The derivation of two-dimensional surface shape from shadows

We study theoretical and implementation issues that arise when solving the shape from shadows problem. In this problem, the shadows created by a light falling on a surface are used to recover the surface itself. The problem is formulated and solved in a Hilbert space setting. We construct the spline algorithm that interpolates the data and show that it is the best possible approximation to the original function. The optimal error algorithm is implemented and a series of tests is shown. We additionally show that the problem can be decomposed into subproblems and each one can be solved independently from the others. This decomposition is suited to parallel computation and can result in considerable reductions in the cost of the solution

Image Understanding and Robotics Research at Columbia University

The research investigations of the Vision/Robotics Laboratory at Columbia University reflect the diversity of interests of its four faculty members, two staff programmers and 15 Ph.D. students. Several of the projects involve either a visiting computer science post-doc, other faculty members in the department or the university, or researchers at AT&T Bell Laboratories or Philips laboratories. We list below a summary of our interest and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative

A regularized solution of shape from shadows

We present a regularized solution to the shape from shadows problem. In this problem the shadows cast on an unknown surface yield data that can be used for the reconstruction of this surface. In the simulation presented here we assume that the data can now be perturbed by noise. It is shown that the regularized approach produces a solution that can handle noisy information while being very similar to the solution obtained by the approximation theoretic approaches used in earlier work. We provide implementation runs where the performance of the algorithm in recovering unknown surfaces is tested. Furthermore, we study the visual effects of smoothing on the various reconstructions

A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data

Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly non-zero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources. In this paper, we describe the mission-independent, wavelet-based source detection algorithm WAVDETECT, part of the CIAO software package. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e. flat-fielded) background maps; (2) the correction for exposure variations within the field-of-view; (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the algorithm's robustness by applying it to various images.Comment: Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61 pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astro-ph submissio

MAMUD : contribution of HR satellite imagery to a better monitoring, modeling and understanding of urban dynamics

In this treatise the discussion of a methodology and results of semi-automatic city DSM extrac-tion from an Ikonos triplet, is introduced. Built-up areas are known as being complex for photogrammetric purposes, partly because of the steep changes in elevation caused by buildings and urban features. To make DSM extraction more robust and to cope with the specific problems of height displacement, concealed areas and shadow, a multi-image based approach is followed. For the VHR tri-stereoscopic study an area extending from the centre of Istanbul to the urban fringe is chosen. Research will concentrate, in first phase on the development of methods to optimize the extraction of photogrammetric products from the bundled Ikonos triplet. Optimal methods need to be found to improve the radiometry and geometry of the imagery, to improve the semi-automatically derivation of DSM’s and to improve the postprocessing of the products. Secondly we will also investigate the possibilities of creating stereo models out of images from the same sensor taken on a different date, e.g. one image of the stereo pair combined with the third image. Finally the photogrammetric products derived from the Ikonos stereo pair as well as the products created out of the triplet and the constructed stereo models will be investigated by comparison with a 3D reference. This evaluation should show the increase of accuracy when multi-imagery is used instead of stereo pairs

Image Understanding and Robotics Research at Columbia University

Over the past year, the research investigations of the Vision/Robotics Laboratory at Columbia University have reflected the interests of its four faculty members, two staff programmers, and 16 Ph.D. students. Several of the projects involve other faculty members in the department or the university, or researchers at AT&T, IBM, or Philips. We list below a summary of our interests and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative. The majority of our current investigations are deepenings of work reported last year; this was the second year of both our basic Image Understanding contract and our Strategic Computing contract. Therefore, the form of this year's report closely resembles last year's. Although there are a few new initiatives, mainly we report the new results we have obtained in the same five basic research areas. Much of this work is summarized on a video tape that is available on request. We also note two service contributions this past year. The Special Issue on Computer Vision of the Proceedings of the IEEE, August, 1988, was co-edited by one of us (John Kender [27]). And, the upcoming IEEE Computer Society Conference on Computer Vision and Pattem Recognition, June, 1989, is co-program chaired by one of us (John Kender [23])