SGP23: Eurographics Symposium on Geometry Processing (CGF 42-5)

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https://diglib.eg.org/handle/10.2312/3607110

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Browsing SGP23: Eurographics Symposium on Geometry Processing (CGF 42-5) by Subject "Computational geometry"

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    Attention And Positional Encoding Are (Almost) All You Need For Shape Matching
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Raganato, Alessandro; Pasi, Gabriella; Melzi, Simone; Memari, Pooran; Solomon, Justin
    The fast development of novel approaches derived from the Transformers architecture has led to outstanding performance in different scenarios, from Natural Language Processing to Computer Vision. Recently, they achieved impressive results even in the challenging task of non-rigid shape matching. However, little is known about the capability of the Transformer-encoder architecture for the shape matching task, and its performances still remained largely unexplored. In this paper, we step back and investigate the contribution made by the Transformer-encoder architecture compared to its more recent alternatives, focusing on why and how it works on this specific task. Thanks to the versatility of our implementation, we can harness the bi-directional structure of the correspondence problem, making it more interpretable. Furthermore, we prove that positional encodings are essential for processing unordered point clouds. Through a comprehensive set of experiments, we find that attention and positional encoding are (almost) all you need for shape matching. The simple Transformer-encoder architecture, coupled with relative position encoding in the attention mechanism, is able to obtain strong improvements, reaching the current state-of-the-art.
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    Lightweight Curvature Estimation on Point Clouds with Randomized Corrected Curvature Measures
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Lachaud, Jacques-Olivier; Coeurjolly, David; Labart, CĂ©line; Romon, Pascal; Thibert, Boris; Memari, Pooran; Solomon, Justin
    The estimation of differential quantities on oriented point cloud is a classical step for many geometry processing tasks in computer graphics and vision. Even if many solutions exist to estimate such quantities, they usually fail at satisfying both a stable estimation with theoretical guarantee, and the efficiency of the associated algorithm. Relying on the notion of corrected curvature measures [LRT22, LRTC20] designed for surfaces, the method introduced in this paper meets both requirements. Given a point of interest and a few nearest neighbours, our method estimates the whole curvature tensor information by generating random triangles within these neighbours and normalising the corrected curvature measures by the corrected area measure. We provide a stability theorem showing that our pointwise curvatures are accurate and convergent, provided the noise in position and normal information has a variance smaller than the radius of neighbourhood. Experiments and comparisons with the state-of-the-art confirm that our approach is more accurate and much faster than alternatives. The method is fully parallelizable, requires only one nearest neighbour request per point of computation, and is trivial to implement.