Zachi Karni

Spectral compression of mesh geometry

We show how spectral methods may be applied to 3D mesh data to obtain compact representations. This is achieved by projecting the mesh geometry onto an orthonormal basis derived from the mesh topology. To reduce complexity, the mesh is partitioned into a number of balanced submeshes with minimal interaction, each of which are compressed independently. Our methods may be used for compression and progressive transmission of 3D content, and are shown to be vastly superior to existing methods using spatial techniques, if slight loss can be tolerated.

Compression of soft-body animation sequences

Abstract We describe a compression scheme for the geometry component of 3D animation sequences. This scheme is based on the principle component analysis (PCA) method, which represents the animation sequence using a small number of basis functions. Second-order linear prediction coding (LPC) is applied to the PCA coefficients in order to further reduce the code size by exploiting the temporal coherence present in the sequence. Our results show that applying LPC to the PCA scheme results in significant performance improvements relative to other coding methods. The use of these codes will make animated 3D data more accessible for graphics and visualization applications.

Energy-based image deformation

We present a general approach to shape deformation based on energy minimization, and applications of this approach to the problems of image resizing and 2D shape deformation. Our deformation energy generalizes that found in the prior art, while still admitting an efficient algorithm for its optimization. The key advantage of our energy function is the flexibility with which the set of “legal transformations” may be expressed; these transformations are the ones which are not considered to be distorting. This flexibility allows us to pose the problems of image resizing and 2D shape deformation in a natural way and generate minimally distorted results. It also allows us to strongly reduce undesirable foldovers or self‐intersections. Results of both algorithms demonstrate the effectiveness of our approach.

Efficient compression and rendering of multi-resolution meshes

We present a method to code the multiresolution structure of a 3D triangle mesh in a manner that allows progressive decoding and efficient rendering at a client machine. The code is based on a special ordering of the mesh vertices which has good locality and continuity properties, inducing a natural multiresolution structure. This ordering also incorporates information allowing efficient rendering of the mesh at all resolutions using the contemporary vertex buffer mechanism. The performance of our code is shown to be competitive with existing progressive mesh compression methods, while achieving superior rendering speed.

Template deformation for point cloud fitting

The reconstruction of high-quality surface meshes from measured data is a vital stage in digital shape processing. We present a new approach to this problem that deforms a template surface to fit a given point cloud. Our method takes a template mesh and a point cloud as input, the latter typically shows missing parts and measurement noise. The deformation process is initially guided by user specified correspondences between template and data, then during iterative fitting new correspondences are established. This approach is based on a Laplacian setting for the template without need of any additional meshing of the data or cross-parameterization. The reconstructed surface fits to the point cloud while it inherits shape properties and topology of the template. We demonstrate the effectiveness of the approach for several point data sets from different sources.

Content-aware image resizing by quadratic programming

We present a new method for content-aware image resizing based on a framework of global optimization. We show that the basic resizing problem can be formulated as a convex quadratic program. Furthermore, we demonstrate how the basic framework may be extended to prevent foldovers of the underlying mesh; encourage the magnification of salient regions; and preserve straight line structures. We show results demonstrating the effectiveness of the proposed method by comparing with four leading competitor methods.

Robust variational reconstruction from multiple views

Recovering a 3-D scene from multiple 2-D views is indispensable for many computer vision applications ranging from free viewpoint video to face recognition. Ideally the recovered depth map should be dense, piecewise smooth with fine level of details, and the recovery procedure shall be robust with respect to outliers and global illumination changes. We present a novel variational approach that satisfies these needs. Our model incorporates robust penalisation in the data term and anisotropic regularisation in the smoothness term. In order to render the data term robust with respect to global illumination changes, a gradient constancy assumption is applied to logarithmically transformed input data. Focussing on translational camera motion and considering small baseline distances between the different camera positions, we reconstruct a common disparity map that allows to track image points throughout the entire sequence. Experiments on synthetic image data demonstrate the favourable performance of our novel method.

Visualization and exploration for recommender systems in enterprise organization

Recommender systems seek to predict the interest a user would find in an item, person or social element they had not yet considered, based upon the properties of the item, the users past experience and similar users. However, recommended items are often presented to the user with no context and no ability to influence the results. We present a novel visualization technique for recommender systems in which, a user can see the items recommended for him, and understand why they were recommended. Focusing on a user, we render a planar visualization listing a set of recommended items. The items are organized such that similar items reside nearby on the screen, centered around realtime generated categories. We use a combination of iconography, text and tag clouds, with maximal use of screen real estate, and keep items from overlapping to produce our results. We apply our visualization to expert relevance maps in the enterprise and a book recommendation system for consumers. The latter is based on Shelfari, a social network for reading and books.