a b s t r a c tWe introduce a new manifold-based construction for fitting a smooth surface to a triangle mesh of arbitrary topology. Our construction combines in novel ways most of the best features of previous constructions and, thus, it fills the gap left by them. We also introduce a theoretical framework that provides a sound justification for the correctness of our construction. Finally, we demonstrate the effectiveness of our manifold-based construction with a few concrete examples.

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Subdivision curves have great importance for many CAD/ CAM applications.. In this paper we propose a simple method to define subdivision schemes on triangulations. It works by translating to the triangulation a perturbation of a planar binary subdivision. To reproduce this perturbation in the surface we use both, shortest and straightest geodesics, so we call this strategy intrinsic projection method. It can reproduce any binary subdivision scheme, regardless whether it is linear or not.

Figure 1. Modeling on the surface of a cow. From left: the control polygons of some curves and a C 1 spline, the corresponding curves, a region is filled and other is trimmed, final result.

The identification and classification of motion patterns in point trajectories has been an important issue in understanding and representing dynamic scenes. This paper proposes an unsupervised approach to identify coherent motion in video. Instead of producing a spatio-temporal segmentation of the raw data, the proposed method analyzes point trajectories along the video sequence to identify sets of points that move coherently. This new way of extracting motion information from videos potentially can be used in different areas of image processing and computer vision.