Variational Shape Reconstruction via Quadric Error Metrics

1Inria, 2Adobe Research, 3Télécom Paris
ACM SIGGRAPH 2023 Conference Proceedings


Inspired by the strengths of quadric error metrics initially designed for mesh decimation, we propose a concise mesh reconstruction approach for 3D point clouds. Our approach proceeds by clustering the input points enriched with quadric error metrics, where the generator of each cluster is the optimal 3D point for the sum of its quadric error metrics. This approach favors the placement of generators on sharp features, and tends to equidistribute the error among clusters. We reconstruct the output surface mesh from the adjacency between clusters and a constrained binary solver. We combine our clustering process with an adaptive refinement driven by the error. Compared to prior art, our method avoids dense reconstruction prior to simplification and produces immediately an optimized mesh.


        author = {Zhao, Tong and Bus\'{e}, Laurent and Cohen-Steiner, David and Boubekeur, Tamy and Thiery, Jean-Marc and Alliez, Pierre}, 
        title = {Variational Shape Reconstruction via Quadric Error Metrics}, 
        year = {2023}, 
        isbn = {9798400701597}, 
        publisher = {Association for Computing Machinery}, 
        address = {New York, NY, USA}, url = {}, 
        doi = {10.1145/3588432.3591529}, 
        booktitle = {ACM SIGGRAPH 2023 Conference Proceedings}, 
        articleno = {45}, 
        numpages = {10}, 
        location = {Los Angeles, CA, USA}, 
        series = {SIGGRAPH '23}