Normalization of a 3D–Shape Similarity Measure with Voxel Representation

Normalización de una Medida de Similitud para Formas 3D con Representación en Voxels

Hermilo Sánchez Cruz¹ and Ramón M. Rodríguez Dagnino²

¹ Departamento de Sistemas Electrónicos Centro de Ciencias Básicas Universidad Autónoma de Aguascalientes Av. Universidad 940, Aguascalientes, Ags. 20100 Phone: (52 449) 9 10 84 22 hsanchez@correo.uaa.mx

² Center of Electronics and Telecommunications Monterrey Institute of Technology (ITESM) Av. Eugenio Garza Sada 2501, Col. Tecnológico, CP. 64849 Monterrey, Nuevo León, México. Fax: (81) 8359 7211 rmrodrig@itesm.mx

Article received on April 9, 2007
Accepted on July 08, 2007

Abstract

In this paper we study some properties of 3D objects such as compactness, the work done in object transformations and the number of voxels to be moved in order to normalize a similarity measure of an appropriate set of 3D objects. Voxel representation and scale normalization allow us to find the total distance of a set of voxels from one object to another. For these purposes, the comparison of objects is achieved by superimposing their centers of mass, using principal axes for their orientation, and Hungarian algorithm for optimal matching in bipartite graphs. All these aspects are determinant in obtaining the minimum work that needs to be done in the corresponding transformations. We present experimental results by including irregular objects taken from the human body.

Keywords: Similarity measure; compactness; transforming; positive voxels.

Resumen

En este artículo estudiamos algunas propiedades de objetos 3D tales como la compacidad, el trabajo realizado en la transformación de los objetos y el número de voxels a mover para normalizar una medida de similitud de un conjunto apropiado de objetos 3D. La representación con voxels y la normalización de la escala nos permite encontrar la distancia total de un conjunto de voxels de un objeto a otro. Para estos propósitos, la comparación de los objetos se logra al superponer sus centros de masa, usando ejes principales para su orientación, y el algoritmo Húngaro para apareo óptimo en gráficas bipartitas. Todos estos aspectos son determinantes para obtener el trabajo mínimo realizado en las transformaciones correspondientes. Presentamos resultados experimentales al incluir modelos de objetos tomados del cuerpo humano.

Palabras clave: Medida de similitud; compacidad; transformación; voxels positivos.

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Acknowledgments

We would like to thank PROMEP program and ITESM, Campus Monterrey, through the Research Chair in Telecommunications, for the provided support in the development of this work.

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