## Daniilidis, Kostas

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Publication View-Independent Scene Acquisition for Tele-Presence(2000-10-05) Mulligan, Jane; Daniilidis, KostasTele-immersion is a new medium that enables a user to share a virtual space with remote participants. The user is immersed in a rendered 3D-world that is transmitted from a remote site. To acquire this 3D description we apply bi- and trinocular stereo techniques. The challenge is to compute dense stereo range data at high frame rates, since participants cannot easily communicate if the processing cycle or network latencies are long. Moreover, new views of the received 3D-world must be as accurate as possible. We address both issues of speed and accuracy and we propose a method for combining motion and stereo in order to increase speed and robustness.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) BÃ¼low, 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 Image Registration Using Mutual Information(2000-01-01) Egnal, Geoffrey; Daniilidis, KostasAlmost all imaging systems require some form of registration. A few examples are aligning medical images for diagnosis, matching stereo images to recover shape, and comparing facial images in a database to recognize people. Given the difficulty of registering images taken at different times, using different sensors, from different positions, registration algorithms come in different shapes and sizes. Recently, a new type of solution to the registration problem has emerged, based on information theory. In particular, the mutual information similarity metric has been used to register multi-modal medical images. Mutual information compares the statistical dependence between the two images. Unlike many other registration techniques, mutual information makes few a priori assumptions about the surface properties of the object or the imaging process, making it adaptible to changes in lighting and changes between sensors. The method can be applied to larger dimensional registration and many other imaging situations. In this report, we compare two approaches taken towards the implementation of rigid 2D mutual information image registration. We look further at algorithm speedup and noise reduction efforts. A full background is provided.Publication Robust Invariants From Functionally Constrained Motion(1998-07-01) Hicks, Andrew R.; Daniilidis, Kostas; Bajcsy, Ruzena; Pettey, DavidWe address in the problem of control-based recovery of robot pose and the environmental lay-out. Panoramic sensors provide us with an 1D projection of characteristic features of a 2D operation map. Trajectories of these projections contain the information about the position of a priori unknown landmarks in the environment. We introduce here the notion of spatiotemporal signatures of projection trajectories. These signatures are global measures, like area, characterized by considerably higher robustness with respect to noise and outliers than the commonly applied point correspondence. By modeling the 2D motion plane as the complex plane we show that by means of complex analysis our method can be embedded in the well-known affine reconstruction paradigm.Publication VC-Dimension of Exterior Visibility of Polyhedra(2001-01-01) Kannan, Sampath; Isler, Volkan; Daniilidis, KostasIn this paper, we address the problem of finding the minimal number of viewpoints outside a polyhedron in two or three dimensions such that every point on the exterior of the polyhedron is visible from at least one of the chosen viewpoints. This problem which we call the minimum fortress guard problem (MFGP) is the optimization version of a variant of the art-gallery problem (sometimes called the fortress problem with point guards) and has practical importance in surveillance and image-based rendering. Solutions in the vision and graphics literature are based on image quality constraints and are not concerned with the number of viewpoints needed. The corresponding question for art galleries (minimum number of viewpoints in the interior of a polygon to see the interior of the polygon) which we call the minimum art-gallery guard problem (MAGP) has been shown to be NP-complete. A simple reduction from this problem shows the NP-completeness of MFGP. Instead of relying on heuristic searches, we address the approximability of the camera placement problem. It is well known (and easy to see) that this problem can be cast as a hitting set problem. While the approximability of generic instances of the hitting set problem is well understood, BrÃ¶nnimann and Goodrich[3] presented improved approximation algorithms for the problem in the case that the input instances have bounded Vapnik-Chervonenkis (VC) dimension. In this paper we explore the VC-dimension of set systems associated with the camera placement problem described above. We show a constant bound for the VC dimension in the two dimensional case but a tight logarithmic bound in the three dimensional case. In the two dimensional case we are also able to present an algorithm that uses at most one more viewpoint than the optimal in the case that the viewpoints are restricted to be on a circumscribing circle - a restriction that is justified in practice.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 Ã— S2 which are acted upon by elements of the direct product group SO(3) Ã— SO(3). We efficiently compute this correlation and obtain our solution using the spectral information of functions in S2 Ã— S2.Publication 3D-Orientation Signatures with Conic Kernel Filtering for Multiple Motion Analysis(2001-12-08) Yu, Weichuan; Sommer, Gerald; Daniilidis, KostasIn this paper we propose a new 3D kernel for the recovery of 3D-orientation signatures. The kernel is a Gaussian function defined in local spherical coordinates and its Cartesian support has the shape of a truncated cone with its axis in the radial direction and very small angular support. A set of such kernels is obtained by uniformly sampling the 2D space of polar and azimuth angles. The projection of a local neighborhood on such a kernel set produces a local 3D-orientation signature. In the case of spatiotemporal analysis, such a kernel set can be applied either on the derivative space of a local neighborhood or on the local Fourier transform. The well known planes arising from single or multiple motion produce maxima in the orientation signature. Due to the kernel's local support spatiotemporal signatures possess higher orientation resolution than 3D steerable filters and motion maxima can be detected and localized more accurately. We describe and show in experiments the superiority of the proposed kernels compared to Hough transformation or EM-based multiple motion detection.Publication Omnidirectional video(2003-01-01) Geyer, Christopher M; Daniilidis, KostasOmnidirectional video enables direct surround immersive viewing of a scene by warping the original image into the correct perspective given a viewing direction. However, novel views from viewpoints off the camera path can only be obtained if we solve the 3D motion and calibration problem. In this paper we address the case of a parabolic catadioptric camera â€“ a paraboloidal mirror in front of an orthographic lens â€“ and we introduce a new representation, called the circle space, for points and lines in such images. In this circle space, we formulate an epipolar constraint involving a 4x4 fundamental matrix. We prove that the intrinsic parameters can be inferred in closed form from the 2D subspace of the new fundamental matrix from two views if they are constant or from three views if they vary. Three dimensional motion and structure can then be estimated from the decomposition of the fundamental matrix.Publication Catadioptric Projective Geometry(2001-12-01) Geyer, Christopher; Daniilidis, KostasCatadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.