Kongbin Kang

Bayesian Pot-Assembly from Fragments as Problems in Perceptual-Grouping and Geometric-Learning

A heretofore unsolved problem of great archaeological importance is the automatic assembly of pots made on a wheel from the hundreds (or thousands) of sherds found at an excavation site. An approach is presented to the automatic estimation of mathematical models of such pots from 3D measurements of sherds. A Bayesian approach is formulated beginning with a description of the complete set of geometric parameters that determine the distribution of the sherd measurement data. Matching of fragments and aligning them geometrically into configurations is based on matching break-curves (curves on a pot surface separating fragments), estimated axis and profile curve pairs for individual fragments and configurations of fragments, and a number of features of groups of break-curves. Pot assembly is a bottom-up maximum likelihood performance-based search. Experiments are illustrated on pots which were broken for the purpose, and on sherds from an archaeological dig located in Petra, Jordan. The performance measure can also be an aposteriori probability, and many other types of information can be included, e.g., pot wall thickness, surface color, patterns on the surface, etc. This can also be viewed as the problem of learning a geometric object from an unorganized set of free-form fragments of the object and of clutter, or as a problem of perceptual grouping.

Algebraic solution for the visual hull

We introduce an algebraic dual-space method for reconstructing the visual hull of a three-dimensional object from occluding contours observed in 2D images. The method exploits the differential structure of the manifold rather than parallax geometry, and therefore requires no correspondences. We begin by observing that the set of 2D contour tangents determines a surface in a dual space where each point represents a tangent plane to the original surface. The primal and dual surfaces have a symmetric algebra: A point on one is orthogonal to its dual point and tangent basis on the other. Thus the primal surface can be reconstructed if the local dual tangent basis can be estimated. Typically this is impossible because the dual surface is noisy and riddled with tangent singularities due to self-crossings. We identify a directionally-indexed local tangent basis that is well-defined and estimable everywhere on the dual surface. The estimation procedure handles singularities in the dual surface and degeneracies arising from measurement noise. The resulting method has O(N) complexity for N observed contour points and gives asymptotically exact reconstructions of surfaces that are totally observable from occluding contours.

A linear dual-space approach to 3D surface reconstruction from occluding contours using algebraic surfaces

We present a linear approach to the 3D reconstruction problem from occluding contours using algebraic surfaces. The problem of noise and missing data in the occluding contours extracted from the images leads us to this approach. Our approach is based first on the intensive use of the duality property between 3D points and tangent planes, and second on the algebraic representation of 3D surfaces by implicit polynomials of degree 2 and higher.

Distributed volumetric scene geometry reconstruction with a network of distributed smart cameras

Central to many problems in scene understanding based on using a network of tens, hundreds or even thousands of randomly distributed cameras with on-board processing and wireless communication capability is the “efficient” reconstruction of the 3D geometry structure in the scene. What is meant by “efficient” reconstruction? In this paper we investigate this from different aspects in the context of visual sensor networks and offer a distributed reconstruction algorithm roughly meeting the following goals: 1. Close to achievable 3D reconstruction accuracy and robustness; 2. Minimization of the processing time by adaptive computing-job distribution among all the cameras in the network and asynchronous parallel processing; 3. Communication Optimization and minimization of the (battery-stored) energy, by reducing and localizing the communications between cameras. A volumetric representation of the scene is reconstructed with a shape from apparent contour algorithm, which is suitable for distributed processing because it is essentially a local operation in terms of the involved cameras, and apparent contours are robust to ourdoor illumination conditions. Each camera processes its own image and performs the computation for a small subset of voxels, and updates the voxels through collaborating with its neighbor cameras. By exploring the structure of the reconstruction algorithm, we design the minimum-spanning-tree (MST) message passing protocol in order to minimize the communication. Of interest is that the resulting system is an example of “swarm behavior”. 3D reconstruction is illustrated using two real image sets, running on a single computer. The iterative computations used in the single processor experiment are exactly the same as are those used in the network computations. Distributed concepts and algorithms for network control and communication performance are theoretical designs and estimates.

A unified linear fitting approach for singular and nonsingular 3D quadrics from occluding contours

A theory and low computational cost linear algorithm is presented for estimating algebraic surfaces of second degree for representing an object in 3D, based on fitting in the dual space (space of tangent planes) computed from images taken by a calibrated camera in a number of positions. The approach and algorithm are designed to handle implicit quadric surfaces, which are regular or singular, in a uniform way without distinguishing the two cases. A significance of these quadric surface estimation results is, as illustrated in the paper, the estimation of complex 3D free form shapes in a computationally simple way in terms of quadric patches. The paper explains how singular quadrics cause instabilities in the 3D surface fitting and representation, and presents regularization, based on this understanding, to produce accurate stable surface representations.