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Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image

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Abstract

The registration of a 3D model over an image can be seen as the alignment of visual correspondences extracted from these two data. This is a challenging task and it is even more complex when the two images have a different modality. This paper introduces an approach that allows matching features detected in two different modalities: photographs and 3D models, by using a common 2D representation. Our approach is based on a modification of the Marching Cubes algorithm aiming to remove ambiguous cases without adding further calculations in each cube. We share the idea about the crucial importance of splitting the equivalence cases into two classes. Considering all the possible states inside/outside in the four corners of a cube side, indeed, there are only four non-trivial cases after eliminating those equivalences through the rotation. The obtained results allow us to validate the feasibility of the proposed methodology.

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Authors and Affiliations

  1. División de Ciencias e Ingenierías, Universidad de Guanajuato Campus León, Lomas del Bosque 103, Lomas del Campestre, 37150, León, Gto., Mexico

    Delia Irazú Hernández Farías, Teodoro Cordova Fraga & José Zacarías Huamaní Luna

  2. División de Ingenierías, Universidad de Guanajuato Campus Irapuato-Salamanca , Carretera Salamanca – Santiago Valley km 3.5 + 1.8 community of Palo Blanco, 36885, Salamanca, Gto., Mexico

    Rafael Guzmán Cabrera

  3. CONACyT-Tecnológico Nacional de México/CENIDET Interior Internado Palmira S/N, 62490, Palmira, Cuernavaca, Mor., Mexico

    Jose Francisco Gomez Aguilar

Authors
  1. Delia Irazú Hernández Farías
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  2. Rafael Guzmán Cabrera
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  3. Teodoro Cordova Fraga
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  4. José Zacarías Huamaní Luna
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  5. Jose Francisco Gomez Aguilar
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Corresponding authors

Correspondence to Delia Irazú Hernández Farías, Rafael Guzmán Cabrera, Teodoro Cordova Fraga, José Zacarías Huamaní Luna or Jose Francisco Gomez Aguilar.

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Hernández Farías, D.I., Cabrera, R.G., Fraga, T.C. et al. Modification of the Marching Cubes Algorithm to Obtain a 3D Representation of a Planar Image. Program Comput Soft 47, 215–223 (2021). https://doi.org/10.1134/S0361768821030051

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  • DOI: https://doi.org/10.1134/S0361768821030051

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