Daniilidis, Kostas
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Publication Trinocular Stereo: A Real-Time Algorithm and its Evaluation(2002-04-01) Mulligan, Jane; Isler, Volkan; Daniilidis, KostasIn telepresence applications each user is immersed in a rendered 3D-world composed from representations transmitted from remote sites. The challenge is to compute dense range data at high frame rates, since participants cannot easily communicate if the processing cycle or network latencies are long. Moreover, errors in new stereoscopic views of the remote 3D-world should be hardly perceptible. To achieve the required speed and accuracy, we use trinocular stereo, a matching algorithm based on the sum of modified normalized cross-correlations, and subpixel disparity interpolation. To increase speed we use Intel IPL functions in the pre-processing steps of background subtraction and image rectification as well as a four-processor parallelization. To evaluate our system we have developed a testbed which provides a set of registered dense "ground-truth" laser data and image data from multiple views.Publication Structure and Motion From Uncalibrated Catadioptric Views(2001-05-25) Geyer, Christopher; Daniilidis, KostasIn this paper we present a new algorithm for structure from motion from point correspondences in images taken from uncalibrated catadioptric cameras with parabolic mirrors. We assume that the unknown intrinsic parameters are three: the combined focal length of the mirror and lens and the intersection of the optical axis with the image. We introduce a new representation for images of points and lines in catadioptric images which we call the circle space. This circle space includes imaginary circles, one of which is the image of the absolute conic. We formulate the epipolar constraint in this space and establish a new 4x4 catadioptric fundamental matrix. We show that the image of the absolute conic belongs to the kernel of this matrix. This enables us to prove that Euclidean reconstruction is feasible from two views with constant parameters and from three views with varying parameters. In both cases, it is one less than the number of views necessary with perspective cameras.Publication Compression of Stereo Disparity Streams Using Wavelets and Optical Flow(2001-01-01) Bülow, Thomas; Mulligan, Jane; Bonnafos, Geraud de; Chibane, Alexandre; Daniilidis, KostasRecent advances in computing have enabled fast reconstructions of dynamic scenes from multiple images. However, the efficient coding of changing 3D-data has hardly been addressed. Progressive geometric compression and streaming are based on static data sets which are mostly artificial or obtained from accurate range sensors. In this paper, we present a system for efficient coding of 3D-data which are given in forms of 2 + 1/2 disparity maps. Disparity maps are spatially coded using wavelets and temporally predicted by computing flow. The resulted representation of a 3D-stream consists then of spatial wavelet coefficients, optical flow vectors, and disparity differences between predicted and incoming image. The approach has also very useful by-products: disparity predictions can significantly reduce the disparity search range and if appropriately modeled increase the accuracy of depth estimation.Publication Paracatadioptric Camera Calibration(2002-05-01) Geyer, Christopher; Daniilidis, KostasCatadioptric sensors refer to the combination of lens-based devices and reflective surfaces. These systems are useful because they may have a field of view which is greater than hemispherical, providing the ability to simultaneously view in any direction. Configurations which have a unique effective viewpoint are of primary interest, among these is the case where the reflective surface is a parabolic mirror and the camera is such that it induces an orthographic projection and which we call paracatadioptric. We present an algorithm for the calibration of such a device using only the images of lines in space. In fact, we show that we may obtain all of the intrinsic parameters from the images of only three lines and that this is possible without any metric information. We propose a closed-form solution for focal length, image center, and aspect ratio for skewless cameras and a polynomial root solution in the presence of skew. We also give a method for determining the orientation of a plane containing two sets of parallel lines from one uncalibrated view. Such an orientation recovery enables a rectification which is impossible to achieve in the case of a single uncalibrated view taken by a conventional camera. We study the performance of the algorithm in simulated setups and compare results on real images with an approach based on the image of the mirror's bounding circle.Publication Surface Representations Using Spherical Harmonics and Gabor Wavelets on the Sphere(2001-01-01) Bülow, Thomas; Daniilidis, KostasIn this paper we present a new scheme for the representation of object surfaces. The purpose is to model a surface efficiently in a coarse to fine hierarchy. Our scheme is based on the combination of spherical harmonic functions and wavelet networks on the sphere. The coefficients can be estimated from scattered data sampled from a star-shaped object’s surface. Spherical harmonic functions