becoming a standard source for input data in many application areas, but image-based modelling still remains the most complete, economical, portable, flexible and widely used approach. In this paper the full pipeline is presented for 3D modelling from terrestrial image data, considering the different approaches and analysing all the steps involved.