Ilan Shimshoni

Visual Homing: Surfing on the Epipoles

We introduce a novel method for visual homing. Using this method a robot can be sent to desired positions and orientations in 3D space specified by single images taken from these positions. Our method is based on recovering the epipolar geometry relating the current image taken by the robot and the target image. Using the epipolar geometry, most of the parameters which specify the differences in position and orientation of the camera between the two images are recovered. However, since not all of the parameters can be recovered from two images, we have developed specific methods to bypass these missing parameters and resolve the ambiguities that exist. We present two homing algorithms for two standard projection models, weak and full perspective.Our method determines the path of the robot on-line, the starting position of the robot is relatively not constrained, and a 3D model of the environment is not required. The method is almost entirely memoryless, in the sense that at every step the path to the target position is determined independently of the previous path taken by the robot. Because of this property the robot may be able, while moving toward the target, to perform auxiliary tasks or to avoid obstacles, without this impairing its ability to eventually reach the target position. We have performed simulations and real experiments which demonstrate the robustness of the method and that the algorithms always converge to the target pose.

Global Shape from Shading

A global shape from shading algorithm which develops a technique to merge local shape from shading results obtained around singular points into the complete shape using the mountaineers theorem was recently presented in Kimmel and Bruckstein (1995). In this comment, we enhance this result by proving the completeness and uniqueness obtained by the global shape from shading algorithm.

Geometric voting algorithm for star trackers

We present an algorithm for recovering the orientation (attitude) of a satellite-based camera. The algorithm matches stars in an image taken with the camera to stars in a star catalogue. The algorithm is based on a geometric voting scheme in which a pair of stars in the catalogue votes for a pair of stars in the image if the angular distance between the stars of both pairs is similar. As angular distance is a symmetric relationship, each of the two catalogue stars votes for each of the image stars. The identity of each star in the image is set to the identity of the catalogue star that cast the most votes. Once the identity of the stars is determined, the attitude of the camera is computed using a quaternion-based method. We further present a fast tracking algorithm that estimates the attitude for subsequent images after the first algorithm has terminated successfully. Our method runs in comparable speed to state of the art algorithms but is still more robust than them. The system has been implemented and tested on simulated data and on real sky images.

Shape reconstruction of 3D bilaterally symmetric surfaces

The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required.The basic idea is that an image taken from a general, non frontal viewpoint, under non-frontal illumination can be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, one-image-variants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence between pairs of symmetric points, and as a result, a dense shape recovery of the object. Furthermore, the unknown lighting and viewing parameters, are also recovered in this process.Unknown distant point light source, Lambertian surfaces, unknown constant albedo, and weak perspective projection are assumed. The method has been implemented and tested experimentally on simulated and real data.

On edge detection on surfaces

Edge detection in images has been a fundamental problem in computer vision from its early days. Edge detection on surfaces, on the other hand, has received much less attention. The most common edges on surfaces are ridges and valleys, used for processing range images in computer vision, as well as for non-photo realistic rendering in computer graphics. We propose a new type of edges on surfaces, termed relief edges. Intuitively, the surface can be considered as an unknown smooth manifold, on top of which a local height image is placed. Relief edges are the edges of this local image. We show how to compute these edges from the local differential geometric surface properties, by fitting a local edge model to the surface. We also show how the underlying manifold and the local images can be roughly approximated and exploited in the edge detection process. Last but not least, we demonstrate the application of relief edges to artifact illustration in archaeology.

Estimating the principal curvatures and the Darboux frame from real 3-D range data

Principal curvatures and the local Darboux frame are natural tools to be used during processes which involve extraction of geometric properties from three-dimensional (3-D) range data. As second-order features their estimations are highly sensitive to noise and therefore, until recent years, it was almost impractical to extract reliable results from real 3-D data. Since the use of more accurate 3-D range imaging equipment has become more popular, as well as the use of polyhedral meshes to approximate surfaces, evaluation of existing algorithms for curvature estimation is again relevant. The work presented here, makes some subtle but very important modifications to two such algorithms, originally suggested by Taubin (1995) and Chen and Schmitt (1992). The algorithms have been adjusted to deal with real discrete noisy range data, given as a cloud of sampled points, lying on surfaces of free-form objects. The results of this linear time (and space) complexity implementation were evaluated in a series of tests on synthetic and real input. We also present one of many possible uses for these extracted features in an efficient and robust application for the recovery of 3-D geometric primitives from range data of complex scenes. The application combines the segmentation, classification and fitting processes in a single process which advances monotonously through the recovery procedure. It is also very robust and does not use any least-squares fittings. The conclusion of this study is that with current scanning technology and the algorithms presented here, reliable estimates of the principal curvatures and Darboux frame can be extracted from real data and used in a large variety of tasks.

ROR: rejection of outliers by rotations

We address the problem of rejecting false matches of points between two perspective views. The two views are taken from two arbitrary, unknown positions and orientations. We present an algorithm for identification of the false matches between the views. The algorithm exploits the possibility of rotating one of the images to achieve some common behavior of the correct matches. Those matches that deviate from this common behavior turn out to be false matches. Our algorithm does not, in any way, use the image characteristics of the matched features. In particular, it avoids problems that cause the false matches in the first place. The algorithm works even in cases where the percentage of false matches is as high as 85 percent. The algorithm may be run as a post-processing step on output from any point matching algorithm. Use of the algorithm may significantly improve the ratio of correct matches to incorrect matches. We present the algorithm, identify the conditions under which it works, and present results of the test.

A fast triangle to triangle intersection test for collision detection

The triangle‐to‐triangle intersection test is a basic component of all collision detection data structures and algorithms. This paper presents a fast method for testing whether two triangles embedded in three dimensions intersect. Our technique solves the basic sets of linear equations associated with the problem and exploits the strong relations between these sets to speed up their solution. Moreover, unlike previous techniques, with very little additional cost, the exact intersection coordinates can be determined. Finally, our technique uses general principles that can be applied to similar problems such as rectangle‐to‐rectangle intersection tests, and generally to problems where several equation sets are strongly related. We show that our algorithm saves about 20% of the mathematical operations used by the best previous triangle‐to‐triangle intersection algorithm. Our experiments also show that it runs 18.9% faster than the fastest previous algorithm on average for typical scenarios of collision detection (on Pentium 4). Copyright

Computing the sensory uncertainty field of a vision-based localization sensor

It has been recognized that robust motion planners should take into account the varying performance of localization sensors across the configuration space. Although a number of works have shown the benefits of using such a performance map, the work on actual computation of such a performance map has been limited and has addressed mostly range sensors. Since vision is an important sensor for localization, it is important to have performance maps of vision sensors. We present a method for computing the performance map of a vision-based sensor. We compute the map and show that it accurately describes the actual performance of the sensor, both on synthetic and real images. The method we use involves evaluating closed form formulas and hence is very fast. Using the performance map computed by this method for motion planning and for devising sensing strategies will contribute to more robust navigation algorithms.

Reliable and efficient landmark-based localization for mobile robots

This paper describes an efficient and robust localization system for indoor mobile robots and AGVs. The system utilizes a sensor that measures bearings to artificial landmarks, and an efficient triangulation method. We present a calibration method for the system components and overcome typical problems for sensors of the mentioned type, which are localization in motion and incorrect identification of landmarks. The resulting localization system was tested on a mobile robot. It consumes less than 4% of a Pentium4 3.2 GHz processing power while providing an accurate and reliable localization result every 0.5 s. The system was successfully incorporated within a real mobile robot system which performs many other computational tasks in parallel.