are used to model the coarse structure of the surface, while spherical Gabor wavelets are used for the representation of fine scale detail. Theoretical background on wavelets on the sphere is provided as well as a discussion of implementation issues concerning convolutions on the sphere. Results are presented which show the efficiency of the proposed representation.Publication Real time trinocular stereo for tele-immersion(2001-10-07) Mulligan, Jane; Daniilidis, KostasTele-immersion is a technology that augments your space with real-time 3D projections of remote spaces thus facilitating the interaction of people from different places in virtually the same environment. Tele-immersion combines 3D scene recovery from computer vision, and rendering and interaction from computer graphics. We describe the real-time 3D scene acquisition using a new algorithm for trinocular stereo. We extend this method in time by combining motion and stereo in order to increase speed and robustness.Publication Motion Estimation Using a Spherical Camera(2004-01-01) Makadia, Ameesh A; Daniilidis, KostasRobotic navigation algorithms increasingly make use of the panoramic field of view provided by omnidirectional images to assist with localization tasks. Since the images taken by a particular class of omnidirectional sensors can be mapped to the sphere, the problem of attitude estimation arising from 3D motions of the camera can be treated as a problem of estimating the camera motion between spherical images. This problem has traditionally been solved by tracking points or features between images. However, there are many natural scenes where the features cannot be tracked with confidence. We present an algorithm that uses image features to estimate ego-motion without explicitly searching for correspondences. We formulate the problem as a correlation of functions defined on the product of spheres S2 × S2 which are acted upon by elements of the direct product group SO(3) × SO(3). We efficiently compute this correlation and obtain our solution using the spectral information of functions in S2 × S2.Publication Structure From Motion With Directional Correspondence for Visual Odometry(2011-01-01) Naroditsky, Oleg; Zhou, Xun S.; Gallier, Jean H; Roumeliotis, Stergios I.; Daniilidis, KostasThis report presents two efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices, where the gravity vector becomes the reference direction. We provide a simple closed-form solution and a solution based on techniques from algebraic geometry and investigate numerical and computational advantages of each approach. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.Publication Radon-based Structure from Motion Without Correspondences(2005-06-20) Makadia, Ameesh; Geyer, Christopher; Sastry, Shankar; Daniilidis, KostasWe present a novel approach for the estimation of 3Dmotion directly from two images using the Radon transform. We assume a similarity function defined on the crossproduct of two images which assigns a weight to all feature pairs. This similarity function is integrated over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to filtering the similarity function with a Dirac function embedding the epipolar constraint. The result of this convolution is a function of the five unknownmotion parameters with maxima at the positions of compatible rigid motions. The breakthrough is in the realization that the Radon transform is a filtering operator: If we assume that images are defined on spheres and the epipolar constraint is a group action of two rotations on two spheres, then the Radon transform is a convolution/correlation integral. We propose a new algorithm to compute this integral from the spherical harmonics of the similarity and Dirac functions. The resulting resolution in the motion space depends on the bandwidth we keep from the spherical transform. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions. The algorithm has been tested in sequences of real omnidirectional images and it outperforms correspondence-based structure from motion.Publication Correspondenceless Structure from Motion(2007-12-01) Makadia, Ameesh; Geyer, Christopher; Daniilidis, KostasWe present a novel approach for the estimation of 3D-motion directly from two images using the Radon transform. The feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint. This integration is equivalent to taking the inner product of a similarity function on feature pairs with a Dirac function embedding the epipolar constraint. The maxima in this five dimensional motion space will correspond to compatible rigid motions. The main novelty is in the realization that the Radon transform is a filtering operator: If we assume that the similarity and Dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres, then the Radon transform is a correlation integral. We propose a new algorithm to compute this integral from the spherical Fourier transform of the similarity and Dirac functions. Generating the similarity function now becomes a preprocessing step which reduces the complexity of the Radon computation by a factor equal to the number of feature pairs processed. The strength of the algorithm is in avoiding a commitment to correspondences, thus being robust to erroneous feature detection, outliers, and multiple motions.